Re: [EM] A modification to Condorcet so that one can vote against monsters.
On 4/14/2012 5:42 AM, Andrew Myers wrote: On 4/14/12 8:31 AM, robert bristow-johnson wrote: On 4/14/12 3:45 AM, ?U(alabio? wrote: ¡Hello! ¿How fare you? It is tedious to rank hundreds of candidates, but sometimes monster is on the ballot and all unranked candidates are last. If the field is so polarized that the voters idiotically refuse to rank other serious candidates other than their candidate and the evil candidate has followers, the bad candidate might win. I suggest that Condorcet should have a dummy-candidate: 0 The ranked candidates. 1 The unranked candidates. 2 The dummy-canditate. 3 The monsters. All unranked candidates have higher ranks than the monsters. One can then rank the monsters by how terrible they are. Basically, it is a way to vote against monsters in Condorcet without having to rank all of the hundreds of also-rans. all this is complicated crap that gunks up elections. it has an ice-cube's chance in hell. I've been observing experimentally how people use a Condorcet election system in practice over the past ten years (since 2003) and in fact the use of a dummy candidate to signal approval has become increasingly common. It seems to be intuitive, at least to web users, and effective. I do agree that trying to distinguish 0 vs. 1 is probably overly complicated. -- Andrew Election-Methods mailing list - seehttp://electorama.com/em for list info You could say Rank all candidates you approve of or even List the candidates you like in order of preference. Ignore all other candidates. Such a ballot would be easier for the average voter to understand and fill out. If there are fifteen people running for office, and you like three, hate three, and don't know anything about the remaining nine, you can just say the equivalent of ABC, and ignore the rest. No dummy candidate would be necessary Sure, it wouldn't give as much information as a ballot that has all of the candidates ranked, but it would make certain forms of strategic voting (such as burying) more tedious and less attractive. Then just use the ballots to find the Condorcet winner. Such a ballot could be used with Approval-Completed Condorcet or Ranked Approval Voting, or any other completion method that takes into account Approval votes. For example, you could say If there is a cycle, compare the two candidates with the lowest Approval score in the cycle, and drop the pairwise loser. Continue until there is a single winner. Or whatever. Mike Rouse Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] SodaHead online Approval Voting poll
I pointed out on SodaHead that the thumbs-up on the upper right of each post was an example of Approval voting, and those who think Approval is too complicated or undemocratic were free to restrict their votes to a single post. :) Mike On 3/21/2012 6:09 AM, Jameson Quinn wrote: What strikes me most about the comments is how many of them are positively proud of their loudmouth know-nothingism. The same people who think it's a liberal plot seem to enjoy showing off their closed-mindedness. That is, they see it not as a rational argument, but as a tribal counting-coup on those egghead liberals. Finding better rational arguments is not going to change such people's minds. I'm not really sure what would. It seems that they make up their minds pretty quickly and reflexively. Now I know that such blowhards are overrepresented on the internet, but the truth is they tend to make more than their share of noise in any context, so it's important to have some strategy to deal with them. ... Separately, I think your point about the demographics is a good one. Obviously, the sample sizes are small and so basically none of it is reliable (statistically significant), but still, it can give some clues. As far as I can see states on that map which have the most-significant (not largest) advantages for Yes, approval are New Jersey, Pennsylvania, Minnesota, South Carolina, Oregon, and Florida. Smaller states would be unlikely to show significance even if there were an advantage, but the small New England states might be promising too. Jameson 2012/3/21 Kristofer Munsterhjelm km_el...@lavabit.com mailto:km_el...@lavabit.com On 03/20/2012 01:51 PM, Jameson Quinn wrote: I know that online polls are silly. But thousands of people see them, and if they see that the idea actually has support, some of them will be more open to consider if it has merit. While the poll has comments of low quality, and the users seem to be against Approval at the moment, I do think even those low-quality comments can be useful. Namely, they give us insight into the objections, fair or not, to Approval itself. There are partisan arguments (this is a liberal plot to deny conservatives their voting power), what can be done about them? Can we point out places where conservatives are being hurt by vote-splitting? Can we point at Ron Paul when responding to a libertarian? Then there are method centric arguments. Some are just confused about what the thing means, as one can see by the oh, and let the voters vote for a single candidate many times type of posts. Others think it violates one-man one-vote. How can we clear that up? Perhaps by rephrasing it in terms of thumbs-up/thumbs-down? If each voter gets ten options to either do thumbs-up (approve) or not (don't approve), then the voting power is the same for each. Maybe that is a better phrasing than approve/not in any case, and maybe it's a better format, too, because it clears up the confusion between haven't made a choice about X (no approval) and have voted, but didn't like X (also no approval). And so on... The demographics, if representative, may also give some idea as to where it will be hard to sell. What kinds of people like Approval the least? Why? I do note that there are very few arguments about chicken dilemma situations. If there are barriers to Approval being adopted, that isn't it - at least not yet. Though one could of course say that the reason nobody objects using the chicken dilemma is that they haven't studied the thing enough to know there actually *is* a chicken dilemma problem. Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Breakthrough in political districting algorithms (I think)
Wow, I haven't thought about space-filling curves for awhile! :)
Back in 1996, I came up with a couple of space-filling curves for the
Fractint L-system. The first one is somewhat similar to Gosper's
Flowsnake, but more jagged. I called it Hextar (hexagonal star). The
second one combined 3 Hextar curves into a closed loop, and in a fit of
creativity I called it Hexter 2.
I'm not sure if you have access to something that will run L-system
files, but here are the instructions for both curves (I kept the
comments intact):
Hextar1 { ; Hexagonal Star 1 by Michael A. Rouse, 1996
angle 6
axiom s ; to make things start at
s=L ; order 1
L=LzfR--fR-f++Lf++L-f+Lf+R--y
R=z++L-fR-f+R--fR--f+Lf++LfyR
z=-
y=+
}
Hextar2 { ; Hexagonal Star 2 ; by Michael A. Rouse, 1996
angle 6
axiom s ; to make things start at
s=Lf++Lf++Lf ; order 1
L=LzfR--fR-f++Lf++L-f+Lf+R--y
R=z++L-fR-f+R--fR--f+Lf++LfyR
z=-
y=+
}
No clue at all if these will yield any different results from Gosper's
Flowsnake, though. If you can't run L-system files but would like to see
them, I can create an image to show you what they look like, from
order-1 to whatever you want.
Michael Rouse
On 7/17/2011 11:51 AM, Warren Smith wrote:
http://rangevoting.org/SpaceFillCurve.html
describes a new, incredibly simple, algorithm for political
districting which is guaranteed to
get within a constant factor (namely 6.34) of the cost of the optimum
districting,
using the cost measure
sum(over all people) (distance to their district centerpoint)^2.
Its output can be fed into further optimizers... but my point is
that no previous polynomial-time algorithm had
ever been able to guarantee being at most
any constant factor worse than optimal.
I hope this paper is not insane -- it seems almost too good+simple to be true.
Email me your questions, comments, complaints, etc about the paper.
(I am also working on a much more complicated polytime algorithm which
if it pans out will be able to guarantee 1+epsilon approximation...)
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Theoretical Issues In Districting
Quote: /Democracy is voters choosing their leaders. But when politicians get to draw their own districts, such as (most http://rangevoting.org/CrossCountryG.htmlegregiously) in the USA, the result is the opposite -- the politicians choose their voters./ When you want to divide cake evenly between two people, you let one person cut the cake, and the other person chooses which slice he gets. In this case, let politicians cut the cake however they like (each candidate, party, or interested group with enough signatures offers a districting map), and then voters choose which one they like best. The mechanics of creating a map would be left up to the ones doing the suggesting, subject to the normal rules of contiguous districts and equal populations. (For the record, I do like the average distance to center method, as well as any method that generates centroidal Voronoi tessellations). Once the district maps were created, voters could choose between different districting maps for the entire state,*or* (since we have cheap computers and printers) each voting precinct might just vote between maps of the proposed district they would vote in-- a Republican might think it's fine to have a weirdly gerrymandered Republican district elsewhere in the state, but may be less likely to vote to belong to one. The nice thing about the second method is that it would encourage groups to focus not only on a grand, statewide vision, but how the voters of each district view their own map. Plus, it would encourage groups to combine efforts on district maps that were clearly superior (two districting maps of California might be identical except for a half dozen districts), and focus their efforts on stressing the importance of their differences. (The Green Party endorses the map created by the Democrats, except in districts 5-9, 17, and 22. And here is why our map is superior in those areas.) And voters could take into account geographic features, historical ties, driving distance, and other factors that are really hard to program, and even harder to legislate for without creating perverse incentives. For added fun, voters could pick maps every two years, to be used for the following election. How is that for responsive politics? As a side note, I actually lean to multi-member districts, or even a single universal at-large election -- people's political interests don't always follow neat geographical boundaries, and a Green in Texas might want to vote for someone who lives in San Francisco rather than a conservative Democrat in their own state. Mike Rouse PS I'm playing with a proxy-range PR system myself -- yes, PR^2 -- but I going through the EM archives to see if anyone proposed it first under another name. :) Using range ballots, it would take the most representative subgroup of candidates for a legislature of a certain size, and then give each winner voting power equal to the number of ballots that they had the highest score on among all the winning candidates. If that sounds in any way similar to another proposal, please send me links! On 6/10/2011 9:35 AM, Warren Smith wrote: A preliminary web page on this topic is now available here http://rangevoting.org/TheorDistrict.html Your comments would be appreciated to help me improve this page. [There is a much longer scientific paper in the works by me others on this, but it unfortunately has been in the works several years already :( I'm too lazy and/or bit off more than could chew.] Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] legislature size
If you were going to use a proxy-type voting system, you could make the following rules: 1. A successful candidate must have votes greater than or equal to the square root of the total number of ballots cast. 2. The total number of successful candidate cannot be greater than the fourth root of the total number of ballots cast (the square root of the square root). In the 2008 election, 122,394,724 people voted for President. The first rule would mean that to be seated in the legislature, a candidate would need at least 11,064 votes, and the maximum number of legislators would be 105. Of course, if you wanted to be closer to Warren's 250 limit, you could take twice the fourth root (~210) or half of the cube root (~248). If you were going to go the proxy (asset) route, there probably should be some simple relation between the total votes cast, the minimum votes needed to be elected, and the total number of legislators, without fixing any single number in stone. On 4/25/2011 2:56 PM, Warren Smith wrote: here's an idea. Find out how many bills a typical legislator writes that make it to a floor vote. If this number if below 1, then the legislature is too large. (Course, there are bullshit do-nothing bills galore. Some way need to be found to exclude them.) If a legislature is to debate each substantive bill for 1 day, that means there can be at most 365 substantive bills per year. Actually thanks to weekends, vacations, etc, more like 250. That means, if there are any more than 250 congressmen, then at least one of them will be unable to write a substantive bill each year. So I conclude legislature size ought to be capped at 250 or less. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] electing a variable number of seats
Do you need to give everyone on the board identical voting power? If not, a proxy method (where each board member's voting power is directly related to how many votes he or she received) might work. Candidate A might have twice the voting power of Candidate B, who might have 30 percent more voting power than C. (You would need more than 3 seats on the board, though -- if there isn't a candidate with a majority, the effective voting power of the three members would be the same, since it would take at least two members of the group to pass something.) There wouldn't be a fixed number of seats, since the number above the cutoff could vary. You could count first-place votes, and only look at rankings if a candidate didn't reach a certain threshold and was dropped, and you needed to transfer the votes to second choices above the threshold. Allowing the individual power to vary with votes received also gives a natural hierarchy among members. Mike Rouse On 2/16/2011 7:38 PM, Charlie DeTar wrote: Howdy, I'm on the board of a small non-profit, and have been tasked with revising the portion of the bylaws that defines how to elect the board of directors. Having had some exposure to better election methods through a colleague, I'm interested in exploring how we might use a ranked voting system effectively. Most of the methods I've seen, however, are intended for electing a single winner -- and for the board of directors, we have multiple seats. Additionally, the number of seats is variable. I'm looking for methods that would more or less optimally (by variable definitions of optimal) elect a variable number of people. Single Transferable Vote seems to be the most talked-about multi-winner ranked system; but the vote transfer process requires a pre-defined number of seats to fill. It seems like the option to have a variable number of seats opens up possibilities for improving representation by adding a winner, or eliminating polarizing candidates by removing one. Thoughts? best, Charlie Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] HB240 could lead to Approval voting in New Hampshire
HB240 is a New Hampshire bill to allow Approval voting for all state offices and Presidential primaries. Here is the link to the Slashdot story: http://politics.slashdot.org/story/11/01/30/1911232/New-Hampshire-Bill-Could-Lead-To-Adoption-of-Approval-Voting#comments I would be very happy to see this signed into law. :) Mike Rouse Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Binary dropping of candidates
It's probably already been discussed before (most likely with a more descriptive name), but the election methods list has been quiet, so... Has anyone looked at making a ranked list of candidates -- either by number of first place votes, as in IRV, or Borda order, as in Nanson/Baldwin -- and dropping candidates in a binary rather than unary way? By way of example, in Instant Runoff Voting, you see if a candidate has a majority. If not, you drop the lowest candidate. If there is still no candidate, you drop the next lowest candidate, and so on. With five candidates, you have something like this: . First round (no one dropped) 1 Second round (one person dropped, ballots redistributed) ...11 Third round (two people dropped, ballots redistributed) ..111 Fourth round (three people dropped, ballots redistributed) (for five candidates, three drops are sufficient) It's a method analogous to a unary counting system. Under a binary dropping method, you have: (Note: If there is no winner after a round, you use the original candidate ranking and proceed to the next round.) 0 First round (no one dropped) 1 Second round (bottom candidate dropped, ballots redistributed) 00010 Third round (second-to-last candidate dropped, ballots redistributed) 00011 Fourth round (bottom two candidates dropped, ballots redistributed) 00100 Fifth round (middle candidate dropped, ballots redistributed) 00101 Sixth round (middle and last candidate dropped, ballots redistributed) 00110 Seventh round (middle and second to last candidate dropped, ballots redistributed) 00111 Eighth round (bottom three candidates dropped, ballots redistributed) In effect, you drop the group of candidates representing the lowest number of first place votes (or lowest combined Borda score, or some other method) that result in one candidate having a majority of first place votes, instead of just dropping the lowest candidate and repeating. Unfortunately, the first-place-only version suffers from being non-monotonic (like IRV does). I'm not sure what criteria a Borda-count variety but it would be interesting to compare the results of a binary-drop IRV and binary-drop Baldwin to other methods. (The Yee pictures might be interesting.) As I mentioned at the start, it's probably already been discussed at some point with a better name, but I thought I'd throw it out there as an interesting variation on the drop the lowest candidate method of vote aggregation. It might have an unusual array of voting paradoxes, anyway. :) Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet completion with two tiebreakers
Oops, made a rather big mistake. It should read (correction underlined): 5. If both methods pick the same candidate, this person wins, otherwise compare the Borda winner with the_*plurality*_ winner. (In other words, in a three-person tie, you'd drop the candidate that was neither the Borda nor the Plurality winner, and compare the remaining two.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] the bullet voting bogeyman for range/approval voting
The degenerate to plurality voting concern is easy to disprove -- even/ plurality/ doesn't degenerate to pure plurality voting, because in every plurality election there are overvotes. In fact, in the infamous Florida debacle of 2000, *there were more overvotes than people who voted for Ralph Nader *-- 111,251 overvotes versus about 97,000 for Nader (it's sadly amusing to see people complain about Nader being in the race while ignoring an even bigger issue). In other words, people /accidentally/ cast an Approval ballot more often than they /purposely/ voted for the spoiler. I can't imagine any scenario where there would be /fewer/ Approval ballots, if they were counted instead of being tossed out. Here's a USAToday link of Florida overvotes in 2000: http://www.usatoday.com/news/politics/2001-05-10-overvotetable.htm Michael Rouse On 8/28/2010 7:56 AM, Warren Smith wrote: The idea has been raised (mainly by instant runoff proponents at FairVote and based apparently intense intuition but zero evidence) that approval or range voting will in practice degenerate to plurality voting. Preliminary indications, based on evidence, are that this is not so: http://rangevoting.org/BulletBugaboo.html However the amount of evidence presented there, is not all that large. I believe one can get more data... but I haven't yet. Suggest some more? [In particular, I am looking for some IRV elections for which we have full ballot data, in which vote-truncation was allowed, with * 8 candidates * 17 candidates and several thousand or more voters, and reasonably important, to compare with some approval voting elections. Suggest?] Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Voting systems theory and proportional representation vs simple representation.
On 3/13/2010 11:53 AM, Abd ul-Rahman Lomax wrote (after I snipped a bit): Attempts have been made to apply this to public elections. I forget the city, but there was a proposal in the early 20th century to hold an election for a City Council where, in the council, representatives would exercise the votes they recieved in the general election. This would have been, for the first time, true and accurate representation before the Council. Because some council members would have many more votes than others, others would have less; this would produce a more representative result than a scheme in which votes are allocated to seats equally, because smaller groups could still obtain seats. (Assume a fixed number of seats. Suppose the top N vote-getters are elected in a vote-for-one election. Look at the minimum number of votes obtained by a candidate who nevertheless obtained a seat. In a system which redistributes votes somehow so that a faction with 2Q votes gets two seats, and Q votes are required to win a seat, and there are N seats, compared to one where the top N candidates get seats, with variable voting power, it's obvious that since for some seats in the latter case, more than Q votes were obtained, some must have less, and thus smaller factions get representation.) I just wanted to point out a hero of mine from my home state, William S. U'Ren (Wiki article here: http://en.wikipedia.org/wiki/William_Simon_U'Ren http://en.wikipedia.org/wiki/William_Simon_U%27Ren ). He was the father of Oregon's Initiative (1902), Referendum (1902), and Recall (1908) movement at the turn of the 20th century. He also campaigned for the popular election of U.S. Senators (well, okay, so there can be an argument about the usefulness of this), and helped establish the first Presidential primary (1910). (I think these dates are accurate.) This is just background for my main point, though. Quoting Wiki, In 1912, he (U'Ren) proposed an amendment to the Oregon Constitution to essentially weigh each legislator's vote on proposed bills according to the number of votes he received in the last election. The abstract from the New York Times of the period reads: SALEM, Ore., June 29. -- It is a remarkable plan of government that has been evolved by the People's Power League for presentation to the people at the coming State election under the initiative. Its intent is to have all the votes cast in any election represented in the legislative assembly by proxy members whose voting power in that body shall be gauged by the number of electors who voted for them. Article in PDF: http://query.nytimes.com/mem/archive-free/pdf?_r=1res=980CEED91E3CE633A25753C3A9609C946396D6CF http://query.nytimes.com/mem/archive-free/pdf?_r=1res=980CEED91E3CE633A25753C3A9609C946396D6CF (I hope that works, New York Times links sometimes go to a login screen). He didn't come close to succeeding in this particular endeavor, but he did show how a politician with a knack for thinking about election methods could alter the course of government. Unfortunately, he has been almost forgotten, even in Oregon, though every election cycle we see his handiwork in voter initiatives and referendums (only rarely is there any grumbling of recall, though it's still possible). Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Professorial Office Picking
Steven E. Landsburg (author of The Armchair Economist), had an interesting problem here: http://www.thebigquestions.com/2010/01/21/office-politics/ (in reference to an original question of the New York Times ethics column here: http://www.nytimes.com/2010/01/03/magazine/03FOB-Ethicist-t.html) Basically, you have a bunch of professors of different seniority wanting a bunch of rooms of different desirability. The original article at the Times suggested a lottery. Steven Landsburg suggested a market, where professors bid what they wanted for a particular room. Here's my comment: ** Why not use a rank order ballot grid? Have room locations across the top (x-axis) and people's names down the left (y-axis). Each professor could rank the rooms in order of their own preference, and rank the potential occupant in each room in order of preference, all on one handy grid. People could then trade their votes (or something more tangible for votes) in order to get the room they want. On a certain date, finalize the votes, determine the allocation of rooms to maximize overall satisfaction, and start moving in. It might be difficult to find the peak utility order (probably NP-hard), but it should be manageable --- you probably don't have to worry about hundreds of professors, and that's what computers are for. Plus, if a professor leaves, you might be able to determine more easily who gets his or her office. As an interesting extension, it may be possible to come up with a similar way to match students, professors, periods, and classes, though that would be even more complex. It would be kind of fun to watch a course election, though, with groups lobbying for particular lectures at particular times, or banding together to get the professor they want. ** I was wondering if those on this list had other suggestions. I make no claim as to the suitability of my suggestion, I just thought it was an interesting problem. Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] (Possibly) new method/request for voting paradoxes. :)
The additional complexity is to break cycles and come up with a complete preference order. In one of the examples below, 5: ABC 3: BCA 4: CAB the cycle was resolved as ABC. I just wanted to show that it picked the Condorcet winner in the absence of cycles. Like other Condorcet methods, breaking cycles is where paradoxes arise, like IIA, but I'm also interested in the other paradoxes it runs into. I'm also kind of curious how the rank orders compare to that of other methods, like Kemeny-Young. Michael Rouse PS It's early on the West Coast. I probably shouldn't write after I just wake up. :) Dave Ketchum wrote: What is the point to all this? Looks much more complex than I sketch below, but I do not see value in the extra effort: For 10 candidates, fill a 10x10 matrix - for A vs B need an entry counting AB and one for BA. With luck about 9 comparisons will identify winner since each identifies a non-winner. If AB = BA, keep both for the moment. If they lose to another, that ends them. If all others lose to them, we have a tie. Could be cycles. Comparing winner against 8 losers should identify innocence vs guilt. Dave Ketchum On Oct 11, 2009, at 12:00 PM, Michael Rouse wrote: This method always selects the Condorcet winner if there are an odd number of voters with no ties or circular ambiguities. *With respect to a particular candidate,* the other candidates must form a single uniquely-preferred rank order, with a single peak in ranking score at the (composite) median voter -- if the median voter places B one place below A, the median voter cannot also rank C one place below A, unless both B and C are tied. The converse is also true -- if A is one place above B, C cannot also be one place above B. If you had a rank order with the Condorcet winner anywhere other than first position, you could always raise the total score by moving the Condorcet winner up the ranking, because the median voter would rank the Condorcet winner above the other candidates. I *think* this means that the final result will be the Condorcet order (in the absence of ties), but I haven't tried checking it yet. Of course, if there are no voters at the median ranking (for example, if exactly half of the voters ranked A as first place and half ranked A as last place, with no voters in the middle -- which is why I mentioned an odd number of voters above), you will have a range of ranks with the same score. For example, combining the votes ABC and BCA will result in a tie between those two rankings, even though a case can be made that BAC would be the preferred ranking, if one must be picked. So there are probably a whole host of paradoxes out there, in addition to the ones inherent in Condorcet methods. :) For ratings differences, do you mean on a range-type ballot? That might be an interesting path to look at. And do you have an example of the before and after matrices for your positive difference suggestion? Michael Rouse PS Of course, it's entirely possible that I made a mistake in reasoning somewhere, so I would be interested in any counter-examples where the Condorcet winner (or Condorcet order) did not match the winner in this system. Jobst Heitzig wrote: Dear Michael, very interesting, I don't think I saw anything like this before. When trying do evaluate a new method, I always try to check very simple criteria first, like neutrality and anonymity (obviously fulfilled here), Pareto efficiency, monotonicity, etc. Concerning the latter two, I was not able to verify them for your method yet. I think you should focus on those before checking more complex things like Condorcet efficiency and so on! Also, immediately a ratings-based generalization came to mind (using ratings differences instead of rank differences). Finally, when only seeking a single winner, you could alternatively build a score for each option X by adding all entries of the final matrix in rows labeled XY and columns labeled with positive differences. Yours, Jobst Michael Rouse schrieb: As usual with such posts, there is a good chance someone has come up with the same (or very similar) method, but I thought it had interesting properties, and was wondering what glaring voting paradoxes it had. In addition, the number of possible orders is overwhelming if there are a large number of candidates, and I'm not sure that can be simplified. Finally, Thunderbird sometimes seems to have weird formatting issues in email, which may screw up the following into unreadability. With that in mind, here it is. Step 1: For each ranked ballot, create a matrix for each pairwise vote, based on the distance and direction between each candidate. For example, on the ballot ABC, you would get: -2-1012 AB0 0010 BA0 1000 AC0 0001 CA1 0000 BC0 0010 CB0 1000 Taking
Re: [EM] (Possibly) new method/request for voting paradoxes. :)
This method always selects the Condorcet winner if there are an odd number of voters with no ties or circular ambiguities. *With respect to a particular candidate,* the other candidates must form a single uniquely-preferred rank order, with a single peak in ranking score at the (composite) median voter -- if the median voter places B one place below A, the median voter cannot also rank C one place below A, unless both B and C are tied. The converse is also true -- if A is one place above B, C cannot also be one place above B. If you had a rank order with the Condorcet winner anywhere other than first position, you could always raise the total score by moving the Condorcet winner up the ranking, because the median voter would rank the Condorcet winner above the other candidates. I *think* this means that the final result will be the Condorcet order (in the absence of ties), but I haven't tried checking it yet. Of course, if there are no voters at the median ranking (for example, if exactly half of the voters ranked A as first place and half ranked A as last place, with no voters in the middle -- which is why I mentioned an odd number of voters above), you will have a range of ranks with the same score. For example, combining the votes ABC and BCA will result in a tie between those two rankings, even though a case can be made that BAC would be the preferred ranking, if one must be picked. So there are probably a whole host of paradoxes out there, in addition to the ones inherent in Condorcet methods. :) For ratings differences, do you mean on a range-type ballot? That might be an interesting path to look at. And do you have an example of the before and after matrices for your positive difference suggestion? Michael Rouse PS Of course, it's entirely possible that I made a mistake in reasoning somewhere, so I would be interested in any counter-examples where the Condorcet winner (or Condorcet order) did not match the winner in this system. Jobst Heitzig wrote: Dear Michael, very interesting, I don't think I saw anything like this before. When trying do evaluate a new method, I always try to check very simple criteria first, like neutrality and anonymity (obviously fulfilled here), Pareto efficiency, monotonicity, etc. Concerning the latter two, I was not able to verify them for your method yet. I think you should focus on those before checking more complex things like Condorcet efficiency and so on! Also, immediately a ratings-based generalization came to mind (using ratings differences instead of rank differences). Finally, when only seeking a single winner, you could alternatively build a score for each option X by adding all entries of the final matrix in rows labeled XY and columns labeled with positive differences. Yours, Jobst Michael Rouse schrieb: As usual with such posts, there is a good chance someone has come up with the same (or very similar) method, but I thought it had interesting properties, and was wondering what glaring voting paradoxes it had. In addition, the number of possible orders is overwhelming if there are a large number of candidates, and I'm not sure that can be simplified. Finally, Thunderbird sometimes seems to have weird formatting issues in email, which may screw up the following into unreadability. With that in mind, here it is. Step 1: For each ranked ballot, create a matrix for each pairwise vote, based on the distance and direction between each candidate. For example, on the ballot ABC, you would get: -2-1012 AB0 0010 BA0 1000 AC0 0001 CA1 0000 BC0 0010 CB0 1000 Taking the rows in order, this shows that A is one position higher than B on this ballot, which conversely makes B one position lower than A on the same ballot. Also, A is two positions above C (C is two positions below A), and B is one position above C (or C is one position below B). Such detail may be unnecessary -- simply looking at position 1 and above is sufficient, if you don't allow ties -- but I wanted to show the symmetry. Step 2. Add all matrices together. As a simple example, let's consider the following 12 votes in a circular tie (to make it interesting): 5: ABC 3: BCA 4: CAB Taking the first line, ABC = -2-1012 AB0 0010 BA0 1000 AC0 0001 CA1 0000 BC0 0010 CB0 1000 Multiplied by 5 gives you: -2-1012 AB0 0050 BA0 5000 AC0 0005 CA5 0000 BC0 0050 CB0 5000 Taking the second line, 3: BCA = -2-1012 AB3 0000 BA0 0003 AC0 3000 CA0 003
[EM] (Possibly) new method/request for voting paradoxes. :)
wait. Any questions, comments, or criticisms (the latter most likely about my math!) are welcome. Especially welcome would be examples of paradoxes, and links to the same (or similar) method discussed in the past. Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Cramster question
Warren has done a lot of research into Range voting. I wonder how well RV works as a Condorcet completion method. Actually, I was on his site the other day (http://www.rangevoting.org/MedianVrange.html), looking at the Balinski-Laraki median range voting method. It made me wonder what the results would be if you took the combined score (or the average) of all range votes above the median for every candidate. It looks like it should satisfy the majority criterion, assuming people have a single top preference (ties at the top score would complicate that a bit). I was at work, though, so I didn't play with the numbers, though if someone has done that, it would be interesting to see. It probably is on the range voting site, though I didn't see it. Michael Rouse Paul Kislanko wrote: I personally like the idea of using Bucklin to break a Condorcet cycle. Suppose alternatives Ax, Ay, and Az prevent there being a Condorcet winner. Then find the best ranks Rx, Ry, Rz for which a majority of the voters rank Ax, Ay, Az AT LEAST Rx,y,z respectively. If one of Rx, Ry, Rz is better than the others, that determines the winner. If Rx=Ry=Rz (or the two best are equal) then use the size of the respective majority (i.e. if 100 voters and 52 give Rx but 51 give Ry then Ax wins the tie with Ay.) If both the R and #votes providing the majority that determines R are the same we have a true tie. Either flip a coin or have a runoff. -Original Message- From: election-methods-boun...@lists.electorama.com [mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Terry Bouricius Sent: Thursday, May 14, 2009 2:48 PM To: Warren Smith; election-methods Subject: Re: [EM] Cramster question Warren, However, using first-choice plurality to settle Condorcet cycles could easily elect the Condorcet-loser (the candidate who loses in every pairwise match-up). There are many far superior cycle breakers. I personally favor ranked-pairs because it is both reasonable, and relatively easy to explain to lay people (unlike many cycle breakers). Terry Bouricius Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Cramster question
I was idly doing a Google search for Condorcet Plurality, and up popped a question on a site called Cramster (I have no clue what the site is about, it just came up in the search). Someone a couple of weeks ago asked: *Question Details:* Condorcet’s method has many nice properties, and some supporter’s of former Vice President Al Gore pointed out that Al Gore was very likely the Condorcet winner. The problem with Condorcet’s method is that it does not produce a winner often. Thus, let us propose a combination of the Condorcet’s method and the plurality system: This combined system deems the Condorcet winner as the winner. In case that the Condorcet’s method does not produce a winner, then use plurality method to select the winner. 1) Does the Condorcet-plurality system produce winner more often than Condorcet’s method? Explain. 2) Does the Condorcet-plurality system satisfy the Pareto condition? Explain. 3) Does the Condorcet-plurality system satisfy Condorcet winning Criterion? Explain. 4) We know that both Condorcet and plurality systems are monotone. Is the Condorcet- plurality combined system still monotone? Explain. 5) Is the Condorcet-plurality system manipulable? If your answer is manipulable, give an example of an election where manipulation can be done. If your answer is not manipulable, prove it. Here is the link: http://qaboard.cramster.com/other-topic-5-551512-cpi0.aspx Hmm, looking at it again, it may be a homework site. Anyway, such questions often bring up interesting discussions on the EM list, so I thought I'd let people know. Michael Rouse PS If the text is scrambled, let me know. I cut and pasted an html document. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Clarke-Groves-Tideman-Tullock voting with money scheme
I was perusing the rangevoting.org site (hi, Warren! :) ) after the latest IRV argument, and I came across something I remembered vaguely but thought was quite interesting, namely the Clarke-Groves-Tideman-Tullock 'perfect' scheme for voting with money (link here: http://scorevoting.net/CTT.html ) It seemed like an interesting idea, but the drawbacks mentioned included the possibility of non-payment and the problem of secrecy. So I looked at the problem from another angle -- what activity does every election have where people let others know who they support, and how much? Bingo, campaign contributions, where donations (at least those above a certain amount) have a name attached to them. Now, I don't know if this breaks all of the other good features of GCTT, but what about considering each dollar of *campaign contributions* the equivalent of a vote, with the amount of money given corresponding to the true worth of the candidate? Set aside a portion of each donation in an account, and after the election either return the money to the original donor, or (in the case where the GCTT criterion is met) giving the made a difference amount to whoever we decide the recipient to be. For example, if Candidate A wins by 1% over Candidate B, and someone gave 2% of the total campaign contributions to the winning candidate, he or she would lose half (or as close to that as the set-aside was) to the lucky person or government agency. Of course, money donated is only roughly correlated to the number of votes someone receives -- Ron Paul had a core of very dedicated campaign contributors, even though several other Republican candidates had an electoral advantage -- so this is just a standard voting system with a strange way of disbursing part of campaign contributions. It would still be interesting to see the money winner versus the vote winner in the election using such a system, however. I would stop there, but then I thought of an interesting gambling version. Unfortunately, I don't have enough math skills to figure out if it's fair, or suffers from serious economic and electoral paradoxes, but hey... :) Let's assume that half of the money given to each candidate can be spent by that candidate for advertising and related campaign expenses, and half is saved in a payoff account. After the election, the payoff account of the winner is split among all the losing donors in proportion to how much they gave to the candidate they supported. If Candidate A was giving $1 million and Candidate B $500K (assuming a two-person race), a win by Candidate A would completely pay back the donors of Candidate B, /plus/ they would make a 50% profit (they get back all of their payoff account and all of the payoff account of Candidate A, or a total of $750K for a $500K investment). If Candidate B won, despite spending only half as much, donors to Candidate A would get back 75% of their money (half of their $1 million donation, plus half of the $500K donation to Candidate B). Like I mentioned, my math skills aren't really up to the task of figuring out either case, but I thought it was an interesting idea. It would be fun to see if it was workable, or if it had a fatal flaw. Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Happy election day, fellow Americans
Today is not a day to complain about plurality voting, single-member districts, or gerrymandering, but to celebrate a fun civic duty. Well, and brag that in Oregon, we have universal vote-by-mail, so we can lounge around with a beer in one hand and a voter pamphlet in the other while filling out our ballot. :) Have a great day, everyone! Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Voting Requirements
Greg Nisbet wrote: Breaking a bit with voting methods, I would like to bring up another issue regarding one's ability to influence politics: suffrage. As the only one here not legally qualified to vote, I must express dissatisfaction with the status quo. There were several historical requirements for being able to vote: 1. Citizenship 2. Residency 3. Age 4. Criminal Record 5. Sex 6. Race 7. Class (arbitrary non-race inherited characteristics) 8. Wealth Half of these requirements are gone, only the first four remain. I disagree with 3 and 4 (and to a lesser extent 1 and 2). I think #1 is necessary by definition. Even if you extended the franchise to everyone, that just means that everyone would be considered citizens. Quoting from Wikipedia (as an example, rather than a reference) Citizenship is membership in a political community (originally a city or town but now usually a country) and carries with it rights to political participation; a person having such membership is a citizen. On the subject of age, rights and responsibilities should be shared among citizens. A child who does not have the same responsibilities as an adult (to defend the country, for example), or is not considered an adult in a court of law, might be excluded from the right to vote. (As a side note, this is one of my disagreements with Selective Service -- my sister served in the Air Force, so I know first hand it is not a lack of ability but political will that keeps the requirements for citizen involvement different for men and women.) As for my own political view, I think Robert Heinlein's idea (Service Equals Citizenship) is rather interesting -- it's certainly fairer than Citizenship Equals Service that accompanies a draft. Make both military and civilian service acceptable, and open it to anyone who can complete a specified period of service to the nation, and you wouldn't have to worry about age or birth requirements -- a 14-year-old Canadian could join if he was willing and able to serve. Of course, this is all part of my sneaky plan to reduce the number of lawyers and politicians, since I'd require both groups to be citizens. :) On a more serious note, my view is that citizenship has a certain value, and confers a certain obligation. Exchanging value for value seems fair, and requiring a person to serve the country they want to vote in is no more onerous than requiring them to play taxes (which are in effect, requiring them to set aside a portion of their time and labor in service to their country). I'm probably in a tiny minority on this subject, though. Here is why: A felony is simply a 'serious' crime. Who defines serious? What stops the government from making dissent a felony and disenfranchising political opponents? If that is too extreme, how do we know the government's definition of a felony is reasonable? There is no external judge and the penalty is inability to influence the system. Hence those affected by the system really cannot contest it. In addition the laws vary by state creating weird discrepancies. Preventing children from voting is IMHO wrong. My argument is simply going to be one of paternalism because I am quite fond of making anti-paternalism arguments. Very few people would argue that 5-8 should be reinstated. Yet 8 might arguably lead to 'better' results. Wealthier people tend to be more educated and if you have educated people making decisions you end up with 'better' decisions. Most people would reject this argument on the grounds of civil rights. Let me put this in perspective. By extending the right to vote to all adults, anyone who does not support some sort of education requirement for voting is conceding that it is not justifiable to disenfranchise on the grounds that you will pollute the ballot pool due to ignorance. I say it simply doesn't make sense that children can be compelled by the government to do various things yet there is no check on its power. We are smart enough to commit crimes, but stupid enough to endanger the already threadbare fabric of American democracy. 1 and 2 are slightly less serious, but I think their role should be changed. I say let noncitizens vote in local elections. They live there and pay their taxes, I see no reason why they shouldn't be able to vote on matters concerning their community. At higher levels, I would argue that the government needs to protect itself from outside interests messing with its politics. So it's more of a national security argument than anything else. Still, America is far too stingy with citizenship. It ought to be kinder to resident aliens. They mean us no harm; they are only trying to make a living. Ius Solis places strong restrictions on those without the privelidge of being born here. This issue is relatively important. Maybe not quite so much as getting FPTP removed, but still pretty high up there. What are your thoughts on disenfranchisement and the like? Election-Methods
Re: [EM] A computationally feasible method (algorithmic redistricting)
There was a discussion of district-drawing algorithms on the election-methods list a few years back. I've always thought that taking centroidal Voronoi cells with equal populations was an elegant way to do it. Here's an example of standard Voronoi cells and the centroidal version I pulled off of Google: http://www.mrl.nyu.edu/~ajsecord/npar2002/html/stipples-node2.html The other possibility I liked was allowing voters to vote for the districts they wanted -- either for the next election, or more entertainingly, the current one. People have a pretty good feel for what mapping is compact and reasonable, and which ones are ridiculous, especially if they can compare them. You could have certain criteria that must be met -- like all districts must be contiguous -- and sort the maps by some metric, like from shortest to longest aggregate perimeter. You could have all qualifying parties submit a map, as well as any group that gets above a certain number of signatures in a petition. Michael Rouse (The last time I posted, things like line breaks disappeared, so I apologize if this happens again.) greg wrote: From: Kathy Dopp [EMAIL PROTECTED] From: Raph Frank [EMAIL PROTECTED] Brian Olson suggests this approach for his anti-gerrymandering proposals. http://bolson.org/dist/USIRA.html and http://bolson.org/dist/ I suggested a similar mathematical method for drawing Congressional districts a few years ago. I like Brian's suggestion - and particularly like his side-by-side state district maps, so I modified my page on drawing districts to include links to his: See http://electionmathematics.org/ and click on Drawing Districts. I've added this link to my collection of algorithmic redistricting proposals. I've been collecting references to algorithmic redistricting proposals on my site on a post related to comments by the 'Rose Report' on the topic. See: http://allaboutvoting.com/2007/12/01/the-rose-report-on-algorithmic-redistricting/ and http://allaboutvoting.com/category/algorithmic_redistricting/ -Greg Wolfe http://AllAboutVoting.com Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[Election-Methods] Is rangevoting.org down? (plus some questions on converting Range to Approval)
, and a smoothed median of 4.248. With my method above, the interpolated median would be the eighth element in the set, or 4.2 (the 4's are symmetrically distributed as 3.6, 3.8, 4.0, 4.2, 4.4, and the second to the highest element in that set is 4.2). It would be interesting to see what resulted from the different ways of calculating it (Rob Brown considered values immediately above and/or below the median -- between the 4's and 5's in this case -- while I just considered the 4's.) I'll leave that there, since I've drifted rather far afield from my question about what happened to rangevoting.org. :) Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
[Election-Methods] Test message/resending Using range ballots as an extension of ranked ballot voting
Hi, everyone. I was just sent a note letting me know my last message was in an unreadable format (a copy of it here: http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20080308/a1502ffe/attachment.html), so I thought I'd resend it using Thunderbird instead of the web-based email program I used before. If someone can let me know if the formatting is garbled (I know the content is often garbled, but that's a given :) ) then please let me know. Thanks! (I wouldn't re-send it, but I'd like it to appear in the archive correctly. Not sure what happened last time, though). The text between the underlines () is what I wrote before. ___ Snipping the message: ** On Mar 3, 2008, at 1:45 , [EMAIL PROTECTED] [EMAIL PROTECTED] wrote: [EMAIL PROTECTED]: Can you also clarify a bit how step 3 is counted when some candidate X is beaten by two other candidates (Y and Z). I find the proposed method interesting since it seems to aim at electing good winners (using a function minimizes the problems caused to the voters, from one point of view). I'd be happy to try. Do you have an example election for me to play with? I'm assuming you mean where I said 3. If there is no Condorcet winner, find the shortest distance (sum of individual ranges) necessary to produce a Condorcet winner. Sorry for some delay in replying. Here's one quick example. 1: A=10 B=2 C=1 D=0 1: A=10 C=7 B=6 D=0 1: B=10 C=6 A=5 D=0 3: C=10 D=5 A=1 B=0 3: D=10 B=4 A=3 C=0 C is now beaten by both A and B, and C has to win them both in order to become a Condorcet winner. What is the shortest distance (sum of individual ranges) for C in this example and how do you count it? ** Okay, here's how I did it by hand (sorry if it's a bit cryptic). Given the following: 1: A=10 B=2 C=1 D=0 1: A=10 C=7 B=6 D=0 1: B=10 C=6 A=5 D=0 3: C=10 D=5 A=1 B=0 3: D=10 B=4 A=3 C=0 The question was: C is now beaten by both A and B, and C has to win them both in order to become a Condorcet winner. What is the shortest distance (sum of individual ranges) for C in this example and how do you count it? Here are the number of pairs each way: AB (1+1+3) AC (1+1+3) AD (1+1+1) BA (1+3) BC (1+1+3) BD (1+1+1) CA (1+3) CB (1+3) CD (1+1+1+3) DA (3+3) DB (3+3) DC (3) Simplifying (numbers in parenthesis indicate surplus votes) and showing the pair relations: AB (1) AC (1) BC (1) CD (3) DA (3) DB (3) To remove the relation AB, it would take 1 vote, the smallest total distance of which is 1 (1-0). To remove the relation AC, it would take 1 vote, the smallest total distance of which is 3 [(10-7) or (3-0)] To remove the relation BC, it would take 1 vote, the smallest total distance of which is 1 (2-1) To remove the relation CD, it would take 3 votes, the smallest total distance of which is 11 [(1-0)+(10-5)+(10-5)] To remove the relation DA, it would take 3 votes, the smallest total distance of which is 12 [(5-1)+(5-1)+(5-1)] To remove the relation DB, it would take 3 votes, the smallest total distance of which is 15[(5-0)+(5-0)+(5-0)] To make A the weak Condorcet winner (A=B,C,D), removing the relation DA is sufficient. The total distance is 12. To make B the weak Condorcet winner (B=A,C,D), removing the relation AB and DB is sufficient. The total distance is 16 (1+15) To make C the weak Condorcet winner (C=A,B,D), removing the relation AC and BC is sufficient. The total distance is 4 (3+1) To make D the weak Condorcet winner (D=A,B,C), removing the relation CD is sufficient. The total distance is 11. Using this method, C would be the winner, since 4 is the shortest distance. The complete order is CDAB. (I use the weak Condorcet criterion, because an infinitesimal amount added to either candidate in a tie is sufficient to create a winner.) Let me know if anything is unclear, and I'll try to give a better explanation (grin). I might play around with the same election and see what removing the lowest order of preferences (and not just the closest preferences) would yield. Michael Rouse. Anyway, if it's garbled but readable enough to see this line, let me know. Or if it came through fine, that would be nice to know, and I might try a test with the webmail program again. Thanks! Mike Election-Methods mailing list - see http://electorama.com/em for list info
[Election-Methods] IRV/Approval/Range comparisons on Wikipedia
I was briefly skimming the discussion area for Instant Runoff Voting in Wikipedia (available here: http://en.wikipedia.org/wiki/Talk:Instant-runoff_voting ), and noticed where one of the contributors complained that comparisons to Approval Voting ignored, quote, its theoretical criteria include susceptibility to strategic voting, which is one of AV's greatest flaws. Approval Voting is notoriously easy to game: you simply don't vote for strong candidates that you actually approve of but are not your first choice. That strategy introduces the same spoiler effect as plurality. Approval also has a terrible history in the U.S. unquote. He then apparently removed material comparing IRV to Range and Approval voting because they were not based on reliable sources. In addition, in a comment about the Yee diagrams, he said all of the voters are voting honestly when in some systems there is an easy and highly advantageous means of tactical voting, though I'm not sure how voting strategically would make the choice diagrams for IRV rational. I'm not trying to start an edit war on Wikipedia, but I do know there are some proponents of both methods who have made, to my mind at least, rather convincing arguments comparing the suitability of IRV to AV and RV. I thought it might be interesting to at least mention peer-reviewed analysis of IRV, Approval, and Range if someone knew of such a study. Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
