[EM] Re: A more briefly-defined method with the best mix of properties
MIKE OSSIPOFF nkklrp at hotmail.com writes: EM members-- This is a copy of a message that I intend to post at the Condorcet mailing list. I have just finished requesting membership in that mailing list. I don't know how often it takes to be approved for membership, and so I'd like to post, to EM, three messages that I intend to post to the Condorcet mailing list. This is the first of those three messages. They're about MDDA: MDDA has been much discussed on EM. Its full name is: Majority Defeat Disqualification//Approval. ... etc. ... Hi Mike, There has been 2 months of debate on the Condorcet list, mostly between Schulze and DMC. You're welcome to join the debate (I certainly can't stop you!), but it would be more helpful if you could assist with comparison of the methods. After all, the purpose is to first convince one Washington State representative, and secondly to give him ammunition to present to the entire legislature. So instead of doing all your work by email and forcing people to reference each message and apply differences and additions in their heads, why not create some pages on electowiki? For example, here's a place to fill in your method: http://wiki.electorama.com/wiki/Majority_Defeat_Disqualification_Approval That's where you could describe it in terms of accepted election methods terminology. But you might also want to create a page with a version of Proposed Statutory Rules: http://wiki.electorama.com/wiki/Proposed_Statutory_Rules_for_MDDA I will even issue a friendly challenge: See if you can write your rules more succinctly and intelligibly (for non-mathematical politicians) than the version I wrote for DMC. -- monkeypuzzle Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: approval strategy in DMC
Simmons, Forest simmonfo at up.edu writes: Jeff Fisher recently opined that DMC voters would likely adopt the strategy of approving all candidates that they considered certain to be beaten pairwise by their Favorite. This would put these candidates in a better position to doubly defeat the candidates that might otherwise beat X. But this strategy would also increase the chances of doubly defeating their compromise Y. The only time this strategy would be safe is when favorite X is so strong that compromise Y is not needed. In that case, X probably doesn't need the over-kill, but deserves to be the winner unless the other factions are united enough to combine against X. Forest Hi Forest, In connection with this, I've made a slight change on the DMC page on electowiki. I've extended the definition somewhat: the ballot is a combination of ordinal ranking (equal ranks allowed) and approval rating. The approval rating information can be either binary approval (approved/not-approved) or finer-grained cardinal ratings ([1,0,-1] or [100,99,...,1,0]). I think this is more of a difference in implementation than the method, since the initial ordering is by total approval. In the above case, a more graduated cardinal rating (say 100-0) would allow a voter to approve weaker candidates with a low, but non-zero, rating. Using the ordinal/ratings method I posted a few days ago, the ballot would not be substantially more complicated than a plain approval-cutoff ballot. Q Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Can we come to consensus? this way?
Abd ulRahman Lomax abd at lomaxdesign.com writes: Not permitting truncation would involve considering ballots as spoiled which are not complete, I think I remember reading that this is actually done in some countries. Personally, I find it just as offensive as spoiling ballots because the voter marked too many candidates Definitely, truncation should be allowed, and should have a simple and rational meaning. There are two possible meanings: truncation on a ranked ballot means that the voter ranks the candidate below all ranked candidates, and equally with all other unranked candidates. If it is an Approval method, an unmarked candidate would similarly be considered not approved. The other meaning possible would be that truncation is an abstention in every pairwise consideration of the unranked candidate. The consequences and implications of this are, however, problematic, and I think voters would not expect this. Presently, not marking a candidate is effectively a vote against that candidate (as long as the voter votes for at least one). Turning that into an abstention would be confusing. Hi Abd, I agree that truncation should have the same effect as equal ranking. After all, if we are interpreting a ranked ballot in pairwise fashion (which places no importance on where the ranking occurs but only on the relative ranking), this is the only possible consistent interpretation. But what is the effect of equal ranking? Is equal ranking is the equivalent of saying I have no opinion in this contest? Or does it mean I don't want my vote to hurt either candidate? Why not both? In other words, should pairwise equal-ranked votes be counted (in the equal-ranked pairwise contest) at all? The other ordered preferences would still be counted, of course. Dave's contention is that in an A-B contest, 2 A=B ballots should be counted as one AB ballot and one BA ballot -- that is, a half-vote for + a half-vote against. I disagree. Two opposing ballots may cancel each other's effect, but they each express ranked preferences in the pairwise contest and should contribute to its importance (e.g. in a WV-based Condorcet completion method). Should two ER ballots similarly increase the weight of that contest? In a WV method, that could have adverse effects -- an A=B ballot could contribute to the loss of both candidates. Your final statement about not marking a candidate is confusing. If ER votes are *not* counted pairwise (as I contend), that would imply that the non-marked candidate receives a vote-against from every marked candidate, but no votes, either for or against, from any other non-marked candidate. I think this is the least confusing interpretation for the voter. Under Dave's ER method (pairwise 1/2 for 1/2 against), *each* non-marked candidate would receive a half-vote for and a half-vote against in *every* non-marked pairwise contest. I'm sorry if I appear to be arguing against you. Perhaps we are both arguing the same side of the issue, and you were simply trying to indicate these same problems to Dave? Q Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: AWP versus DMC
James Green-Armytage jarmyta at antioch-college.edu writes: What is the simplest explanation of DMC? 1. Drop any candidate defeated by any other higher-approved candidate. We call any dropped candidates /definitively defeated/. Call the remaining candidates the Provisional Set (or P-set). 2. Drop candidates defeated by lower-approved members of the P-set. 3. There is one winner, the /definitive majority/ winner. The AWP explanation above is not as simple as approval, MMPO, IRV, etc., but not staggeringly complex. I agree to some extent. If DMC is adopted, I'm in favor of tabulating the approval-pairwise (or cardinal pairwise) array in addition to the pairwise array+ approval scores. Then at some future time, voters can decide if the slight additional complexity is worthwhile. At the very least, the information would be available. By the way, I've thought of a fairly simple way to add ratings to an ordinal ballot: Voters rank the candidate 1st, 2nd, 3rd, etc., but can then give a rating of 0 to 100 to each rank, using the following method: 1) The default rating of rank 1 is 100. 2) For lower ranks with candidates, the default rating is the same as that of the next higher rank. 3) Unranked candidates (or ranks with without candidates) are rated 0. This way, a relatively simple ballot could simply rank 1st, 2nd and 3rd choices (with equal rank allowed) and by default they would each receive a rating of 100. But if someone wants to enter a 4th choice with rating of, say, 70, they simply rank X as 4th and set 4th's rating to 70. 1st, 2nd and 3rd still have their default ratings of 100. As stated previously by Adam Tarr, DMC extends to ratings quite easily. DMC should generally be considered in tandem with the Pairwise [Bubble] Sorted methods -- starting with a seed rank using some measure (approval, ratings, borda), pairwise sorting gives the complete ranking, while DMC (as above) finds the winner directly. See the electowiki page for more information: http://wiki.electorama.com/wiki/Pairwise_Sorted_Methods Q Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Obvious(?) extension of DMC to range
On 30 Aug 2005 at 12:13 UTC-0700, Adam Tarr wrote: Seems simple enough. DMC, on a rated (graded?) ballot. In stead of using approval score to measure defeat strength, use average rating. Good method? I dunno. I have no objection to this, and it could be an even better method. The voter then has more precise control over exactly how much their vote contributes to a candidate's approval rating. But there are three drawbacks I see: - Ratings to ordinal conversion could be confusing. Not a showstopper, just requires some education. - There needs to be a way to give several candidates equal ratings but also rank them differently: For example, W, X, Y and Z are each given the same rating, say 100 points, but the voter wishes to rank them as W X=Y Z. - Resulting complexity of ballot. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: reason #17
On 29 Aug 2005 at 16:06 UTC-0700, Forest Simmons wrote: More discussion on this is found in the thread which contains the following seminal message: http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015316.html explaining how DMC, AWP, and Approval Margins (AM) are related to each other, and how they fit into the family of Condorcet methods, and also comparing their effectiveness against burying. Here's when I first saw the light that DMC was the best Condorcet proposal: http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015418.html Forest is too modest. DMC/RAV finds the same winner as a method he proposed earlier. At one time, he called it, variously, Approval Sorted Condorcet, Approval Seeded Bubble Sort, or Bubble Sorted Approval. Lately I've taken to calling it Pairwise Sorted Approval. It was first proposed in March 2001: http://lists.electorama.com/pipermail/election-methods-electorama.com/2001-March/005448.html The main difference (advantage?) of the DMC/RAV formulation is that it finds the winner directly. But the social ordering that results from determining the DMC winner, removing that winner, finding the DMC runner up, etc. is exactly the pairwise-sorted approval ordering. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: DMC / 2-party domination
On 30 Aug 2005 at 08:51 UTC-0700, Kevin Venzke wrote: What do you disagree with? That FBC-failure in a single general election held with Condorcet or Condorcet/Approval hybrid will lead to 2 party dominance. My point was that the dominance begins in the primary. If you disagree that DMC fails FBC, I don't have a failure example at the moment. But I would be shocked if DMC satisfies FBC, since DMC is a Condorcet method. When I read your second paragraph, you seem to be arguing that even methods which satisfy FBC will fail it if there are primaries. But that doesn't seem to be a disagreement with anything I said. When I referred to the argument... I was referring to Warren's argument. Perhaps that's where you disagreed. I don't know what TTFN means. Ta-ta for now! -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: 15 reasons to support DMC
On 28 Aug 2005 at 16:55 UTC-0700, Dave Ketchum wrote: I continue to question adding Approval to Condorcet - can it really be worth the pain of trying to be understood? PS - a few days ago I found out about the Condorcet group, that DMC is important there, and looked for a definition - finding that NONE of the subject lines led me to such. Is a definition now easily findable on both Condorcet AND EM? Googling for Definite Majority Choice takes you here: http://wiki.electorama.com/wiki/Definite_Majority_Choice Here is a summary, stripped of extra terminology: , | - Ordinal ballot with approval cutoff. | | * For example, each slate of candidates could have an extra | fictional candidate, Not Approved. | | The approval score is the number of votes FOR a candidate | AGAINST Not-Approved. | | - Eliminate candidates who are defeated one-to-one by any other | higher-approved candidate. | | - Among the set of remaining candidates, eliminate any candidate who | is defeated by a lower-approved candidate. ` In the case of no ties, there is a unique winner. I won't discuss strategy, but many of the same considerations apply as in Approval Voting. I'm leaving my current job on the 31st, and it may be a month or so before I start again at my new one, so don't expect to hear from me for a while. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: DMC / 2-party domination
On 29 Aug 2005 at 12:59 UTC-0700, Kevin Venzke wrote: Here is another question - will DMC lead to 2-party domination, or not? To really answer this, it would help to understand optimal voting strategy in DMC, which is probably beyond reach. The argument that some ranked methods lead to 2-party domination is based on the possibility that voters will use favorite betrayal to ensure that they don't sink their most viable frontrunner. So it seems to me that, using this reasoning, any method which fails Mike Ossipoff's favorite betrayal criterion will lead to 2-party domination. DMC doesn't satisfy the favorite betrayal criterion. I disagree. I think that favorite betrayal occurs in the primaries, before the general election slate is even drawn up. TTFN, -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: open primary followed by election
On 26 Jul 2005 at 18:28 UTC-0700, Forest Simmons wrote:
[Q] continued with comments and other suggestions, including the use
of Jobst direct support and also approved style ballots in the
primary, posing the question of how to make the best use of Jobst's
ballots.
Let's use a standard term -- First Choice -- rather than direct
support. I meant to use the ballot format as the example, not the
terminology.
The use of approval in the first round has to have real weight behind
it. It should penalize insincere approval of un-electable candidates
from the other side by giving non-first-choice approved candidates a
chance of knocking off your first-choice favorite.
My idea for a first round:
candidate with 50% first choice votes wins, no runoff
Otherwise, candidate with highest approval 50% wins, no runoff.
Otherwise, go to a 2nd round runoff.
This is like a variation of ER-Bucklin, isn't it? With single vote
for 1st place, ER(whole) in 2nd-place, and no 3rd-place votes. It is
also a little like one of Kevin Venzke's 3-slot methods.
Are you suggesting not allowing a winner at the first round? Or do
you mean to use your second round method only if no candidate wins
more than 50% of first place votes?
I like this idea, and It seems to me that ranked ballots would not
be necessary in the second round (the runoff election) if the
information from the first round (the primary) were used to form a
reasonable lottery L as a standard of comparison.
Here's an example of how those ballots could be used:
1. After the primary (using Jobst style ballots) list the
candidates in approval order.
Sure. But this is really just sugar, a visual reminder to the voter
of how things stand. Does it really penalize insincere approval?
2. Go down the list to the highest approval level at which a
majority of ballots express approval for some candidate at or above
that level. Eliminate the candidates below that level.
I see this is an elimination stage, but I don't quite follow what's
going on here. Say we're testing an approval elimination level of 5%.
Do 50% or more of the ballots approve any of the candidates above that
level? How do I figure that out?
For example, say that seven candidates have approval 5%. Is there a
summable way to quickly see the fraction of ballots that approve at
least one of those 7 candidates? Because of overlaps, this isn't the
same as adding up approval for each of the 7 candidates: I'd have to
count ballots that approve
1 out of the 7
2 out of the 7
3 out of the 7
4 out of the 7
5 out of the 7
6 out of the 7
7 out of the 7
Not summable on the first count, right? You need a recount. Of
course, you'd only have to do this if the first round were not
definitive (again, what is your standard?), so it would be like doing
a recount anyway. But I'd still like to see an example.
Not terribly understandable or publicly acceptable as it stands, I'd
say.
3. Form a lottery L in which the remaining candidates'
probabilities are proportional to their direct supports.
Proportional with respect to the 1st-choice votes for non-eliminated
candidates, I assume? This is less than the total number of ballots.
So how valuable is this lottery? Does it make the 1st-place vote too
valuable? Is going to encourage compromise in picking your
first-place candidate?
4. The second round is pure approval. If no candidate receives
more than 50%
... second round ... (right?)
approval, then lottery L is used to choose the winner. Otherwise,
the candidate with the greatest approval in the second round is the
winner.
Note that in the second round, approval has a definite meaning: you
approve candidate X iff you like X better than the lottery L.
So you approve a candidate X if you like the candidate better than
their odds in the lottery. You would do this almost always (for a
favorite or compromise candidate) unless X had tremendous (if not
total) probability in L.
If there are N remaining candidates, it takes only N comparisons (of
the form X?L) to fill out this approval ballot, whereas an ordinal
ballot would take at least N*lg(N) comparisons ( of the form X?Y),
where lg(N) is the integer part of the base two log of N.
Approval is certainly the easiest ballot of all the EM alternatives.
But the question is whether Approval will pick a better candidate
than, say, DMC.
Note, also, that if L supports just one candidate X, then the only
way that the lottery L can be the winner is if candidate X is a
Condorcet Winner.
I don't quite follow this ... I gather that you mean that some
candidates W, Y and Z are included in the 2nd round with X, but none
of them get any first place votes, so L supports only X.
L is the winner iff none of {W,X,Y,Z} get higher than 50% approval.
The electorate is splintered, so the best we can do is pick a number
out of a hat.
In general (even when L gives
[EM] Re: rank/approval cutoff ballot
On 20 Jul 2005 at 18:51 UTC-0700, Abd ulRahman Lomax wrote: At 03:47 PM 7/20/2005, Dan Bishop wrote: [...]I think a good solution would be for elections to have two rounds: 1. A qualifying primary, done entirely with write-in ballots, and counted using Approval. Candidates with a sufficient number of votes would advance to... 2. A runoff election, using ranked ballots. Not a bad idea. Runoff elections have an additional advantage: an opportunity for a reduced field to compete. With fewer candidates, there is more ability of the electorate to see who they are. (If) This now sounds like a primary and general election. That might be one way to spin it. Consider, for example, that Washington State's top-two runoff was declared unconstitutional last Sunday: http://seattletimes.nwsource.com/html/politics/2002384176_webstateprimary15.html This list was discussing approval-based primaries back in early 2004, if I recall correctly. Back then, I was thinking about something like this (borrowed from Jobst's Imagine Democratic Fair Choice page on electowiki): I | I also support | approve directly: |of: --+-- AnnaX | O Bob O | O Cecil O | X Deirdre O | X Ellen O | O --+-- (vote | (vote for for| as many exactly | as you one) | want) The real trick is deciding what to do with the results! In Washington state, parties objected to the top-two runoff, because some supporters of a strong candidate might vote for the weaker of the opposition. If the approval cutoff is too limiting, the approval primary would still be susceptible to that strategy. So there should be some tally method that encourages sincere (and generous) approval of alternatives. The best way to do that is to allow the approval winner to win outright in some circumstances. What about this primary method: Approval ballot (as above) A candidate with more than 50% first place votes wins outright. Otherwise, if there is at least one candidate with more than 60% (75%? what is the safe cutoff?), the approval winner wins outright. Otherwise, all candidates with more than 1% approval are advanced to the general election and listed in order of first-place vote totals, with approval scores also noted. The general runoff election would use some ranked ballot method, e.g. a ranked approval ballot with DMC tally :-). Write-ins would be allowed on the approval-primary ballot, but not on the general election ballot. The primary would have to be close enough to the general election to be meaningful -- within 60 days, for example. A 1% cutoff is similar to current rules about what parties are allowed to be listed on the ballot. The parties would then not be able to protest that their chosen candidate was being unfairly excluded -- approval less than 1% indicates that they are on the fringes anyway. They could still enact some legislation to differentiate their sanctioned candidate from mavericks. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: rank/approval cutoff ballot
On 21 Jul 2005 at 12:45 UTC-0700, Araucaria Araucana wrote: What about this primary method: Approval ballot (as above) A candidate with more than 50% first place votes wins outright. Correction: If there is at least one candidate with more than 50% first place votes, the first-place vote winner wins outright. Otherwise, if there is at least one candidate with more than 60% (75%? what is the safe cutoff?), the approval winner wins outright. Actually, 50% might be fine. That would strongly discourage promotion of weak opponents. Otherwise, all candidates with more than 1% approval are advanced to the general election and listed in order of first-place vote totals, with approval scores also noted. The general runoff election would use some ranked ballot method, e.g. a ranked approval ballot with DMC tally :-). Write-ins would be allowed on the approval-primary ballot, but not on the general election ballot. An alternative to not allowing write-ins would be to allow up to N official write-ins, with, say, 1000 valid signatures turned by 1 week before the election. They would be assigned one of N extra codes allowed in that race. I think Abd made a suggestion to this effect already. The primary would have to be close enough to the general election to be meaningful -- within 60 days, for example. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: rank/approval cutoff ballot
[I'm back from vacation, and recovered somewhat from finding that I will be laid off at the end of August.] On 20 Jul 2005 at 08:35 UTC-0700, Abd ul-Rahman Lomax wrote: other comments on James' ballot All valid concerns. The only thing I might add is that for Approval-cutoff ballot + Approval-Condorcet hybrid methods, it isn't really necessary to have a fixed ranking system if you include a Neutral Preference pseudo-candidate. Most people would rank only their approved candidates anyway, and you can count approval via votes for a candidate against the NP candidate. I do think the whole concept of a ballot should be reconsidered Increasingly, voters will be able to vote at computer terminals. Generally, I don't like the trend, the way that it is being implemented, but there is a way that would make it safe. In this idea, the terminal allows a *huge* number of candidates. It incorporates a search function that would allow any voter to quickly find a candidate by any portion of the name, and it would also allow listing candidates by party or slate. (The terminal would come up blank, no candidates shown, initially. Unless perhaps a candidate could get listed in the initial screen by presenting a hefty petition.) It allows the voter to pull up a customized list of candidates, and the voter then can rank them. Unmarked candidates would be considered neutrally ranked. (Exact procedure would depend on the vote analysis system. In asset voting it really doesn't matter. Ranked asset voting would apply ranking first, then, if ranking is exhausted, the votes would be applied according to a formula to the ranked candidates -- approved only! -- or maybe only first rank.) I agree with this almost entirely, except for the default neutral rank for unmarked candidates. But of course, you already state that it depends on the tally method (aka vote analysis system). And, of course, the terminal would print a paper receipt (there would be redundant printers in case of printer failure). The voter would inspect the receipt to verify its accuracy and would then deposit it in a secure box. And we reach the key point! Paper ballot is the only true one counted. The terminal is merely an assistant. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: James: Definition, electowiki
On 22 Jun 2005 at 16:48 UTC-0700, Abd ul-Rahman Lomax wrote: I'd recommend that anyone who wants to personally keep a copy of a page put up on a wiki keep a copy themselves, offline. [ + plus other good advice ] Very wise recommendations, but one might assume from Mike Ossipoff's posting style that he has no personal computer of his own and uses only web-based email. Which might explain some of his seemingly cavalier attitude about recommending that other people do his work for him -- he simply lacks the facilities (and hence the expertise) to do it himself. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: James: Definition, electowiki
On 22 Jun 2005 at 14:13 UTC-0700, MIKE OSSIPOFF wrote: Does electowiki or EM have available web pages where EM members can post things that can't be modified by someone else afterwards? The modifiability of what one posts to the electowiki tends to discourage me from using it. Mike -- A wiki is for discussion and consensus, not for Pronouncements from On High Written For All Eternity Upon Stone. See this WhyWikiWorks page, among others: http://moinmoin.wikiwikiweb.de/WhyWikiWorks I like this comment in particular (about the wiki concept and its various software incarnations): So that's it - insecure, indiscriminate, user-hostile, slow, and full of difficult, nit-picking people. Any other online community would count each of these strengths as a terrible flaw. Perhaps wiki works because the other online communities don't. --PeterMerel :-) Only once have I had to correct somebody else's modification of a page I started on Electowiki. I've modified other edits, but only to improve clarity. I'm probably reaching a bit here, but it appears to me that you might be a bit of a perfectionist, which can lead to procrastination. If you are always seizing on the imperfection of Wiki as a reason for avoiding it, you will never begin at all. One way to get past the need to do something perfectly the first time is to deliberately Do It Wrong, just to get it started. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: the simplest election reform
On 15 Jun 2005 at 18:32 UTC-0700, Dave Ketchum wrote: On Thu, 16 Jun 2005 00:15:50 +0200 (CEST) Kevin Venzke wrote: Ted, --- Araucaria Araucana [EMAIL PROTECTED] a crit : Approval voting is a reasonable first step. But what do you do about current top-two runoffs, or primaries in general? You should be glad to be rid of top-two runoffs - too often, by locking out the third candidate, they lock out the truly best liked candidate - think of voter desires as follows, but voting Plurality plus top-two: You all are missing the point of my original question. Abd advocates allowing overvotes to instantly enable approval voting. But sneaking approval in this way doesn't solve the more general problem of eliminating the primary. I *do* want to eliminate the primary, since it is merely an artifact of plurality/SVFPP. So sure, I say go ahead and allow overvoting. But don't lose sight of the end goal. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: the simplest election reform
On 16 Jun 2005 at 14:30 UTC-0700, Anthony Duff wrote: Perhaps there was something specific about the primary that you want eliminated, but every party has to be able to choose a candidate. Sure, let parties choose their candidate, but on their own dime. I don't buy the argument that it is in the public interest to publicly fund a primary to choose the candidates. It maintains the status quo of two major parties (in the US, at least). If ranked ballots or approval are enacted, why not allow all the primary candidates on the general election ballot anyway? With a strong ranked scheme or approval it shouldn't hurt the official party representatives, and could possibly even help them. The primary losers don't have to actively campaign, but disaffected party voters could register some kind of statement without actually losing their votes. For example, some 500 voters in last November's Washington State governor's race voted for Ron Sims, the Democratic primary loser, probably as a statement against Christine Gregoire's 1960's membership in a black-excluding sorority. Presidential campaigns are a different beast, anyway. Any voting change is going to have to start locally, with city, county and statewide offices. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: the simplest election reform
On 15 Jun 2005 at 14:25 UTC-0700, Abd ulRahman Lomax wrote: It *might* be a much easier reform to accomplish. Approval is extremely simple to understand and, as often noted, no ballot changes are needed, beyond some changes in ballot instructions. The fact appears to be that these changes would simply make the real conditions of voting more closely correspond to what people who are not informed would already expect. You have to know that overvotes will be discarded, and many voters don't know that, and I have never seen the fact printed on a ballot. Without specific knowledge, I would simply assume that all votes would be counted, and, indeed, it appears that many voters do have that idea. Any reform at all might break the logjam. This one would probably change outcomes gradually, not all at once, except possibly in some close races. Approval voting is a reasonable first step. But what do you do about current top-two runoffs, or primaries in general? Most of the highly-regarded single-winner methods discussed here involve eliminating the primary in addition to changing the ballot and tally methods. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Voting Systems Study of the League of Women Voters of Minnesota
dialogue about approval and detection of tampering Another thought occurred to me. With either Approval or ranking, it is easy enough to un-vote for a candidate by simply drawing a line through all of the candidate's fill-in spots. A machine reader can be set to count multiple ranks or excessive ink as lowest rank or non-approved. This prevents tampering via overvotes and makes the intention clear if the ballot is read by hand. And it takes mere moments to strike out all non-preferred candidates. Zip, zip, zip, and you're done. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: MMPO, contd
On 3 Jun 2005 at 18:59 UTC-0700, Forest Simmons wrote: Near the end of his message Mike wrote ... It seems to me that the first step of sprucing-up was to eliminate every candidate who isn't in a certain selection set. The set of candidates who could win without violating BC? And then was that followed immediately by the collapsing of beat-clone-sets? A two-part procedure?Anyway, I guess I'll keep looking. But Forest, could you post the full complete definition when you get a chance to? Forest replies: The certain selection set evolved over time from Smith, to Uncovered, to Banks, to Duda, to Minimal Covering Set, and yes, that step was followed by clone collapsing, but I abandoned the spruce up quest for two reasons: 1. It satisfied Smith, which I came to believe was too restrictive. [And we suspect that Smith is incompatible with the FBC.] 2. Spruced up random ballot turned out to be non monotonic, due to the restriction to the Uncovered Set (or its more restrictive subsets). And I suspect that clone collapsing by itself could also impair monotonicity; I'm not sure. So the method never came to a definitive form. The nearest it came to a definitive form was in a posting that I wrote in reply to somebody that wanted to do a Wiki page on it. I'll try to find that if you want me to. Ted Stern was following the discussion pretty closely back then; perhaps he can find it. This is a fairly complete description of sprucing up. http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-December/014325.html 1) Eliminate covered candidates 2) Collapse 'beat clones'. Search for anything by Forest or containing 'spruced' or 'sprucing' in the subject in the December 2004 archive, and you'll find most of it. http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-December/thread.html Eventually Markus posted examples of how a spruced up method would fail monotonicity. January? February? Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: CIBR examples, and its CC failure
On 27 May 2005 at 11:46 UTC-0700, Ken Kuhlman wrote: While your CC failure example is helpful, my favorite is Condorcet's original critique of Borda: 30:ABC 10:BCA 10:CAB 1:CBA 29:BAC 1:ACB Condorcet picks A Borda CIBR pick B. Here's the explanation (summarized from Saari): If symmetrical ballots, (which represent ties should cancel), are factored out, the election outcome should be unchanged. The symmetrical ballots in Condorcet's critique are: 10:ABC 10:BCA 10:CAB and 1:CBA 1:BAC 1:ACB The reduced profile is then: 20:ABC 28:BAC I've seen this Borda-advocate logic before. Eliminating 'symmetric' votes is just eliminating votes. Among others, you've effectively ignored the net 9 vote preference for A over B among all the C voters. So you've effectively told them, Tough luck, your votes were considered invalid, so we're not going to consider your lower-ranked preferences. Even if your voting block thinks that A is the lesser of two evils (and would contribute to a majority expressing that one-to-one preference), we're going to pick B anyway. To me, symmetry refers to reversing the ballot orders on all the ballots. Let's say we do this. Then whichever method you pick, Condorcet or Borda, the reverse-winner is C. So you should be able to go back to the original election and see who would win with the loser, C, eliminated. If you eliminate C from the original election, the voters prefer A to B, Borda or Condorcet. But introducing C to the ballots doesn't change the Condorcet winner, just the Borda winner. Borda is far more prey to weird IIA-violation effects than Condorcet. I've also been following your CIBR arguments. It seems to me that you're setting up a straw man for Borda, since clone independence is not Borda's worst failing. Burying is much worse and you haven't addressed that at all. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: A Condorcet-like method that satisfies FBC (I believe)
On 18 May 2005 at 15:14 UTC-0700, Kevin Venzke wrote: long explanation of method For clarity, here is a brief definition of the method I'm suggesting: The voter places each candidate into one of three slots. v[x,y] is the number of voters voting X over Y. t[xy] is the number of voters ranking X and Y together in the top slot. Define a set S containing every candidate Z for whom there is no other candidate W such that v[z,w]+t[zw]v[w,z]. If S is empty, then S contains all the candidates. Elect the member of S who is in the first or second slot on the most ballots. (I admit that it's weird to have everyone compress in the second stage in the same way, regardless of who is in S. In ordinary Condorcet//Approval, the second stage never occurs unless S contains all the candidates. But I don't see any other neat way of picking a winner from S, especially if S contains more than two candidates.) Hi Kevin, This is a very interesting idea. But I don't see any reason why it couldn't be applied to a 'standard' approval cutoff ranked ballot. v[x,y] is your notation for the standard pairwise array. t[xy] is your notation for another pairwise array (symmetric). Let's consider two other summable arrays that could be tabulated from an approval cutoff ballot: ab[x,y] = number of voters Approving Both x and y. This array is summable, and a[y,x] = a[x,y], so it is symmetric. sp[x,y] = number of voters approving x but not y. This is James Green-Armytage's Strong Preference array, also summable. The kernel of your method is that you don't want to penalize a candidate for a weak defeat; i.e., one that is has more weak preferences (both in the top-slot in your proposal, but I'm suggesting that both approved could be used instead -- let's discuss a class of methods and not get specific for now) than the winning margin. A strong defeat is when the winning margin is greater than the number of weak preferences. So your first round is to check whether any candidates have no strong defeats. If any exist, eliminate any strongly defeated candidates. That's all well and good -- we've eliminated candidates that a majority has agreed should not be elected. Your question is what do to on subsequent rounds, and you choose to pick the approval winner among the remaining candidates. I think this might actually fail FBC because a lower-ranked candidate could have higher approval. Here's another idea: combine this with something sort of like Bucklin: f[x,y] = # of voters putting x and y in first place fs[x,y] = # of voters putting x and y in either first or second place and approving both fst[x,y] = # of voters putting x and y in 1st/2nd/3rd place and and approving both For rounds 1-4, if some candidates would remain, eliminate strongly defeated candidates (within the set of remaining candidates) according to the round's measure of strong defeat: Round 1: Strong defeat XY means v[x,y] - ab[x,y] v[y,x] Round 2: Strong defeat XY means v[x,y] - fst[x,y] v[y,x] Round 3: Strong defeat XY means v[x,y] - fs[x,y] v[y,x] Round 4: Strong defeat XY means v[x,y] - f[x,y]v[y,x] Round 5: Elect DMC winner among remaining candidates. No candidate is eliminated until it is strongly defeated by another candidate, according to the strong defeat measure in the round. So if X and Y are not strongly defeated by Z, but one of them strongly defeats Z, Z can be eliminated and then the preference between X and Y is considered. This is sort of off the top of my head, so play with it as you will. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: fixing DMC page on electowiki
Hi Abd, As you say, we are all busy people. Unfortunately I don't have time to reply to each of your most recent points right now. In both my post and my writings on the DMC web page, I was trying to explain the method, not the motivation behind it. I'm afraid that for the moment I'll have to leave that for others. There are some links on my electowiki user page that might be helpful, though. Good luck with your local efforts! Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Arrow's Theorem flawed?
Curt Siffert siffert at museworld.com writes: I recently posted this addendum to the Arrow's Theorem page on wikipedia: It was immediately deleted for bias. The theorem is criticized by many vote theorists, however, for depending on flawed requirements. [...] It is the final (IIAC) criterion that is most controversial. Some vote theorists believe there are scenarios of voting behavior where failing the IIAC is considered rational behavior by a voting society. One such example is where one candidate's supporters are far more loyal than another's, and the introduction of a third candidate would split the support of the third candidate. If failing IIAC is not always a flaw, then the voting methods that fail only this criterion would not necessarily be considered flawed. In other words, some vote theorists believe Arrow's theorem improperly asserts that passing the IIAC is a requirement to be considered a satisfactory voting method. This would render follow-up theorems, such as the Gibbard-Satterthwaite theorem, flawed as well. Was I out in left field for writing this? I was under the impression that many vote theorists agreed with this characterization. Just a thought, but stating many vote theorists without providing supporting links to referreed articles might have led to the bias decision. I'm not saying that your argument is like those supporting Intelligent Design or denying Global Warming, but perhaps as a result of the furor on those other topics, the wikipedia maintainers are a little sensitive to unsubstantiated claims. -- Q Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: fixing DMC page on electowiki
On 10 May 2005 at 19:56 UTC-0700, Abd ulRahman Lomax wrote: At 01:25 PM 5/10/2005, Araucaria Araucana wrote: It appears that you are reading my comments out of context, and are also misunderstand the intent of a wiki -- it is a *collaborative* site. See these links: [deleted] Perhaps it doesn't matter, but I operate several wikis, and I've contributed to Wikipedia (though I'm certainly not a wiki expert). I don't know why Mr. Araucana got the idea that I didn't understand this basic concept. Please, call me Q (see sig). And please don't take offense [there's a bit too much of it on the list at present!]. I've heard it said that written language is only 7% effective -- much more is conveyed in intonation and body language. Email has a long time-lag, so to avoid too many separate messages, I tend to err on the side of too much information. You may choose to interpret this as being patronizing, but it isn't meant to be. I do apologize for underestimating your abilities, but it was your first posting, and I didn't have anything else to go on. My default assumption is that posters to this list usually are stronger at theoretical math than web skills. So the least-approved candidate ... is the winner? Explain this thing to me Okay, here goes: First, a Condorcet method is a procedure for holding a set of one-on-one elections simultaneously, using ranked ballots. Some on this list have proposed calling it Instant Round Robin. http://wiki.electorama.com/wiki/Condorcet_method Ranked ballots (equal ranking allowed) are tabulated into a pairwise matrix (call it M). A vote in location M(i,j) means a vote for candidate i against candidate j. So if the total M(i,j) is greater than M(j,i), candidate X(i) defeats candidate X(j). http://wiki.electorama.com/wiki/Condorcet_method#Counting_with_matrices Because the final total can sometimes be cyclic (i.e., no candidate is undefeated), we are interested in finding a satisfactory completion method. There are several strong methods (e.g. Ranked Pairs, CSSD, River) that use ranked ballot information alone, but they may be too complex for an initial reform proposal. Therefore, some have proposed combining Condorcet with Approval Voting. Here's some background on Approval: http://wiki.electorama.com/wiki/Approval_voting To combine approval with a ranked ballot, we use an approval cutoff: http://wiki.electorama.com/wiki/Approval_Cutoff When both pairwise and approval information are available, it is possible to reorder the pairwise array in descending order of approval. Here is an example of an election with approval cutoff ballots, before and after reordering: http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting#Example I'm excerpting the ballots and reordered pairwise matrix from that example. A winning off-diagonal score is 461 and greater. 98: Abby Cora Erin Dave Brad 64: Brad Abby Erin Cora Dave 12: Brad Abby Erin Dave Cora 98: Brad Erin Abby Cora Dave 13: Brad Erin Abby Dave Cora 125: Brad Erin Dave Abby Cora 124: Cora Abby Erin Dave Brad 76: Cora Erin Abby Dave Brad 21: Dave Abby Brad Erin Cora 30: Dave Brad Abby Erin Cora 98: Dave Brad Erin Cora Abby 139: Dave Cora Abby Brad Erin 23: Dave Cora Brad Abby Erin +---+ || against | ||--| || Erin | Abby | Cora | Brad | Dave | |+--+--+--+--+--| | | Erin | 708 | 410 | 461 | 298 | 610 | | |--+--+--+--+--+--| | | Abby | 511 | 645 | 461 | 458 | 485 | | |--+--+--+--+--+--| | for | Cora | 460 | 460 | 460 | 460 | 460 | | |--+--+--+--+--+--| | | Brad | 623 | 463 | 461 | 410 | 312 | | |--+--+--+--+--+--| | | Dave | 311 | 436 | 461 | 609 | 311 | +---+ There are no undefeated candidates == there is no Condorcet winner. So, using DMC (aka Ranked Approval Voting), let us begin by ignoring the row and column of the least-approved candidate, Dave. We then see that Brad defeats all remaining candidates. We're done -- Brad wins. As it happens, there are several candidates who are undefeated by other candidates with higher approval. Erin, Abby and Brad all qualify. In DMC, we call this set the definite majority set. Among the definite majority set, Brad defeats all others. *** It is a corollary of the definite majority set's construction that *** the winner is the least-approved member of that set. Compare with this idea: http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes See also the various criteria that have been proposed for voting methods. IMO, DMC/RAV may not be the best possible single-winner election method
[EM] Re: fixing DMC page on electowiki
On 9 May 2005 at 18:02 UTC-0700, Abd ul-Rahman Lomax wrote: At 06:45 PM 5/9/2005, Araucaria Araucana wrote: Some anonymous person from IP location 71.98.149.61 modified the Definite Majority Choice page (http://wiki.electorama.com/wiki/Definite_Majority_Choice) a couple of days ago, changing The least-approved candidate in the definite majority set pairwise defeats ''all'' higher-approved candidates, including all other members of the definite majority set, and is the DMC winner. to The most-approved candidate in the definite majority set pairwise defeats ''all'' higher-approved candidates, including all other members of the definite majority set, and is the DMC winner. I'm changing it back to the original, since the change is incorrect. Let's just say that, if Mr. Araucana is correct, Definite Majority Choice is so thoroughly confusing that it will never be the Majority Choice, much less the Definite Majority Choice It's pretty confusing even if he is *not* correct. Hi Abd, welcome to the list. It appears that you are reading my comments out of context, and are also misunderstand the intent of a wiki -- it is a *collaborative* site. See these links: Why Wiki Works:http://c2.com/cgi/wiki?WhyWikiWorks Wiki page on Wikipedia: http://en.wikipedia.org/wiki/Wiki So ... have you read the entire web page? What in particular do you find confusing? On every electowiki page there is a tab near the top entitled discussion. If you click there, you can add comments or questions. I encourage you to do so, after creating a login account, of course. Finally, note that comments are most welcome when they are well considered and constructive. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html Election-methods mailing list - see http://electorama.com/em for list info
[EM] fixing DMC page on electowiki
Some anonymous person from IP location 71.98.149.61 modified the Definite Majority Choice page (http://wiki.electorama.com/wiki/Definite_Majority_Choice) a couple of days ago, changing The least-approved candidate in the definite majority set pairwise defeats ''all'' higher-approved candidates, including all other members of the definite majority set, and is the DMC winner. to The most-approved candidate in the definite majority set pairwise defeats ''all'' higher-approved candidates, including all other members of the definite majority set, and is the DMC winner. I'm changing it back to the original, since the change is incorrect. To whomever changed the text: I don't mind other people editing the page, but please 1) Don't be anonymous or I'll assume you're a spammer or site defacer. Create an electowiki account and sign in: http://wiki.electorama.com/wiki/Special:Userlogin and enable cookies so you don't have to do this every time. Please include an email with your account so that other users can send you mail. Don't worry, this is done via forms so your address is never publicly revealed. If you want a spam-resistant gmail address, contact me off-list -- I have plenty of invites left. 2) Try to understand the page you are changing so you don't distort its meaning. If you have questions, contact one of the previous page editors (click on their User page, and select the E-mail this user link from the lower left sidebar menu). Thanks, Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria (Q = Qoph = monkey/knot -- see http://www.ship.edu/~cgboeree/alphabet.html) Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: British Election and Duverger's Law
On 6 May 2005 at 00:52 UTC-0700, Alex Small wrote: Long time no post. I'm wrapping up the writing on my dissertation, but I couldn't resist jumping in to post on the British election. The Liberal Democrats are putting in their strongest showing since the 1920's. What's interesting from the non-partisan standpoint of this list is that Britain uses plurality voting from single-member districts, and yet the LibDems got 22% of the popular vote at last count and approximately 9% of the seats. The usual rule of thumb is that plurality voting from single-member districts encourages the formation of a 2-party system. That's certainly the case in the US, both nationally and in the 50 states (which can be seen as 50 different units to compare). The appeal of the LibDems is even more surprising when you consider that it's a parliamentary system. The stakes in a legislative race are even higher, so at first glance I would think that there's even more of an incentive to vote for one of the 2 major parties. Finally, while most of the other parties in the British Parliament are regional/ethnic parties representing Wales, Northern Ireland, and Scotland, the LibDems are more about issues and ideology rather than ethnic/regional identity. Now, it may be tempting to explain these results solely in terms of current events: Tony Blair has alienated elements of the left and center, and the Tories are such an abysmal mess that even Gray Davis has lost respect for them. But the LibDems have persisted despite the fact that they've been the third party in size for 80+ years. I'm more surprised by their persistence over time than I am by their current popularity. Does anybody know why Duverger's Law has been so stubbornly resisted in Britain for 80+ years? I'd be genuinely curious to know. Alex Duverger's Law is not absolute, and I think it assumes some party stability and regional homogeneity. Extracting from the top of the wikipedia entry (which ought to be imported into electowiki): ,[ http://en.wikipedia.org/wiki/Duverger%27s_law ] | Duverger's Law is a principle which asserts that a | first-past-the-post election system naturally leads to a two-party | system. The discovery of this principle is attributed to Maurice | Duverger, a French sociologist who observed the effect and recorded | it in several papers published in the 1950s and 1960s. In the course | of further research, other political scientists began calling the | effect a ülawý. | | While there are indeed many FPTP systems with two parties, there are | significant counterexamples: Scotland has had until recently | first-past-the-post and similar systems but has seen the development | of several significant competing political parties. Many | commentators regard the United Kingdom's Liberal Democrat party, | since the 2005 General Election, as forming a 'third party' and | creating a three-party system. Canada and India have multiple | regional parties. Duverger himself did not regard his principle as | absolute: instead he suggested that first-past-the-post would act to | delay the emergence of a new political force, and would accelerate | the elimination of a weakening force - proportional representation | would have the opposite effect. | | Additionally, William H. Riker noted that strong regional parties | can distort matters, leading to more than two parties nationwide, | even if there are only two parties competitive in any single | district. He pointed to Canada's regional politics, as well as the | U.S. presidential election of 1860, as examples of often temporary | regional instability that occurs from time-to-time in otherwise | stable two-party systems (Riker, 1982). ` In the US 1860 election, there was not only regional instability, but the Whigs were disintegrating and the Democratic and fledgling Republican parties (and others) were scrambling for dominance in a highly charged race. This entry appears to be very recently updated, BTW. Monk -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Approval Later-no-Harm,
On 6 May 2005 at 10:44 UTC-0700, Chris Benham wrote: Ted, James (and anyone interested), In my last post (Thu.May5) I suggested this criterion: If x wins, and afterwards some identical ballots that approve x are uniformly changed only so that they approve more candidates than previously; then if there is a new winner it must be one of the candidates approved on these altered ballots. This is supposed to be a simple test for the property that approving more candidates should never change the winner from an approved (on the original ballots) candidate to a disapproved (on both sets of ballots) candidate. This is very similar to this monotonicity-like criterion: If x wins, and afterwards some ballots are changed only to increase the approval scores of some other candidates; then if there is new winner it must be one of the candidates whose approval scores have been raised. I was going to say that I didn't see why these were different. But now I see -- the difference is that in the first, the approval is extended on ballots that approve X, and in the second version, it can be any set of ballots, X-approving or not, and they don't have to be identical. Or maybe it is better to put it the other way: If x wins, and afterwards some ballots are changed only to decrease the approval scores of one or more other candidates; then x must still win. Yes, this seems more succinct. But what to call it, Mono-reduce opposition approval? But you lost me here. I'm don't think the two last definitions are equivalent. In the first mono-like criterion, X is the winner before approval-extension. In the second, X is the winner with expanded approval. Call the second winner Y instead, for clarity. Then if Y is the new winner after the first definition, the only way to go back is to remove approval for Y in the second definition. Also, are you assuming that when approval is extended it is being applied only to lower-ranked candidates than those already approved? That would be normal for ranked ballots with approval cutoff. Another criterion that applies to rankings/approval methods interests me, which I might call Disapproval Later-no-Harm: Ranking a disapproved candidate must never harm an approved candidate. (A stronger version would add or a higher-ranked disapproved candidate). This is incompatible with Condorcet, and in a future post I'll suggest a method that meets it. This goes around and around ... If you have such a method, I don't think it will satisfy the Condorcet Criterion. But I'm interested anyway ;-) -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] 2004 baseball grid, revisited
Last fall Jobst analyzed the 2004 team-to-team stats of the American League as an example of using River. I decided to revisit the example since I hadn't followed his work the first time, and found that his River analysis had an error. In the example, scores were listed as percentages of head-to-head matches won. Jobst suggested that I try to find something like Approval to use to see how DMC would work. I started using row sums. If I were using winning games instead of percentages, the row sum would be total games won, exactly what is used to rank teams currently. The row sum of wv is equivalent to the Borda score. It then occurred to me that dividing the row sum by N-1 is the average number of winning votes. When applied to winning percentages, this gives the average percentage of games won, a perfectly reasonable way to rank baseball teams, if not candidates. So here is that example, reposted. Because the average percentage is hard to tell apart, I put brackets around it. Best viewed with fixed-width font (e.g. Courier) and a wide screen: Original matrix (row averages on diagonal): Tms abcdefghijklmn o a ( Bal) [50] 53 33 50 100 67 33 44 260 78 58 71 58 28 b ( Bos)47 [60] 67 43 86 67 56 33 58 89 56 74 44 74 50 c ( CWS)67 33 [51] 53 42 68 44 47 43 22 78 67 67 43 44 d ( Cle)50 57 47 [50] 47 58 56 37 33 67 56 50 11 71 56 e ( Det) 0 14 58 53 [42] 42 22 37 57 44 56 50 44 67 50 f ( KC)33 33 32 42 58 [33]0 37 17 22 29 33 44 50 33 g ( LAA)67 44 56 44 78 100 [60] 56 56 53 65 86 47 44 39 h ( Min)56 67 53 63 63 63 44 [55] 33 29 56 44 71 67 61 i ( NYY)74 42 57 67 43 83 44 67 [62] 78 67 79 56 63 56 j ( Oak) 100 11 78 33 56 78 47 71 22 [58] 58 78 55 67 56 k ( Sea)22 44 22 44 44 71 35 44 33 42 [39] 29 37 22 50 l ( TB)42 26 33 50 50 67 14 56 21 22 71 [43] 22 50 83 m ( Tex)29 56 33 89 56 56 53 29 44 45 63 78 [54] 78 56 n ( Tor)42 26 57 29 33 50 56 33 37 33 78 50 22 [42] 44 o (Intr)72 50 56 44 50 67 61 39 44 44 50 17 44 56 [50] Grid reordered in descending order of row average: Tms ibgjhmcadolenk f i ( NYY) [62] 42 44 78 67 56 57 74 67 56 79 43 63 67 83 b ( Bos)58 [60] 56 89 33 44 67 47 43 50 74 86 74 56 67 g ( LAA)56 44 [60] 53 56 47 56 67 44 39 86 78 44 65 100 j ( Oak)22 11 47 [58] 71 55 78 100 33 56 78 56 67 58 78 h ( Min)33 67 44 29 [55] 71 53 56 63 61 44 63 67 56 63 m ( Tex)44 56 53 45 29 [54] 33 29 89 56 78 56 78 63 56 c ( CWS)43 33 44 22 47 67 [51] 67 53 44 67 42 43 78 68 a ( Bal)26 53 330 44 71 33 [50] 50 28 58 100 58 78 67 d ( Cle)33 57 56 67 37 11 47 50 [50] 56 50 47 71 56 58 o (Intr)44 50 61 44 39 44 56 72 44 [50] 17 50 56 50 67 l ( TB)21 26 14 22 56 22 33 42 50 83 [43] 50 50 71 67 e ( Det)57 14 22 44 37 44 580 53 50 50 [42] 67 56 42 n ( Tor)37 26 56 33 33 22 57 42 29 44 50 33 [42] 78 50 k ( Sea)33 44 35 42 44 37 22 22 44 50 29 44 22 [39] 71 f ( KC)17 330 22 37 44 32 33 42 33 33 58 50 29 [33] Intr is inter-league play. I didn't count Intr victories when doing River. Percentages 50 are winning, 50 is a tie. After reordering, the winner is quickly seen to be Boston, which agrees with River. I found that the 2004 National League grid was similar -- St. Louis was the winner with both DMC-AvgPct and River. I find it interesting that both league winners were predicted by Condorcet -- possibly one could use this in betting pools ;-). But the DMC method is much faster to find by hand than River. One could of course use Borda/Row-average-seeded DMC for elections as well. That would be equivalent to Pairwise Sorted Borda. And no extra approval cutoff would be required. But using Borda score as the seed ranking would overly encourage strategic burying and eliminate the ability to adjust the approval cutoff without changing ranking. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] (humor) not the lesser of two evils
How would you all rank this candidate? http://www.mediarebellion.com/i/hosted/cobra/Chthu%205.jpg ;-) -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Generic Name for the Gerald Ford candidate
On 27 Apr 2005 at 21:43 UTC-0700, Araucaria Araucana wrote: S immons, Forest simmonfo at up.edu writes: Russ said ... I'd label it something like [End Approved Candidates]. Forest replies... I like yourEnd Approved Candidates or perhaps Approval/Disapproval Cutoff Rank. How about, I disapprove candidates ranked after this rank:? Some other suggestions that have been entertained are .. 1. Minimum Acceptable Candidate (MAC) 2. Least Passing Grade (LPG) [for use with grade ballots] 3. None of the Below (NOTB) I'm sure that somebody with the gift of gab can improve on these suggestions. I'm starting to lean toward Neutral Preference Rank. I'm thinking that a CR-like point system, +1 for candidates you favor, 0 for neutral, -1 for oppose, would make more sense to the voter. Much the same as 1 approve / 0 not approve. On further thought, I think Neutral Preference may be sufficient, and it avoids the charged 'NPR' acronym. ;-) I should clarify that I am not advocating a CR method of 1,0,-1, but the approval cutoff can be explained as if that method were being used: - Ranking above Neutral Preference means you have a positive opinion about the candidate. The higher you rank X above NP (i.e., more ranks between X and NP), the higher your positive opinion of X. - Ranking below Neutral Preference means you have a negative opinion about the candidate. The lower you rank X below NP, the lower your opinion of X. - Satisfactory results come from placing the Neutral Preference line just below your highest-ranked most electable candidate. It might also be of use to count an NP-equal-ranked candidate with 1/2 of the vote each way (1/2 NPX, 1/2 XNP), but that isn't required. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: AWP versus DMC and AM
On 28 Apr 2005 at 00:54 UTC-0700, Chris Benham wrote: James, Here is an example of yours that we've been discussing. Preferences 26: ACB 22: ABC 19: CBA 06: CBA 22: BCA 05: BAC Direction of defeats AC 52-48 CB 51-49 BA 52-48 Approvals: A48, B46, C47. Interesting example. But you forgot to consider approval cutoff strategies: What happens if the 22 BCA voters move the approval cutoff upward, to get 22: BCA You get Approvals: A48, B46, C25. Consider the pairwise array with approval on the diagonal: A B C A 48 48 52 B 52 46 49 C 48 51 25 B is now the DMC (and MRAV/AM) winner. Even if the 19: CBA voters moved their cutoff up as well, B would still win. This illustrates a Later-no-harm violation of the approval cutoff in DMC/AM: B- and C-preferring voters actually get the better effect of defeating A if they do NOT approve each other. B would also have been elected if the 6: CBA voters had moved their cutoff below B. As with all of these hypothetical examples, I should point out that the margins are extremely slim, smaller than could be predicted by any standard poll. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Reply to A. A. about sloppy quoting
MIKE OSSIPOFF nkklrp at hotmail.com writes: I'd said: You said: Could you please show proof that WV (RP/Beatpath/River) passes Consistency and CWP does not? Hi Mike, I'm getting weary of the sloppy quoting I reply: What sloppy quoting? Did you or did you not say: Read what I said. Remember what I've contacted you about before. I meant standard email protocol: Name address wrote [on date]: etc. with threaded Subject header. I do appreciate that you've managed to fix your apostrophes, and I see that sometimes you can insert leading signs. Read the other suggestions and give them a try. Please! Honestly, you're a bit like my cousin who says strange that those 4 other clocks are wrong -- I know my wristwatch is accurate! I've checked it 10 times when he is 5 minutes slower than the official US atomic clock. A.A. Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Generic Name for the Gerald Ford candidate
Simmons, Forest simmonfo at up.edu writes: Russ said ... I'd label it something like [End Approved Candidates]. Forest replies... I like yourEnd Approved Candidates or perhaps Approval/Disapproval Cutoff Rank. How about, I disapprove candidates ranked after this rank:? Some other suggestions that have been entertained are .. 1. Minimum Acceptable Candidate (MAC) 2. Least Passing Grade (LPG) [for use with grade ballots] 3. None of the Below (NOTB) I'm sure that somebody with the gift of gab can improve on these suggestions. I'm starting to lean toward Neutral Preference Rank. I'm thinking that a CR-like point system, +1 for candidates you favor, 0 for neutral, -1 for oppose, would make more sense to the voter. Much the same as 1 approve / 0 not approve. -- Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: auto-truncation
On 26 Apr 2005 at 13:43 UTC-0700, Kevin Venzke wrote: H i, --- Araucaria Araucana [EMAIL PROTECTED] a écrit : Consider this case. Original true preferences: 27: AB 24: BA 49: C A is the Condorcet winner. Now consider what happens if B defects via truncation: 27: AB 24: B 49: C Under RP(wv), Beatpath(wv) or DMC, B wins. B voters have gotten a better result by dropping a lower preference. This is an example of the Later No Hurt violation of Condorcet completion methods -- B voters hurt their favorite by adding a lower-ranked preference. But if A puts the approval cutoff above B, B can't win in DMC: 27: AB 24: B 49: C C wins, anyway you cut it, as you found. There's no LNHurt situation here because B can't win either way. So the best the B voters can do is to add a preference for A. That's what I mean by the poison pill (by the A voters). Is it clear now? I have an even better idea that doesn't require an approval cutoff: If there is no CW, elect the Borda loser. (Somewhat less arbitrary, more clearly punishment.) Kevin Venzke I didn't see a smiley, but I assume one was implied. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: auto-truncation
On 22 Apr 2005 at 18:42 UTC-0700, Russ Paielli wrote: Araucaria Araucana araucaria.araucana-at-gmail.com |EMlist| wrote: Consider this case. Original true preferences: 27: AB 24: BA 49: C A is the Condorcet winner. Now consider what happens if B defects via truncation: 27: AB 24: B 49: C Under RP(wv), Beatpath(wv) or DMC, B wins. B voters have gotten a better result by dropping a lower preference. This is an example of the Later No Hurt violation of Condorcet completion methods -- B voters hurt their favorite by adding a lower-ranked preference. But if A puts the approval cutoff above B, B can't win in DMC: 27: AB 24: B 49: C C wins, anyway you cut it, as you found. There's no LNHurt situation here because B can't win either way. So the best the B voters can do is to add a preference for A. That's what I mean by the poison pill (by the A voters). Is it clear now? Ahhh...yes, now I see what you meant. As you pointed out, however, this particular situation is apparently no worse for DMC than it is for popular (on EM) Condorcet methods (or Approval). Are you saying that, with an approval cutoff (i.e., ranking allowed for unapproved candidates) that DMC actually has an advantage over those Condorcet methods? If so, then I am certainly willing to reconsider allowing an approval cutoff. Yes, I am saying that this is a major advantage for DMC. It has the same effect as ATLO, but does not require a recount. AWP has the same advantage. But AWP requires an extra pairwise array for the strong preference votes. You should actually try reading James' papers on CWP and AWP -- the extra AWP array is actually the same as DMC's with all above-cutoff votes and below-cutoff votes set to equal-rank. I actually think AWP would be an excellent proposal (say along the lines of Jobst's grand compromise). I just worry about the complexity of implementation. Note, however, that the added equipment requirement for an approval cutoff could delay the adoption for decades, but I won't get into that now. Or you could add an extra candidate to set the cutoff level. No new equipment. Let me just suggest another possible approach to the problem: auto-truncation. This idea is probably unoriginal, and it is also probably meritless, but let just throw it out there anyway as a long shot. This idea could be applicable to other methods too, but lets just consider DMC/RAV. Suppose we determine a tentative winner using the standard DMC rules. Now we suppress (tentatively eliminate) all the non-first-choice votes for that tentative winner, then determine a new winner. For all the voters who had the new winner ranked above the previous tentative winner, keep that previous winner suppressed, but for all who didn't, unsuppress (restore) the votes for the previous winner. Repeat until the process converges to a stable winner. Will this procedure always converge? If so, has it been proposed before, and is it equivalent to some other, perhaps simpler, method? Is this procedure summable? It sounds like it requires recounts. So a good DMC strategy is Rank all candidates you are willing to see elected, from your favorite to your hold-your-nose-and-swallow-just-barely-tolerated candidate. Why not just go all the way down? Who says they wouldn't? Most voters would equal rank the remaining candidates anyway. But consider (a) the Later-no-harm violation, and (b) time required to rank 150 candidates [extreme CA governor recall case]. Put your approval cutoff just below the candidate with the best shot at winning. (I think this is Forest's Approval voting criterion). Here, that means that the A voters cutoff below A. B voters, realizing this is the strategy, will add a lower preference for A. C voters, if they realize they're in the minority, might then decide to rank their preferred opposition alternative below the cutoff. If they despise A, they might actually vote for B in sufficient numbers to turn the election around. But you don't get this effect if you remove the approval cutoff. Those schemes might or might not be acceptable. I realize they seem very simple to you, but I think they may still be too complicated for major public elections. Also, I don't like the idea of requiring the voter to actually write a number. That's asking for trouble because the written number will sometimes be ambiguous. I find writing a number to be much faster than filling in an optical cell! I don't think optical cells are the answer either. What you want is a nice, simple touch-screen (or mouse based) system. And yes, of course you need to generate paper ballots too. Absentee ballots? I envision something like the Graphical Voter Interface (GVI http://ElectionMethods.org/GVI.htm) that I developed a while back Can't see the screenshots: Permission Denied The area you are trying to access has been closed off
[EM] Re: Be careful what you wish for
On 22 Apr 2005 at 19:46 UTC-0700, Russ Paielli wrote: Araucaria Araucana araucaria.araucana-at-gmail.com |EMlist| wrote: Well, that has a kernel of truth to it -- candidates are going to try to game the system, whatever it is. So whatever method you set up, it needs to have a certain unpredictable aspect to it, even (or especially) if it is deterministic, so voters will give up and simply state their true preferences. I don't think I can go along with that. If a little bit of randomness helps discourage strategy, then a lot of randomness will help even more. Why not just toss dice? The only effective strategy is to somehow load the dice. You're missing the point -- Consider a contentious election with no CW: 1) If winning votes are crucial in resolving cycles, it can lead to burying and compromise strategies. 2) If approval is the sole winning criterion (or there is a too-strong bias toward approval), it can lead to bullet approval. etc. I'm trying to warn about the law of unintended consequences. IMO, DMC does a good (maybe not the best) job of promoting generous approval cutoff and sincere ranked preferences. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: why ranking should be allowed for approved candidates only
On 20 Apr 2005 at 22:51 UTC-0700, Russ Paielli wrote: Ted, I'm still not getting it. Let me lay out my calculations more explicitly just to be sure I'm not making any silly mistakes. I'll use | to indicate the approval cutoff (I like to be different). snip Do you agree with these results? You're missing the point, which is, how does approval cutoff change the result? You would have seen what I meant if you had changed the cutoff to a simple ranking. I will summarize this well-discussed example for you. It is worth careful study. Consider this case. Original true preferences: 27: AB 24: BA 49: C A is the Condorcet winner. Now consider what happens if B defects via truncation: 27: AB 24: B 49: C Under RP(wv), Beatpath(wv) or DMC, B wins. B voters have gotten a better result by dropping a lower preference. This is an example of the Later No Hurt violation of Condorcet completion methods -- B voters hurt their favorite by adding a lower-ranked preference. But if A puts the approval cutoff above B, B can't win in DMC: 27: AB 24: B 49: C C wins, anyway you cut it, as you found. There's no LNHurt situation here because B can't win either way. So the best the B voters can do is to add a preference for A. That's what I mean by the poison pill (by the A voters). Is it clear now? So a good DMC strategy is Rank all candidates you are willing to see elected, from your favorite to your hold-your-nose-and-swallow-just-barely-tolerated candidate. Put your approval cutoff just below the candidate with the best shot at winning. (I think this is Forest's Approval voting criterion). Here, that means that the A voters cutoff below A. B voters, realizing this is the strategy, will add a lower preference for A. C voters, if they realize they're in the minority, might then decide to rank their preferred opposition alternative below the cutoff. If they despise A, they might actually vote for B in sufficient numbers to turn the election around. But you don't get this effect if you remove the approval cutoff. Those schemes might or might not be acceptable. I realize they seem very simple to you, but I think they may still be too complicated for major public elections. Also, I don't like the idea of requiring the voter to actually write a number. That's asking for trouble because the written number will sometimes be ambiguous. I find writing a number to be much faster than filling in an optical cell! I envision something like the Graphical Voter Interface (GVI http://ElectionMethods.org/GVI.htm) that I developed a while back Can't see the screenshots: Permission Denied The area you are trying to access has been closed off by the server administrator. just for kicks. It has a column of buttons, each about a half inch high by 3 inches wide, with a candidate's name and party on each one. You select them in order of preference by simply touching them on a touchscreen (or clicking on them with a mouse on a conventional monitor). You can always backtrack, of course. You can specify equal rankings by touching a selected candidate a second time (GVI doesn't currently allow that, but it could be added). Woowee. Screen takeover. Watch those colors and fonts! I'm not sure I find that more intuitive. Anyway, I favor paper ballot counting, period. Machines would be used only for assistance. What does your software do then? Remember that there is little or no time for training, so the interface needs to be as simple as possible -- especially for Democrats! 8^) No slurs, please ;-). Techno-illiterates come in all stripes. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: why ranking should be allowed for approved candidates only
Russ Paielli 6049awj02 at sneakemail.com writes: Araucaria Araucana araucaria.araucana-at-gmail.com |EMlist| wrote: On 17 Apr 2005 at 14:28 UTC-0700, Russ Paielli wrote: By only allowing the approved candidates to be approved, we can significantly simplify the procedure for both the voter *and* the equipment manufacturer. And we can do so at very little cost in terms of voting expressibility. If you are serious about actually getting a new voting system adopted, I urge you to reconsider allowing ranking of unapproved candidates. Hi Russ, The strategic ability to rank below the cutoff is what enables DMC/RAV to discourage defection cases like this: 27: AB 24: B (truncates A preference) 49: C Without that strategic disincentive, voters in this election might simply bullet vote and you end up with C. For the votes you show, I figure that DMC/RAV picks C. If ranking of unapproved candidates is disallowed and the 27 AB votes are changed to just A, then C still wins. If we start with your votes and change the 24 B votes to BA, then A wins. If we start with the AB votes changed to A, then change the B votes to BA, A wins. I must be missing your point. According to my tallies for the four variations mentioned above, it makes no difference whether the 27 AB votes are changed to A only or vice versa. It is true that if the 24 B votes are untruncated to BA, that gives the election to A. But so what? If A was the B voters *approved* second choice, they shouldn't be overly disappointed. What did I miss? C wins any which way because A voters put the approval cutoff above B to discourage defection. If B voters don't want C to win, they must not truncate to create a cycle. That is the anti-defection strategy (on A's part) I'm talking about. It's sort of like a poison pill. DMC/RAV is the simplest summable voting method to discourage this kind of defection. But it works ONLY with an approval cutoff. If the ballot has to be simplified, 3 approved + 2 disapproved ranks are pretty simple. This allows a voter to rank 3 choices as I don't care for ballots that have arbitrary restrictions on how many candidates can be approved or disapproved or arbitrary conventions about which candidates are approved or disapproved. I also think that such arrangements will inevitably lead to confusion. Granted, even if we only allow the approved candidates to be ranked, we will still have some confusion, but it just seems more natural and intuitive to me. Think of it as a generalization of Approval voting: you only select the approved candidates, except that now you can rank them too if you wish. By the way, if you don't wish to rank them you can make them all equal. Then your vote will have the same effect it would have in Approval. If you think Approval is a good method, how can you complain about that? I'm well aware that equal ranking is possible. I'm not satisfied with approval alone because it loses preference information. Just good enough is the enemy of the great. 1 2 3 1 2 4 1 4 5 to move up the approval cutoff. Or as grades, A B C A B F A D F I don't like grading schemes either. They just don't seem right to me for public elections. It isn't necessary to have limited ranks or fixed cutoffs at all. Say that OCR is used to read filled in ordinal ranks, with large boxes that the voter fills in with big numbers: +---+ +---+ +---+ | 0 | | 0 | | 1 | +---+ +---+ +---+ +---+ +---+ +---+ | 0 | | 0 | | 2 | +---+ +---+ +---+ +---+ +---+ +---+ | 0 | | 0 | | 3 | +---+ +---+ +---+ Just like the 1040EZ hand-written tax form (at least the version from a few years back. Add an extra Minimum Rank Approved candidate to each race, and you get the approval cutoff with no extra software -- just use the votes vs. MRA to fin the approval scores. If no vote for MRA are entered, all ranked choices are approved. Machine reading would be adequate for 95-99% of the ballots, the remainder could be entered by hand. Machine assisted ballots are also easy -- you could use a PDF form for the election that would be printed out and not saved. Only the paper ballot would be counted. -- monkeypuzzle Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Election-methods Digest, Vol 10, Issue 34
On 18 Apr 2005 at 22:04 UTC-0700, Russ Paielli wrote: While we're on the topic of murderous governments, I'd like to try a fun little quiz for anyone who cares to give it a try. The following paragraph expresses views remarkably similar to Mike's. Can you guess who wrote it and who he worked for? (I have cut a few giveaway words to make the game a bit more challenging.) --Russ We are socialists because we see the social question as a matter of necessity and justice for the very existence of a state for our people, not a question of cheap pity or insulting sentimentality. The worker has a claim to a living standard that corresponds to what he produces. We have no intention of begging for that right. Incorporating him in the state organism is not only a critical matter for him, but for the whole nation. The question is larger than the eight-hour day. It is a matter of forming a new state consciousness that includes every productive citizen. Since the political powers of the day are neither willing nor able to create such a situation, socialism must be fought for. It is a fighting slogan both inwardly and outwardly. It is aimed domestically at the bourgeois parties and [cut] at the same time, because both are sworn enemies of the coming workers' state. It is directed abroad at all powers that threaten our [cut] existence and thereby the possibility of the coming socialist [cut] state. Cheap trick, Russ ;-). http://www.calvin.edu/academic/cas/gpa/haken32.htm This turnaround thing has been done before. See Emmett Grogan's autobiography Ringolevio, for example (late in the book): http://www.amazon.com/exec/obidos/tg/detail/-/0806511680/103-9777613-3982217?v=glance But a good exercise in avoiding emotional appeals. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: why ranking should be allowed for approved candidates only
On 17 Apr 2005 at 14:28 UTC-0700, Russ Paielli wrote: I also suspect that ranking of unapproved candidates is likely to be very strategic anyway -- shedding little light on the true preferences of the voters. Voters are less likely to vote sincerely on candidates they dislike than candidates they like. I personally would probably just bury the unapproved candidate that I thought had the best chance of winning. Condorcet methods don't give a large advantage to burying, in general. Please think through your argument. By only allowing the approved candidates to be approved, we can significantly simplify the procedure for both the voter *and* the equipment manufacturer. And we can do so at very little cost in terms of voting expressibility. If you are serious about actually getting a new voting system adopted, I urge you to reconsider allowing ranking of unapproved candidates. Hi Russ, The strategic ability to rank below the cutoff is what enables DMC/RAV to discourage defection cases like this: 27: AB 24: B (truncates A preference) 49: C Without that strategic disincentive, voters in this election might simply bullet vote and you end up with C. If the ballot has to be simplified, 3 approved + 2 disapproved ranks are pretty simple. This allows a voter to rank 3 choices as 1 2 3 1 2 4 1 4 5 to move up the approval cutoff. Or as grades, A B C A B F A D F I would be happier with a 3-choice ballot (approval implied) than the current single-vote, but I worry about creating a system that regresses to the status quo. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: More thoughts on approval margins
On 15 Apr 2005 at 16:03 UTC-0700, Monkey Puzzle wrote: I think I'm getting the sieve idea into better focus now. Is the following method is equivalent to Approval Sorted Margins? Ranked ballots with approval cutoff. Strong defeat = pairwise defeat by higher-approved candidate Strong losers = set of all strongly defeated candidates Provisional set = set of non-strongly-defeated candidates Each provisional winner defeats all higher-approved members of the set. This is Forest's P set. Convenient that Provisional starts with P, isn't it? ;-) New definition: Clear upward defeat of X by Y: Y has lower approval than X, but pairwise defeats X and is not defeated by any other candidate with approval in between theirs. Marginal defeat: Pairwise defeat of provisional candidate X by strong loser Y under these conditions: (1)Z = the least-approved provisional winner who strongly defeats Y. (2) Approval(X) - Approval(Y) Approval(Z) - Approval(X) TODO: Need a more succinct description of this. Revised definition of marginal defeat: (1) Y has a clear upward defeat over X (2) Z defeats Y and is the least-approved candidate with greater approval than X. (3) Approval(X)-Approval(Y) Approval(Z)-Approval(X) The last part of the definition is the definition of secondary defeat strength. Here I use approval margin, but any measure, such as winning votes, AWP's strong preference votes, etc., could be used. Marginal losers = set of all marginally defeated candidates Strong set = set of candidates neither strongly nor marginally defeated. The least-approved member of the strong set defeats all higher-approved strong candidates and wins the election. The approval winner and the highest-approved member of the Smith set are always strong candidates. I think a good name for this method would be Marginal Ranked Approval Voting (MRAV). I've created a page for it here: http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting One interpretation of the marginal defeat is that a marginal loser doesn't have enough approval buoyancy to rise above the strong-defeated candidates, and is peeled off of the edge of the provisional set. Strategy should be similar to Approval Margins and identical in 3-candidate cases. The MRAV strong set could be used for a DFC-like random ballot method. Suggestions? Discussion? -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: AWP versus DMC and AM
James et al., You may find the revisions on http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting to be of interest. If you don't see the changes, refresh your browser -- you may also have to empty your browser cache. James, try MRAV using strong preference as the secondary defeat strength on some examples, and tell me if you get a result different from what you would expect. Forest, Chris, I think that with the revised definitions the method is now correctly equivalent to Approval Sorted Margins [aka PSA-Min(AM)]. Note that in the example I give, the DMC winner, Brad, is found on practically the first step. Well, I'm not counting the matrix reordering. But determining whether Brad is marginally defeated takes many additional steps. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] IRV bill on Washington State Governor's desk
http://www.komotv.com/stories/36271.htm http://www.oregonlive.com/metronorth/oregonian/index.ssf?/base/metro_north_news/1113472928308700.xml Note the last line of the 2nd link. The reporter ended with the comment that single-vote is easier to count. That seems to be the anti-IRV establishment line. I don't know the specifics of the bill. It apparently sets up a 5 year study by the office of the sec'y of state on alternative voting methods in local elections. IRV currently has more publicity, but if other voting systems are allowed, this could be an opportunity for a Condorcet-based method. The web page for the state rep sponsoring the bill is http://www1.leg.wa.gov/house/moeller and an email link is provided. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Letter to author of voting system article
On 13 Apr 2005 at 20:20 UTC-0700, Paul Kislanko wrote: Mike, I mean no offense, but if you didn't know to whom you were writing a letter, why do think it's important for voters to know strategies and such when considering which voting methods to employ? C'mon. If you cared enough to cc the list, either you were cc'ing the list or making something up. I think the problem here is that Mike may not work from a single computer and does not know how to record his bookmarks remotely. He also doesn't read the election-methods list as mail -- he replies to things he reads from the archives. That's why none of his replies are threaded. But that doesn't explain why he can't find his sent email -- even free web email has a 'sent-mail' folder. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: RAV/DMC
Hi Kevin, Interesting post, see inserted comments below. On 10 Apr 2005 at 22:42 UTC-0700, Kevin Venzke wrote: Dear Jobst, --- Jobst Heitzig [EMAIL PROTECTED] wrote: You also wrote: Of course RAV just substitutes an approval measure for WV or Margins. It's unchanged, that increasing the strength of one candidate's wins can cancel another candidate's wins. That is also a strange interpretation. Of course, as some of us including me realized or proved, DMC/RAV is *logically equivalent* to a number of well-known defeat dropping methods when defeat strength is defined in a certain way. But defeat strengths are not at all the idea of neither RAV or DMC, and those methods don't cancel any wins. I don't agree that this is a strange interpretation, or that defeat strength is not the idea of RAV. When I (re)proposed this method in November, you and I spoke primarily in terms of defeat strength, and already in my initial message I noted the method was the same as electing the least-approved candidate who beats everyone with greater approval: http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-November/014115.html Excellent! Yes, that appears to be the first observation. I should add a link to this post into the DMC page when I get the time, or you can do so if you like. I'm interested in other parts of the message though -- you stated there that you had a special technique for avoiding having to fill in 25 votes in the ABCDEFGHIJKLMNOPQRSTUVWXYZ case, but I didn't see how your 2004-11-04 message explained that. Maybe I'm just dense or preoccupied. It seems to me that you were quite critical of RAV/DMC and I still don't know why you changed your mind: http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-November/014127.html http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-November/014148.html You wrote: Then you came up with the topic of how to measure defeat strength best without having to count all winning votes, and suggested to use approval scores. I pointed out that when using approval of A to measure the strength of AB, you count some people towards that strength who actually prefer B to A, and that this possibility will be counter-productive when trying to convince people to go voting. I guess you and Russ think that if we interpret away defeat strengths, then this problem disappears?? Kevin Venzke My interpretation of why Jobst 'changed his mind' was that Forest's reinterpretation of RAV was much more persuasive than any other previous explanation, including your one-line summary. And since Jobst is more interested in counter-strategy measures using random ballots, he is looking not only for a winner but a set of near winners. Forest's P (aka Definite Majority) set is simple to define and calculate and satisfies Jobst's criteria of including the Approval Winner and some set of highly-approved candidates. And yes, interpreting away defeat strengths (and the resulting simplicity of the explanation) is what makes the method attractive as an initial public proposal. But the reinterpretation is also what exposes the P set. Possibly the Sieve of Eratosthenes-like nature of the P set is what appeals to mathematically-minded folks like us. (for non-math-geeks: http://ccins.camosun.bc.ca/~jbritton/jberatosthenes.htm) Note that Forest's Approval Seeded Bubble Sort proposal (in my terminology, Pairwise Sorted Approval) from early 2001 also finds the same winner as RAV, and also has some set of candidates, Q, that are ranked higher than the AW. But Q may contain a cycle, and P does not. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Ballot Design
On 8 Apr 2005 at 08:38 UTC-0700, Lloyd Caesar wrote: This may be a bit off topic. It's about art not science. How should an STV ballot be designed for ease of use and ease of counting. (For the rules, let's say, paper ballots, computer count, manual recount if necessary) A simple list of names with spaces next to them forwriting in a number is clear for voters but difficult for poll-workers who can't use a computer for the count(without foolproof OCR) and have to decipher handwriting. Names with numbered circles to fill in (SAT style) reqquire as many numbers as there are candidates, possibly a huge number in say a multi-party 9-seat (about the largest practical) election. Furthermore, voters can lose track of the numbers as they move around the ballot and accidentally spoil their ballots. What might work? any ideas? Hi Lloyd, How about an abacus-like approach? 500 50 5 ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) 100 200 300 400 10 20 30 40 1 2 3 4 Here's how you might represent various numbers: 3: 500 50 5 ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) (X) ( ) 100 200 300 400 10 20 30 40 1 2 3 4 7: 500 50 5 ( ) ( )(X) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) (X) ( ) ( ) 100 200 300 400 10 20 30 40 1 2 3 4 62: 500 50 5 ( ) (X)( ) ( ) ( ) ( ) ( ) (X) ( ) ( ) ( )( ) (X) ( ) ( ) 100 200 300 400 10 20 30 40 1 2 3 4 489: 500 50 5 ( ) (X)(X) ( ) ( ) ( ) (X) ( ) ( ) (X) ( )( ) ( ) ( ) (X) 100 200 300 400 10 20 30 40 1 2 3 4 -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice
On 5 Apr 2005 at 23:51 UTC-0700, Russ Paielli wrote: Araucaria Araucana araucaria.araucana-at-gmail.com |EMlist| wrote: I happen to think that DMC is the simplest-to-grasp version of all three methods. Here is one way to find the winner: Eliminate any candidate defeated by another candidate with higher total approval. Among the remaining candidates, the candidate with the lowest approval defeats all others and is the DMC winner. I was just thinking about this procedure some more, and I came up with a simple way to visualize the procedure (for simple-minded folks like me). Order the pairwise matrix with Approval scores decreasing (or non-increasing) on the diagonal, as usual. Then color the winning cells of the pairwise matrix black and the losing cells white. The winner is then the candidate who has a solid black row all the way from the left column to the diagonal. If I am not mistaken, no more than one candidate can have that, barring ties. Sorry, you are mistaken -- that is not a unique characteristic. If no candidate has it, then the Approval winner is also the CW and takes the enchilada. Color the diagonal as a winning cell and you don't have to have a special case rule. The RAV procedure can be visualized exactly the same way, thus demonstrating that DMC and RAV are equivalent, if I am not mistaken. That's what I said! They are equivalent since they find the same winner. But the CW concept is a big leap. The procedure can be automatic without mentioning the Smith set or Condorcet winner. If you will allow to modify the visualization slightly: - Reorder the pairwise array as you specify above. - Instead of black and white, I'd suggest highlighting winning (and approval!) scores, rather than blacking them out and obscuring their values! With a yellow highlighter pen, you look for a solid yellow row up to (and including) the diagonal. Here is the crucial difference: - You need to start checking left-side to diagonal cells starting with the last (least-approved) candidate, and work up the diagonal until you find the first candidate with a solid row of wins to the left of the diagonal. For DMC, I would first travel down the diagonal from the upper left, looking for defeats to the right of the diagonal. Then I would draw lines (strike out) through the rows and columns of those correspondingly defeated candidates to indicate that they have been eliminated, and move to the next diagonal cell (even if it has been eliminated). You can stop once there are no more non-eliminated candidates with lower approval. Once all lower-approved candidates have been eliminated, move back up the diagonal again until you find the lowest-approved non-eliminated candidate. The higher-approved remaining candidates are the other members of the definite majority set. Each of them will also have a solid row of wins from the diagonal to the left side. Re your other message about the name: Ranked Approval Voting is fairly descriptive and probably as good as any other choice, but it is just as fuzzy as IRV's Ranked Choice Ballot -- it describes the ballot method and only hints at how they're tallied. It also implies that Approval Voting is the primary characteristic of the method and that the ranking is a slight modification, when what we're doing is actually the opposite. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice
On 4 Apr 2005 at 23:39 UTC-0700, Russ Paielli wrote: I was just looking at the wiki page for DMC: http://wiki.electorama.com/wiki/Definite_Majority_Choice I saw this statement: DMC chooses the same winner as (and could be considered equivalent in most respects to) Ranked Approval Voting (RAV) (also known as Approval Ranked Concorcet), and Pairwise Sorted Approval (PSA). Do we know for sure that DMC always chooses the same winner as RAV and PSA? If so, then in what respects are they *not* equivalent? Before commenting on a wiki page, please note that you might have to purge your browser's cache and reload the page to get the latest version. I've run into this problem recently myself. The excerpt you cite is due to my suffering from the same affliction as old what's-his-name, uh, John Kerry: I can't resist inserting every possible mathematical qualification into what I'm describing. I should probably take out the first parenthetic remark, as it serves no purpose. I may have done so by the time you refresh your browser, in fact. DMC, RAV and PSA are all equivalent in the sense that they choose the same winner. Period. This is the same kind of equivalence as CSSD being equivalent to Beatpath. The way that they are not equivalent is that they don't follow exactly the same path to get to that winner. I happen to think that DMC is the simplest-to-grasp version of all three methods. Here is one way to find the winner: Eliminate any candidate defeated by another candidate with higher total approval. Among the remaining candidates, the candidate with the lowest approval defeats all others and is the DMC winner. Everyone is familiar with the idea of most or least points, so a voter looking at the pairwise array could find the winner in a few seconds, by inspection. No mention of Smith sets, no ranked pairs, no fancy algorithms, clean and simple. If these methods are equivalent, then I think we need to eventually try to somehow agree on a common name for public promotion. We might also be wise to agree on the simplest explanation, with the more complicated explanations used as backup material for those who are intellectually curious. Yes, of course. But see above -- can you get simpler than that? The actual name and acronym may be critical to the public salability 'marketability' might be the word you're after. of the method, so we need to be very careful in selecting it. We shouldn't rush into it. Definite Majority Choice seems too generic and not descriptive enough to me, but I am not necessarily opposed to it. I like RAV (which I proposed myself), but I don't consider it an ideal name either. In any case, we must avoid at all cost using the word dropping in the name (it sounds too much like something birds do). Well, Condorcet was called 'true majority rule' in the March 2004 Scientific American article. The DMC winner is chosen from candidates remaining after eliminating definitively defeated candidates. So if you want to quibble, Definitive Majority Choice might be more accurate. But I think we want to avoid having more than one 4-syllable word in the name ;-). Yes, the name can be important. But you have to watch out for the initials also. For example, I was thinking of something called Pairwise Ordered Sorting a while back and realized POS would be an unfortunate acronym. One of these days I should crank out a list of possible names/acronyms of this method for discussion and perhaps an eventual vote. If you don't mind, I would recommend focusing your efforts on understanding the method first. Compare especially to PSA and Approval Sorted Margins. I think Approval Sorted Margins is the best alternative to DMC from an anti-strategic standpoint. Note that no change would be required in the ballot to switch from DMC to ASM, and it uses the same pairwise array with total approval on the diagonal. I have yet to see a case in which ASM gives a different result than James' AWP or Chris Benham's AM. I would prefer to see ASM reduced to a much more concise form before considering it as a first public proposal, but it could be proposed as a more secure alternative after the DMC ballot is adopted. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Equivalent defeat strength for Approval Sorted Margins / Approval Margins
On 5 Apr 2005 at 11:12 UTC-0700, Forest Simmons wrote: Ted, I've been working on that, but the answer is not yet clear. Part of the problem is that only pairs that are currently adjacent in the list are considered for swapping (the equivalent of firming up the defeat ). So if at some time the current list order is ABCDEF, and (A,B) is the out-of-order adjacent pair with the smallest approval difference (a-b), while the approval difference (b-d) is even smaller, the BA defeat would be set in stone before (or ultimately instead of?) the DB defeat. Whether this ultimately causes a problem, I do not know. Forest You're right, Ranked Pairs with defeat strength in increasing order of approval margin would not be equivalent. We've got to get the total approval ordering in there somehow. Are you familiar with Minimum Degree reordering? It's a sparse direct solver (AKA Gaussian elimination) method, intended to reduce matrix fill-in. ASM is somehow reminiscent. Here's one reference: http://www.mathworks.com/access/helpdesk/help/techdoc/math/sparse17.html I should note that MD is neither the sparsest or most stable LU decomposition method. Most commercial sparse solvers use METIS instead: http://www-users.cs.umn.edu/~karypis/metis/metis/ Of course we're not interested in fill-in here -- the pairwise array with defeated scores set to zer always has density (N+1)/(2N), not sparse at all. But in some sense we're also looking for the most stable reordering, with no zeroes on the upper off-diagonal. -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
Summary of discussion: Ted (AKA Araucaria) things AWP could do a better job of resisting strategic manipulation in some cases, but doesn't think it is as easy to explain to the public. James things they are equally difficult to explain and that relative merit should rule the discussion. I think we are two different planes that can never intersect. But all of my posts thus far have been directed toward finding a strong public proposal, so I can't let the methods stand on their technical merits alone. So James, before you try to once again push CWP and AWP on technical grounds, answer this: I can explain DMC in three simple sentences: Eliminate any candidate defeated by any other higher-approved candidate. The remaining candidates form what we call the Definite Majority Set. The winner is the single undefeated candidate in the Definite Majority Set. This is, IMO, simple and comprehensible to most people, though they may argue the benefit of such a procedure and may worry (possibly with just cause) about its vulnerability to manipulation. Before replying once again with the same restatement of your opinions, could you address these points? - Approval Sorted Margins (AKA Approval Margins Sort?) appears to pick the same winner as Approval Margins or Approval-weighted Pairwise, at least in the examples given by you and Chris Benham. But it has, IMO, a simpler implementation. Could you examine that method in comparison to AWP? http://wiki.electorama.com/wiki/Approval_Sorted_Margins (to digress slightly, I think the name Pairwise Sorted Approval by Minimum Margin or something of that sort might be more descriptive). Just to be clear on why I think ASM might be marginally more feasible but not AWP or CWP: it's the extra pairwise array. Do I have to explain further? Chris Benham's Approval Margins proposal doesn't have an extra pairwise array, but I have yet to see an easy explanation for it. - The Definite Majority Set has a nice ring to it. It gives a favorable standing to non-winning members of that set, which always includes the Approval Winner. The AWP Smith Set won't always contain the Approval Winner. Can you find some alternate definition of the AWP winner that allows higher approved candidates (including the Approval Winner) to 'lose with honor'? - James, I read your paper on CWP, about 6 months ago. I appreciate that you put a lot of work into them. But their technical nature and PDF format render them somewhat inaccessible to even election-methods list members. I think your technical ideas have great merit, but you still need to sell me on implementation. Why not try putting together an electowiki page. If you're going to promote CWP, then design a ballot to go with the page. And then discuss examples. You can always link in your articles as External Links. The worst that might happen is that others could clarify your ideas. ;-) -- Araucaria On 2 Apr 2005 at 19:20 UTC-0800, James Green-Armytage wrote: James G-A replying to Ted, on the subject of AWP and DMC... I agree that AWP (have you decided to pick between RP, Beatpath or River?) No, I haven't chosen, nor do I feel the need to choose. I consider all three of these base methods to be very good, and I see no particular reason to limit the definition of CWP or AWP by choosing one over the other. does a better job in this particular case, and all else being equal, I would be happy with an AWP proposal. But all things are not equal. How do you explain to your 80 year old auntie about ordering the defeats, or that RP sometimes gets a different result than Beatpath or River? If you can show that AWP always causes the 3 strong pair-ranking methods to get the same answer, I would be convinced. This doesn't make sense to me. Are you saying for example that people will look askance at beatpath if they know ranked pairs to be equally good, and that they will look askance at ranked pairs if they know beatpath to be equally good? I doubt it. I think that all three methods are about equally good. If we pick beatpath, people who like ranked pairs are likely to be happy, and vice versa. Also, if the proposal is based on ranked pairs, and I am trying to explain the method to someone who is not comfortable with complex voting theory, I have no need to explain beatpath and river to them. All I have to do is explain ranked pairs. Until then, I think DMC or some variant is the Condorcet method with best chance of public acceptance. That's your opinion. My opinion is that if DMC and AWP are roughly equal in explainability, and that any method that combines some other ballot with a ranking ballot will be more difficult from a superficial standpoint than a method like sequential dropping (wv). Hence, if such superficial considerations are intense, both DMC and AWP are likely to be beyond reach. If the public is open to
[EM] Re: summary answers
On 4 Apr 2005 at 06:08 UTC-0700, Jobst Heitzig wrote: Dear Curt! You wrote: 1) Are there cases where you would consider a candidate outside the Schwartz set to be the proper winner? 2) Are there cases where you would consider a candidate outside the Smith set to be the proper winner? Yes, definitely: When x,y,zn/2, then in the sincere situation x ADBC y BDCA z CDAB the winner should be one of A,B,C, with probability x/n, y/n, z/n, respectively, since D is not approved by anyone. DFC (Democratic Fair Choice) gives this result! [Later corrected to allow a small probability for D] Hi Jobst, I don't see anything wrong with choosing a 100% central candidate with 0% approval. In fact, I think it is the most desirable outcome in your example. But then, I'm from the school of thought that when there is no popular consensus on how to govern, it's better for the government to be as weak as possible. ;-) Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
On 30 Mar 2005 at 06:51 UTC-0800, Chris Benham wrote: Jobst, You wrote (Thur.Mar.24): First, I'd like to emphasize that DMC, AWP, and AM can be thought of as being essentially the same method with only different definition of defeat strength, so it seems quite natural to compare them in detail as you started. Recall that the DMC winner is the unique immune candidate when defeat strength is defined as the approval of the defeating candidate, so with that definition, Beatpath, RP, and River become equivalent to DMC. Chris Jobst: Please take careful note -- the DMC defeat strength assertion has not been proved rigorously, to my knowledge! It is worth a very careful look before basing any other assumptions on it. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: DMC,AWP,AM
On 30 Mar 2005 at 10:51 UTC-0800, Forest Simmons wrote: Chris, I wonder if the following Approval Margins Sort (AMS) is equivalent to your Approval Margins method: 1. List the alternatives in order of approval with highest approval at the top of the list. 2. While any adjacent pair of alternatives is out of order pairwise ... among all such pairs swap the members of the pair that differ the least in approval. Hi Forest, I started an electowiki page for you to work on: http://wiki.electorama.com/wiki/Pairwise_Sorted_Methods Feel free to elaborate in your ample free time ;-) Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
On 26 Mar 2005 at 04:05 UTC-0800, James Green-Armytage wrote: Hi Juho, Some replies follow, on the subject of voter strategy and approval-weighted pairwise. These comments should also be helpful for others who don't understand why I consider AWP to be clearly better than DMC and AM. [... arguments ...] 3 candidates: Kerry, Dean, and Bush. 100 voters. Sincere preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 25: BKD 23: BDK Kerry is a Condorcet winner. Altered preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 21: BKD 23: BDK 4: BDK (these are sincerely BKD) There is a cycle now, KBDK I agree that AWP (have you decided to pick between RP, Beatpath or River?) does a better job in this particular case, and all else being equal, I would be happy with an AWP proposal. But all things are not equal. How do you explain to your 80 year old auntie about ordering the defeats, or that RP sometimes gets a different result than Beatpath or River? If you can show that AWP always causes the 3 strong pair-ranking methods to get the same answer, I would be convinced. Until then, I think DMC or some variant is the Condorcet method with best chance of public acceptance. In any case, my general comment about strategy not existing in a vacuum still applies here: though Bush does win under DMC using your proposed strategy, it is very risky. What if 3 of the 5 DKB voters move their cutoff below K? Yes, they would be compromising, but in approval and not in rank. B voters attempting to game DMC are gambling on how important that approval cutoff decision will be, and could end up with a Dean victory for their efforts. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
Hi Chris, Nice example. But there is still a counter-strategic incentive under DMC -- see below. On 24 Mar 2005 at 08:11 UTC-0800, Chris Benham wrote: Suppose there is pre-polling and so the L supporters decide to approve C, while the C supporters sincerely divide their approvals. Further suppose that the R supporters all decide to completely Bury C. Then we might get: 49 RLC 06 CRL 06 CRL 06 CLR 06 CLR 27 LCR Now all the candidates are in the top cycle: LCRL. The approval scores are L82, R55, C51. Approval Margins: LC 82-51 = +31 CR 51-55 = -4 RL 55-82 = -27 AM elects L, backfiring on the Buriers! Unfortunately this time DMC eliminates C, and then the Buriers' candidate R wins. Approval-Weighted Pairwise: LC 49 CR 45 RL 06 AWP gives the same good result as AM! Yes, with perfect polling knowledge, the R strategy might work. But Rock/Paper/Scissors strategy like this doesn't occur in a vacuum. If R voters are coordinated enough to bury C in both approval and rank, they have to operate on the assumption that CRL voters might also suspect something and might all disapprove R instead of splitting. Without CRL's 6 approval votes, R would be eliminated by the definitive CR defeat. R's ordinal-burial of C would backfire and elect L. If I were an R voter, that would be the *last* thing I'd want! Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Some hard example for Approval Voting
On 22 Mar 2005 at 14:04 UTC-0800, Rob LeGrand wrote: Jobst wrote: Unfortunately, I get the impression that in the following example there is no such equilibrium: 3 DCAB 3 DABC 5 ABCD 4 CBDA So, can anybody forecast what will happen with these preferences under Approval Voting?? Interesting example. Bucklin gives B, IRV gives D, Borda gives A and most methods popular here (beatpath, River, Ranked Pairs) give C. There is no Condorcet winner, so there is no Approval equilibrium; any leader will be quickly toppled if everyone uses strategy A (which is always sincere in the sense you give above). Strategy A allows individual voters to move the current result in the most advantageous direction with no notion of being part of a new majority coalition; new coalitions emerge naturally from the smart strategic moves. Declared Strategy Voting in ballot-by- ballot mode running for many rounds using Approval and strategy A elects them with approximate probabilities A 25.05%, B 12.99%, C 27.54% and D 34.42%. It is indeed an interesting example. Consider Definite Majority Choice (DMC, aka Ranked Approval Voting) as an alternative: All Approval cutoffs at 1st place: Approval order D,A,C (B=0). == D wins. All Approval cutoffs at 2nd place: Approval order B,A,C,D. == A wins. All Approval cutoff at 3rd place: Approval order C=B, A, D. == A wins. Rob's voting calculator page shows that it isn't just Borda that gives an A win, it's Borda, Bucklin, Copeland, Nanson, and many others. I think this reflects the effect of the Approval (cumulative higher ranking) bias in DMC. Plurality and IRV (and wv RP/Beatpath/River) would have picked a winner with less than 50% approval -- in fact the (sincerely) least-approved of all candidates. Under DMC, the only voting block that could win by bullet-approval cutoff is the 3:DABC group. But if any other block uses a more generous cutoff, A will win (or possibly C in one or two cases). So there is no clear advantage for DABC to bullet-approve. Just the opposite, in fact. With sincere approval cutoff at 2nd place, the set P (candidates not defeated by any higher-approved opponent) contains A and B. A wins with a solid 114 victory over B, but with weak approval -- barely over 50%. But overall, B loses quite respectably with higher approval. B's faction could win the next election by winning over 4 of the 11 AB voters (26.7% of the electorate). And in the meantime, A will be working *very* hard to avoid that reversal. A centrist winner who pays attention to issues of concern to many. Isn't that the outcome we're striving for here? Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: ruminations on ordinal and cardinal information
On 21 Mar 2005 at 18:46 PST, Russ Paielli wrote: My first comment is that this proposal is significantly more complicated than my (or Kevin's) Ranked Approval Voting (RAV) proposal, which simply drops the least approved candidate until a CW is found. Russ, could you please clarify this? I was under the impression that RAV was the following: Do While # of candidates 1 # Iterate to find the Smith set: While there is a candidate with no wins, eliminate the candidate End While # eliminate least approved candidates until a CW is found If number candidates is 1, delete least-approved candidate End Do In other words, you reduce to the Smith Set, then eliminate the least-approved candidate. If you simply eliminate the least approved candidate without first iterating to the Smith Set, you might delete a Condorcet Winner. Could you or Kevin fill in the appropriate Electowiki page with your sense of what RAV is supposed to be? http://wiki.electorama.com/wiki/index.php?title=Ranked_Approval_Votingaction=edit Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Washington State IRV initiative text
Here is the text for the Washington State IRV initiative that failed to get onto last November's ballot. Note that the text is somewhat long and complicated, since it has to include IRV implementation details. I suspect that is why they didn't get enough signatures -- voters here tend to distrust long initiatives, whatever simplistic promotional claims are made in the preamble: http://www.secstate.wa.gov/elections/initiatives/text/i318.pdf This could actually be an excellent opportunity for a Condorcet proposal (e.g. DMC). If the both the summary and the actual method can be described more concisely than IRV, the proposal might be more likely to get onto the ballot. For an interesting comparison, see a proposal from Florida. Perhaps the Florida state constitution isn't as stringent about initiative format: http://election.dos.state.fl.us/initiatives/fulltext/38572-1.htm Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: ruminations on ordinal and cardinal information
On 20 Mar 2005 at 01:38 PST, Jobst Heitzig wrote: Dear Russ! I completely agree with what you wrote! Just like you, I think that [Russ Paielli wrote earlier:] an ideal election method must integrate both ordinal and cardinal information, and the cardinal information should be simple approval (yes/no for each candidate). I would even go so far to claim that the ideal election should also give special relevance to a third kind of information: direct support. For example by using Random Ballot to choose from a small set of most acceptable candidates such as Forest's P. Or, a new idea, if you find randomization inacceptable, by electing the member of P with the most direct support! Yours, Jobst Hi Jobst, To summarize: the approval-augmented method on the table is ranked ballots plus approval cutoff (by whatever means), then eliminating Approval-consistent defeated candidates (see http://wiki.electorama.com/wiki/Techniques_of_method_design#Defeats_and_defeat_strength for Jobst's definitions of defeat strength). The set of candidates remaining is denoted as P. Those advocating a deterministic method (Direct Majority Choice) propose picking the pairwise winner from P. This is Condorcet and Smith-efficient. Since you (and Forest) feel that picking the least-approved member of P is counterintuitive, you're proposing picking the winner from P based on either Random Ballot or maximum Direct Support. I disagree. First point: High Approval score indicates broad consent that the candidate is minimally acceptable. But it doesn't indicate highest preference. The main effect of Approval in DMC is to use it to discount the pairwise defeats of candidates with less widespread support. But it is still possible for a minority block of voters to express lesser-of-evil preference among candidates approved by the majority. This helps avoid the polarizing potential of IRV picking the 'core support among the majority' winner (IRVists' secret agenda?). Approval Cutoff also has an effect similar to AERLO/ATLO, which we should also consider strongly desirable -- we want to encourage voters to express a preference between approved candidates without fear of hurting on or the other. If you end up ignoring that preference, you're no better off than with straight Approval. Second point: In the USA, at least, it may be more desirable for the pairwise winner to have lower approval. This seems paradoxical, but it tends to keep the winner from making overly radical changes. The US founders distrusted government enough that they put in checks and balances to make the process *less* efficient. Thirdly, choosing the Direct Support winner from P will tend to discourage a more generous approval cutoff and encourage bullet cutoffs. You're right back with something little better than Plurality again. Consider your DMC tie problem: 1 ABC 1 BCA 1 CAB 3 A=B=C This means the electorate is polarized three ways: http://wiki.electorama.com/wiki/Voting_paradox With DMC, however, a fourth candidate will see the opportunity and step in to fill the center -- if not in that election, then in a future one: 1 ADBC 1 BDCA 1 CDAB 3 A=B=C=D One of the goals of a new voting system is that we want to give the best candidates an opportunity to win without being eliminated in runoffs. In this case, D would lose the approval and direct support races, but would be the best compromise candidate wherever the cutoff line is placed. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: ruminations on ordinal and cardinal information
On 21 Mar 2005 at 12:52 PST, Jobst Heitzig wrote: Second point: In the USA, at least, it may be more desirable for the pairwise winner to have lower approval. This seems paradoxical, but it tends to keep the winner from making overly radical changes. Sorry, but I think some radical changes in the US are just what the US (and the world) need :-) Beware of starting fires. You never know which way the wind will blow. If I may point out, Bush believes he received majority support and is spending his political capital. If 90% of the US voting population had voted, instead of something in the 60's, Bush would have no 'majority' approval (if even elected!), and might correspondingly be a bit more cautious and conciliatory in his agenda. The one-third of the US electorate that doesn't vote is sitting there (partly) because the two other parties avoid substantive issues, but can't be dislodged under the current system. The US founders distrusted government enough that they put in checks and balances to make the process *less* efficient. There is something similar in Germany: the federal government often depends on the agreement of a majority of the federal states' representatives, and this often leads to nothing happening at all... Inaction is not always bad, especially when a behemoth like the US is moving around. But a Condorcet winner won't necessarily be the blandest candidate. In fact, I would expect the Approval Winner to be even less controversial or confrontational. Central support can actually lead to more action, not less. A centrist agenda can appeal to all sides for support, not just the majority coalition. In times of clear need and the right candidate to lead in that direction, I would expect the Approval Winner to be the Condorcet Winner. But now the main point: Consider your DMC tie problem: 1 ABC 1 BCA 1 CAB 3 A=B=C With DMC, however, a fourth candidate will see the opportunity and step in to fill the center -- if not in that election, then in a future one: 1 ADBC 1 BDCA 1 CDAB 3 A=B=C=D Well, thank you for giving this example. Since it shows perfectly why I think that the Condorcet Winner (in this case D) is sometimes NOT a good choice at all! Most probably this D is just someone who has no program and says nothing but empty phrases which oppose noone. I at least don't think D should be elected here since s/he has too few approval and/or direct support! This is a good demonstration of Arrow's theorem ;-). But it is not necessarily true that D would do nothing or have no program. If that were the case, no block would cast a near-top compromise vote for D. I'm just saying that *this* worst case (no above-cutoff support for D) results in 50% approval for D. There's no reason (with more than 6 voters) why D might not actually garner more approval, potentially 100%. But to get strong compromise-candidate support, D has to have a centrist platform. The center is not a vacuum. Maybe I'm just being optimistic, but I don't think you can get into the center with empty phrases. You actually have to stand for something, more like 'moderation in all things, all things in moderation'. Then if you don't waste time bickering on the extremes, you can actually accomplish more of substance. In any case, we're probably rehashing Approval vs. Condorcet arguments that go back many years on this list. I'm just trying to look beyond a single election case. Somebody always loses a single-winner race, so if you want good candidates to run, it behooves you to give the runners-up a chance to look as good as possible. By choosing the pairwise winner from set P, losing candidates in that set (assuming a close race) still look pretty darn good. All they have to do to win the next time is move up one or two ranks. And to do that they have to broaden their appeal. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Definite Majority Choice, first round public proposal (draft)
Below is a draft of a first round proposal for a single general-election voting method replacement. Comments humbly requested. Could the explanation be made any clearer? As discussed previously, Definite Majority Choice (hat-tip to Forest for the name) is just another name for Ranked Approval Voting (RAV), Approval Runoff Condorcet (ARC), and finds the same winner as Pairwise Sorted Approval. I believe that it finds the same winner as both Ranked Pairs and Beatpath when defeat strength is measured by the Approval of the pairwise winner. Among non-eliminated candidates, there are no pairwise cycles, thus removing the biggest objection of IRV advocates to Condorcet methods. Note that Pairwise Sorting on a previously seeded ordering is also known as Local Kemenization and is used in Rank Aggregation methods -- see, e.g., http://www10.org/cdrom/papers/577/. So if all else fails, you could say that DMC finds the Google winner! Credits: Forest Simmons, Jobst Heitzig, Russ Paielli, Chris Benham, Kevin Venzke, and of course Steve Eppley, Markus Schulze and Mike Ossipoff. Anybody else I should cite? Who first proposed Graded Ballots? Adam Tarr? -- Ted ,[ definite-majority-choice-graded-ballot ] | Definite Majority Choice: | | Voters can grade their choices from favorite (A) to least preferred | (ungraded), and give some or all of their graded choices a passing | grade, signifying approval. | | Ranked ballots are added into a Round-Robin array, and the approval | scores of each candidate are also tabulated. | | To determine the winner, | | - Eliminate any candidate that is defeated in a one-to-one match | with any other higher-approved candidate. So by 2 different | measures, a definite majority agrees that candidate should be | eliminated. | | - If more than one candidate remains, the winner is the single | candidate that defeats all others in one-to-one (pairwise) | contests. | | How to vote: | | Graded ballot: | | ABCDEFG | | X1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) | | X2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) | | X3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) | | X3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) | |Lowest ( ) ( ) ( ) ( ) ( ) ( ) ( ) |Passing |Grade |(optional) | | You can give the same grade to more than one candidate. By default, | each graded candidates get a passing grade and one Approval point. | | Ungraded candidates are graded below all others and get no Approval | points. | | Optionally, a voter can specify a Lowest Passing Grade (LPG), which | means that any graded candidates with lower grades get no approval | points. | | If this were a vote for president, one could compare the LPG selection | to Gerald Ford. One might disagree whether he was a good or bad | president, but anybody better than him would be a good president, and | anybody worse than him would be bad. | | The main reason to grade candidates below the Gerald Ford mark would | be if you're not optimistic about the chances for your higher-ranked | favorite and compromise candidates. Grading candidate X below the LPG | mark gives you a chance to say I don't like X and don't want him to | win, but of all the alternatives, he would make the fewest changes in | the wrong direction. Then you have some say in the outcome, instead | of leaving the choice among the alternatives to the most vocal and | extreme parts of other factions. ` -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, first round public proposal (draft)
On 18 Mar 2005 at 11:01 PST, Araucaria Araucana wrote: Below is a draft of a first round proposal for a single general-election voting method replacement. Comments humbly requested. Could the explanation be made any clearer? To facilitate collaboration on this proposal, I've started an electowiki page on DMC here: http://wiki.electorama.com/wiki/Definite_Majority_Choice Have at it ... Jobst has already weighed in with an opinion about Majority (follow the discussion tab at the top). Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Total Approval Ranked Pairs
On 16 Mar 2005 at 17:32 PST, Forest Simmons wrote: Russ worried that putting in an approval cutoff might be too costly. The cost is the same as adding one extra candidate, the ACC (Approval Cutoff Candidate). Voters that truncate the ACC candidate are implicitly approving all of their ranked candidates, since any ranked candidate is considered to be ranked above all truncated candidates. About the Approval Cutoff Candidate, as both name and concept. In general I think it is an excellent idea, but I would still suggest using graded ballots (grades A through F, more if you prefer), but without fixing the approval cutoff below C. Then instead of calling the approval cutoff ACC, you could call it the Lowest Passing Grade. If not entered, it would default to the lowest assigned grade. If you still want to call it ACC, you could use this analogy to explain it: a long time back, I read an article which judged any movie by comparing it to The Truth about Cats and Dogs (which I have never seen). The premise was that if it's better, it's a good movie ;-), and if not, it's a bad movie. Substitute candidates for movies, mutatis mutandi ;-). Russ went on to say that he wasn't too crazy about any of the proposed names for ARC/RAV. If we want to beat IRV we have to get majority into the title. I suggest that we call it Definite Majority Choice which would be consistent with the following description: I like this name. I abbreviate it as DMC below. 1. Rank as many candidates as you want. One of these candidates is the Approval Cutoff Candidate (the ACC). Or Lowest Passing Grade ;-). 2. For each candidate X (besides the ACC) count how many of the ballots rank X above the Approval Cutoff Candidate. This number is candidate X's approval score. 3. Now withdraw the ACC, which has served its purpose. 4. For each candidate X determine if there is another candidate Y with higher approval score than X, such that Y is also ranked higher than X by a majority. If this is the case, we say that Y is definitely preferred over X, and that X is a definite majority choice loser. [In Fine Print] By majority we mean a majority of those voters that express a preference between X and Y. 5. Eliminate all definite majority choice losers. This step might be slightly questionable, but only to theorists. It could eliminate members of the Smith Set. But (I think) such a Smith Set member would be the Pairwise-Sorted Approval (PSA) loser of a cycle and would never win in PSA anyway. The key advantage here is that the remaining set of non-DMC losers (P) will have no cycles. There will be no inconsistencies for IRVists to object to. 6. Choose as winner the candidate that is ranked above each of the other remaining candidates by a majority. Let's compare this method to Pairwise Sorted Approval. In PSA, starting with the Approval ordering (highest to lowest), candidates are bubbled up as they defeat any higher-seeded opponents above them. Denote by Q the final set of candidates ranked by PSA above the Approval Winner. Q includes your remaining set P of non-DMC losers. I.e., if you eliminate from Q any candidates defeated by a higher-approved (seeded) candidate, you get P. The resulting PSA social ranking among P candidates is in non-decreasing order of approval. So if you rank your P candidates in non-decreasing order of approval, you should automatically get their corresponding PSA ordering (minus the eliminated losers). In fact the DMC winner will be the least approved member of set P, right? In any case, your algorithm gets the same winner as PSA. The winner by any of these equivalent formulations is is equivalent to the Ranked Pairs (and Beatpath, too!) winner, when the defeat strength is measured by the approval of the pairwise winner in a pair. [In each case it is to be understood that the majority is a majority of those that express a preference.] [End of method description] What do you think? I'm convinced. Personally, I would rather see the last step replaced with 6'. Of the remaining candidates, pick as winner the one which is ranked highest on a randomly chosen ballot. But I realize that the advantage of this version over the deterministic version is too subtle for the general voting public to appreciate. But just for the record, I would call this stochastic version Majority Fair Chance. Perhaps the citizens of a country like Rwanda could appreciate the method. Forest I'm satisfied with DMC as a first round proposal. Eliminating DMC losers is as easy to describe as IRV, and there will be no cycles among remaining candidates. To digress slightly -- Forest, what are your thoughts about seeding with Cardinal Ratings vs. Approval? If the proposal is passed, the voters could be given the option of either initial ranking method. One way to implement it could be by using extra candidates like the ACC (aka LPG). You could have 10 CR 'extra
[EM] Re: How to describe RAV/ARC
On 15 Mar 2005 at 14:12 PST, Forest Simmons wrote: Here's my sales pitch (to EM members) for RAV/ARC: When candidate X beats Y in both approval and by head-to-head choice, let's say that X strongly beats Y. If X strongly beats Y then both approval and pairwise methods agree that Y should not win. What happens if we eliminate all of the candidates that are strongly beaten? The remaining candidates form a set P that are totally ordered by the ordinary pairwise beat relation. The top of this totally ordered chain is the RAV/ARC winner. That ends my EM sales pitch for RAV/ARC. [I would use a different pitch for the general public.] [First post using gmail address instead of mailinator] Hi Forest, According to this sales pitch, RAV/ARC does not have quite the same effect as Approval-seeded Bubble Sort [aka Total Approval Ranked Pairs, Tournament Voting (approval-seeded)]. Using ABS, it is possible that a candidate X could end up ranked below the Approval Winner AW, but because a higher-seeded candidate Y defeats X but is defeated by AW, X cannot end up in your set P. Consider the following situation with the following RP (wv) ordering: A1A2 A2A3 A3A1 A1AW, A1X, A1Y A2AW, A2X, A2Y A3AW, A3X, A3Y AWY YX XAW Seeding by descending order of approval, we start with AW A2 A1 A3 Y X There are two cycles: A1A2A3A1, AWYXAW. ABS ends up with the following social ordering: A1A2A3AWYX A1 wins, and also wins via other strong wv methods. Now consider the three interesting situations here: - The approval winner is not in the Smith Set. - Pairwise, XAW, but approval wise, Approval(AW)Approval(X). Pairwise and Approval disagree. So X should be a member of your set P, but it isn't in ABS. Do you want the least approved candidate, also not a member of the Smith Set, to be included in P? Or is the higher-ranked approval Beatpath AWYX considered a pairwise defeat? - Approval order above AW is not strictly increasing. So is ABS equivalent to RAV/ARC as you and Jobst have asserted, or is it slightly different? Or is your pitch inaccurate? Ted (aka Monkey Puzzle) -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: How to describe RAV/ARC
Substantial abbreviation of previous messages.
On 16 Mar 2005 at 15:54 PST, Forest Simmons wrote:
On Wed, 16 Mar 2005, Araucaria Araucana wrote:
On 15 Mar 2005 at 14:12 PST, Forest Simmons wrote:
Here's my sales pitch (to EM members) for RAV/ARC:
When candidate X beats Y in both approval and by head-to-head choice,
let's say that X strongly beats Y.
If X strongly beats Y then both approval and pairwise methods agree that Y
should not win.
- Pairwise, XAW, but approval wise, Approval(AW)Approval(X).
Pairwise and Approval disagree.
So X should be a member of your set P, but it isn't in ABS.
But X is strongly beaten, so by definition of P, candidate X is not a
member of P.
Ah, okay -- X is strongly beaten by Y and hence cannot be a member of
P.
And I see that A3, since defeated by A2 both via approval and
pairwise, likewise cannot be a member of P.
So P is the set of candidates not strongly beaten by any other
candidate.
All I claimed above is that the set P is totally ordered in two
diametrically opposed ways.
I made no claim about anything outside of P.
I think you were mislead by the technical use of the word total
thinking, perhaps, that it referred to the totality of the original
candidates, which it did not.
Do you want the least approved candidate, also not a member of the
Smith Set, to be included in P? Or is the higher-ranked approval
Beatpath AWYX considered a pairwise defeat?
- Approval order above AW is not strictly increasing.
There is no candidate with approval above that of the AW.
I meant in the Bubble Sorted ordering above AW.
So is ABS equivalent to RAV/ARC as you and Jobst have asserted, or is it
slightly different? Or is your pitch inaccurate?
The RAV/ARC pitch is accurate, but in the section on lotteries after
my RAV/ARC pitch, I made one mistake:
I claimed in passing that if you didn't eliminate the strongly
beaten candidates, the candidates that were as high or higher than
the AW in the sorted list would constitute the set P. But as your
example shows, this set Q is sometimes a proper superset of P.
Whether we should choose (by random ballot) from P or from Q
deserves further study.
So in my reply comment just above, I meant the Bubble Sorted ordering
within Q.
Thanks for the clarification. As we can see from this example, the
Smith Set {A1,A2,A3} can sometimes not include the approval winner,
and your set P of non-strongly-defeated candidates may not include
every member of the Smith set.
Here's an argument for Q vs. P. A3 voters might move their approval
threshold above AW if they think they're being excluded unfairly from
the lottery.
Another thought -- what if CR-seeding is used instead of Approval?
Voters might prefer a sliding cutoff rather than an abrupt one. The
boundary gets a little fuzzier doesn't it?
Digressing slightly -- I think a good general name for the bubble sort
methods would be Pairwise Sorted othermethod. For example,
Pairwise Sorted Approval (PSA), Pairwise Sorted Cardinal Ratings
(PSCR), etc. In other words, pairwise sorting (bubble sorting should
be understood) of some other method's ranking.
Your random ballot method could be called something like Random Ballot
Resolution (Pairwise/other method), since it is intended to resolve
the disagreement between Pairwise comparisons and whatever other
method you are using as a hybrid.
For example, RBR(pairwise/approval) or RBR(pairwise/CR).
Now, can you figure out a good way to pitch this to the masses? PSA
or PSCR might be within grasp, but if even I have trouble with it, the
strong defeat concept in RBR(P/A) could be very tricky to explain.
Ted
--
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