Re: [EM] Markus, criteria similiar to majority rule definition
Dear Mike, I wrote (28 March 2005): > Suppose V is the number of voters. > > Suppose d[X,Y] is the number of voters who > strictly prefer candidate X to candidate Y. > > Suppose p(z)[X,Y] is the strength of the strongest > path from candidate X to candidate Y when the strength > of a pairwise defeat is measured by "z" (e.g. "z" = > "margins", "z" = "winning votes", "z" = "votes against"). > > Then I proposed the following criterion in 1997: > >If p(wv)[A,B] > V/2 and p(wv)[B,A] < V/2, >then candidate B must be elected with zero >probability. > > Steve Eppley proposed the following criterion in 2000: > >If d[A,B] > V/2 and p(wv)[B,A] < V/2, >then candidate B must be elected with zero >probability. You wrote (29 March 2005): > Yes, but to outdo a majority pairwise vote, it's necessary > for that MPV to be in a cycle of MPVs _all of which are at > least as strong as it is_. In 1997, I proposed the following method (Schulze method, Schwartz sequential dropping, cloneproof Schwartz sequential dropping, beatpath method, beatpath winner, path voting, path winner): If p(z)[A,B] > p(z)[B,A], then candidate B must be elected with zero probability. Markus Schulze Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Conversationis with people new to voting systems
This isn't complicated: CR is better received by people than Approval is. ...even if someone tells us that he can't imagine it in use. If people later realize that the greater "resolution" is unnecessary, that would be great. Then they'll switch toi Approval. In the meantime, though, people are a lot more receptive to CR than to Approval. Periodically people independently propose CR. Mike Ossipoff _ Dont just search. Find. Check out the new MSN Search! http://search.msn.click-url.com/go/onm00200636ave/direct/01/ Election-methods mailing list - see http://electorama.com/em for list info
[EM] Markus, criteria similiar to majority rule definition
Markus-- You said: Then I proposed the following criterion in 1997: If p(wv)[A,B] > V/2 and p(wv)[B,A] < V/2, then candidate B must be elected with zero probability. Steve Eppley proposed the following criterion in 2000: If d[A,B] > V/2 and p(wv)[B,A] < V/2, then candidate B must be elected with zero probability. I reply: Yes, but to outdo a majority pairwise vote, it's necessary for that MPV to be in a cycle of MPVs _all of which are at least as strong as it is_. That's how my majority rule definition differs from your criterion and from Steve's Beatpath Criterion. By the way, Steve's Beatpath Criterion is very useful for determining compliance with the majority defenisive strategy criteria. A method that meets BC meets all the majority defensive strategy criteria. I've never defined BC in a universallly applicable way, because I've only used it for testing rank methods for compliance with the majority defensive strategy criteria. Mike Ossipoff _ Express yourself instantly with MSN Messenger! Download today - it's FREE! http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/ Election-methods mailing list - see http://electorama.com/em for list info
[EM] James--Majority rule definition, 29 March, 0632 GMT
I'd said: If a majority prefer X to Y, that's a majority pairwise preference (MPP). The strength of that MPP is measured by the number of voters who prefer X to Y. You say: Well, obviously that's one way to define the strength of a pairwise defeat. Margins provides another way, and cardinal pairwise yet another. I reply: No, that obviously is _not_ a way of defining the strength of a pairwise defeat. It's a way of defining the strength of a majority pairwise preference, however. One way (but only one way :-) of defining a majority pairwise preference is as an instance of a majority praeferring one candidate to another. And one way of defining the strength of that majoritly pairwise preference has to do with how big a majority that is. Completely arbitrary, of course :-) I'd said: An MPP for X over Y is outdone if there is a sequence of MPPs from Y to X, consisting of MPPs that are all at least as strong as the MPP of X over Y. To violate majority wishes means to elect someone who has an MPP against him that isn't outdone. You say: Lately, I have been defining majority rule violation as the selection of an option outside the Smith set. I reply: The Smith set has nothing to do with majority. You continue: This is close to your definition I reply: No. It bears no resemblence to my definition. You continue: ..., except that you get more specific by assuming that there is a single normative definition for "defeat strength" I reply: We all have heard that there are other definitions for "defeat-strength". Whether they're normative or not, I've told why they aren't as useful for meeting criteria about guarantees of minimizing strategy need. And I've told why they aren't as good in terms of the goal of not overruling avoidably many voters. If saying that something is normative means saying that it's what should be, then I've told you why wv is normative. Now you're talking about majority rule, and so now, instead of majority pairwise preferences, it's majority pairwise votes (MPVs). I suggested measuring the magnitude or strength off such a vote by the magnitude of the majority. Call me original :-) You continued: , and then proceeding to define majority rule along the lines of what Jobst calls the "uncovered set". (I think that's basically it, right?) I reply: You'd have to ask Jobst. But even if my definition of majority rule is the same as Jobst's definition of the uncovered set, then if that means that I defined majority rule along the lines of the uncovered set, that was purely accidental and coincidental. You continue: I have to object to the defeat strength part of your definition, in part on the behalf of cardinal pairwise. Winning votes is surely one way to define defeat strength, and it is not a bad one, but I do not accept it as the one and only definition I reply: I have never said that wv is the only way to define defeat strength. Perhaps you would like me to define defeat strength in all of the possible ways. Forgive me, but it seemed best to only define it in one way, and, if it's ok with you, I chose wv. You don't say how you'd rather define the magnitude of a majority pairwise vote. Margins? You'd like to define the magnitude of a majority vote in terms of the majority and the minority? Most of us woiuld define the magnitude of a majority vote by the magnitude of the majority. In fact, that fundamentally makes more sense than defining the magnitude of a majority vote in terms of the minority. It's normative :-)...,even though I hadn't said that before. Note that I don't say that you can't define it differently, but you must accept that it's ok if we don't all define it as you do. You continue: , and I doubt that very many other people will either [accept my definition of majority rule] I reply But why is that important to you, how many people accept my definition of majority rule. For me, the value of my definition of majority rule is that it's used in my definition of offensive strategy. But my definition of offensive strategy isn't important, even to me. As you've no doubt heard, defensive strategy, the need for defensive strategy, is my strategy concern. So maybe you could change what you're saying, and say that you object to my definition of majoritiy pairwise preference (MPP) and say that you want to define it in terms of margins, instead of being so arbitrary as to derfine the magnitude of a majority pairwise preference in terms of the majority that it refers to. What I said about MPV applies to MPP. But what makes you think that it's important if people accept my definition of the magnitude of a majority pairwise preference, and, hence, my definition of defensive strategy. The defensive strategy criteria aren't based on my definition of defensive strategy. Only their name is based on that definition. So are you fighting about a name? The matter of whether or not a method meets a criterion is unaffected by the cr
Re: [EM]Definite Majority Choice, AWP, AM
Hello James and All, On Mar 26, 2005, at 14:05, James Green-Armytage wrote: Yes, but you've not yet understood the virtue of cardinal-weighted pairwise and approval-weighted pairwise. I request that you read my cardinal pairwise paper, as most of the arguments used therein apply to AWP as well. http://fc.antioch.edu/~james_green-armytage/cwp13.htm No Condorcet method can escape the possibility of the burying strategy, but CWP and AWP make it so that you can't change the result from a sincere CW to someone who is very *different* from the sincere CW (except by large cycle strategies that are probably to complex to be realistic). I think there is some confusion here. My intention was not to criticize the cardinal pairwise or other methods but just to comment on the (voting method independent) evaluation criteria that were used when studying the voting examples. My statement was thus that if sincere votes would be X but real votes are Y, it is very difficult (maybe not possible in practice) to construct a voting method that would take X into account when making decisions. This is because only Y is known and it is too difficult to guess what X was (or to identify which individual votes are strategic in Y). We can only use some generic means (=no reference to the actual sincere votes X) when trying to eliminate strategies. Agreed? Concerning the rest of your mail I think your analysis of this example is good, and related voting methods that add new information to basic ranking are a very fruitful area of study. Since I commented the evaluation criteria only, my intention was not to say that K/Kerry should not win this election. I only said that being a sincere Condorcet winner is not a good argument to favour K. I agree that the ratings give additional information that can be used to determine how the cycles should be solved, and in this case evidence supports Kerry quite well. I believe I'm quite in line with you here. The best voting methods or voting organizers can do in this situation is to try to discourage strategic voting. If the reward-strength/probability of a given strategy obviously outweighs the risk strength/probability, then we should assume that voters will tend to use the strategy. Perhaps they won't, but we should err on the side of caution, especially where flagrant incursions are concerned. Anything else would be naive and dangerous. I agree. But in addition to "risk strength/probability" we should cover also things like difficulty to understand/apply, difficulty to agree on the strategy etc. Also the "level of distortion" (a strategy may lead e.g. to election of the second best or the worst candidate) should be taken into account when evaluating the need to defend against different strategies. Happy birthday to you. Best Regards, Juho Election-methods mailing list - see http://electorama.com/em for list info
[EM] James: Strategy definitions and criteria, 29 March, 0521 GMT
You said: "Burying" means one thing in the context of funereal services. I reply: No, I didn't say that Blake uses "burying" differently from its usage in funerals, or even that he uses it differently from its physical meaning. I said that he uses it differently from the meaning that it always has, its general meaning, without regard to any one particular context. To bury something means to put it under something else, or to conceal it. That's exactly the meaning of burying that I use when I refer to favorite-burial strategy in Plurality or IRV. If that isn't burying to Blake or to you, then you're using a different meaning of burying, different from what the word means to others. But I have no complaint if you or Blake invent new meanings for words. You continue: In the context of voting strategy, it has been given a definition by Blake I reply: Yes, a meaning different from the accepted general meaning of the word. You'd said: Your strategic analysis centers on what strategy voters should use to promote the election of the candidate whom they regard to be the sincere CW. I replied: No, in regards to my criteria and strategy definitions, I'm not interested in what strategy voters should use. I'm interested in what strategies they should need in order to protect the win of a CW, or to protect majorilty rule. You say: That sounds like pretty much the same thing to me. I reply: Quite possibly it sounds to you like the same thing, but it isn't the same thing, and isn't even a similar thing. What someone should do, and what someone should need to do are actually entirely different things. I don't ask you to understand that, and I'm not going to explain it to you. You can take my word for it. I'd said: Excuse me, James. Give me a grounding in the basics :-) Read Blake's EMR page at Condorcet.org. I don't subscribe to all of his definitions, and I don't agree with him on all controversial issues (e.g. margins vs. wv), but I think that some of his terms (e.g. burying, compromising, push-over, crowding) form a useful basis for understanding strategic possibilities in different methods. I reply: Thank you for that grounding in the basics. :-) If Blake's website is the basics, then I fully admit that I'm not grounded in the basics. You say: "Normative" often stands in contrast to "positive". A positive judgement is a judgement about how things are, while a normative judgement is a judgement about how things should be... specifically what rules and organizational systems should be used. I reply: But "should" needs context, and so your definition of "normative" isn't complete. Suppose that, by the actual vote count in 2004, combined with the number of Black Democrats who were denied their right to vote, Kerry won. That Kerry win was normative, in the context of the vote count and the intentions of people who tried to vote but were prevented from voting. But suppose instead we're talking about what kind of a president we should have. Suppose additionally that we shouldn't be sending Americans to die, and killing thousands of Iraqis, in order to complete the conquest of Iraq, and suppose that it would be better to have a president who, unlike Kerry, doesn't say that he wants to do that. Then, in that broader context, the election of Nader or someone like him was normative. James, it's normative that you not use words that you can't define. You continue: In this context, I meant to say that by incorporating the concept of the CW into your strategy criteria,... I reply: SFC and my Condorcet's Criterion mention the CW. You continue: ...you are already assuming that Condorcet methods are normative, i.e. that they should be used. I happen to agree that they should be used, but I think that basic strategy terms should be established independently from this conclusion. Your definitions are loaded. That is, obviously designed to support methods that you have already decided to advocate. I reply: James, apparently things can be obvious to you without being true or even appearing to be true. By your reasoning, then, if Condorcet wrote Condorcet's Criterion, then, since Condorcet's proposed methods meet Condorcet's Criterion, that means that Condorcet's Criterion is "loaded", because it was obvioulsly designed to support methods that Condorcet had already decided to advocate. You presumably believe that Condorcet said something like: "I've previously decided [for unspecified reasons] that I want to advocate certain pairwise-count methods that will elect a candidate who pairwise-beats each of the others. How shall I promote those methods? Aha! I'll say that if a candidate pairwise-beats all of the others then he should win. I don't really believe that for a minute, but I'll say it if it will help promote the methods that I want to propose, the methods that elect a candidate who pairwise-beats all of the others, methods that I promote for some entirely different reason." James
[EM]Definite Majority Choice, AWP, AM
Ted, Russ, Forest, James,Juho and others, I think that Ted's draft public "Definite Majority Choice" proposal is excellent, in the sense that anything that might be slightly better would be more complicated and/or less intuitive. Two contending methods that use the same style of ballot are James G-A's Approval-Weighted Pairwise and my Approval Margins. I've found a couple of examples that illustrate differences between the three methods. The first is copied from a Sep.22,04 James G-A post. 3 candidates: Kerry, Dean, and Bush. 100 voters. Sincere preferences 19: K>D>>B 5: K>>D>B 4: K>>B>D 18: D>K>>B 5: D>>K>B 1: D>>B>K 25: B>>K>D 23: B>>D>K Kerry is a Condorcet winner. Altered preferences 19: K>D>>B 5: K>>D>B 4: K>>B>D 18: D>K>>B 5: D>>K>B 1: D>>B>K 21: B>>K>D 23: B>>D>K 4: B>D>>K (these are sincerely B>>K>D) There is a cycle now, K>B>D>K On the "sincere preferences" ballots, the approval scores are B48, K46, D43, while on the "altered preferences" ballots, the approval scores are B48, D47, K46. Approval Margins uses a "defeat-dropper" method, measuring the strengths of the defeats by the margins between the approval scores (but like AWP,determines their "directions" purely by the rankings.) Approval Margins: D>K 47-46 (m+1) K>B 46-48 (m-2) B>D 48-47 (m+1) B's defeat, with an approval margin of -2, is the weakest and so is "dropped". B, the Buriers' favourite but the sincere (and voted) Approval winner,wins. DMC gets the same result by eliminating D and K. AWP differs from AM in the way that it weighs defeats. Quoting James: For a given defeat A over B, the magnitude of the defeat is defined by the number of voters who place A above their approval cutoff and B below their approval cutoff. Approval-Weighted Pairwise: D>K 06 K>B 46 B>D 44 AWP elects the sincere CW, K! I used to think that electing the voted approval loser was absurd if we assume that the votes are sincere, but by that logic we should resolve all top cycles by electing the Approval winner. From that point of view, sometimes electing the approval loser is only a degree "worse" than not always electing the approval winner! Still, I don't see this example being a great advertisement for AWP versus AM because the winner is the sincere Approval winner. My next example is the one I used in my last post on AM. An old example given by Adam Tarr. Sincere rankings: 49 R>C>L 12 C>R>L 12 C>L>R 27 L>C>R C is the CW. 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 R>L>>C 06 C>R>>L 06 C>>R>L 06 C>>L>R 06 C>L>>R 27 L>C>>R Now all the candidates are in the top cycle: L>C>R>L. The approval scores are L82, R55, C51. Approval Margins: L>C 82-51 = +31 C>R 51-55 = -4 R>L 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: L>C 49 C>R 45 R>L 06 AWP gives the same good result as AM! Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] Manipulation Proofing Approval
Approval's weakness is that it is vulnerable to media manipulation. To counteract this we could look at all of the approval winners under all possible media manipulations, and then choose by random ballot from these. Less ambitious, but feasible and adequate: Choose by random ballot from among all of the Strategy A winners. An alternative X is a strategy A winner iff there exist alternatives Y and Z such that X is the approval winner when all voters place their approval cutoff on the Z side of Y. The media tends to encourage the use of strategy A by playing up two candidates, and giving one of them a slight edge over the other. Under pure Approval, the media could pick a strategy A winner X by playing up the Y and Z candidates, slightly favoring Y. How do we find the strategy A winners? For N alternatives, we need to sum an N by N by N dimensional array. The (i,j,k) entry is a one or a zero depending on whether the ballot in question would approve candidate k given candidate i is the most likely to win, and candidate j has the rest of the probability. Candidate k is a strategy A winner iff for some i and j, the (i,j,k) entry in the array sum is larger than the (i,j,m) entry for all m not equal to k. Basically, we are manipulating in favor of each candidate to remove the advantage of the ones that are favored by the media. That's all I have time for now, but what do you think of this idea? Forest Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Democratic Fair Choice
On Tue, 29 Mar 2005, Jobst Heitzig wrote: Dear Folks! Under the working title "Democratic Fair Choice", I described on our Wiki a detailed voting procedure composed from ideas by Forest (most) and me (some): http://wiki.electorama.com/wiki/Imagine_Democratic_Fair_Choice I tried to make it more interesting by writing it as a fictitious television show reporting on an actual election -- hope you have some fun reading it. In short, this is what I suggest: 0. Each candidate simultaneously publishes a ranking of all candidates. 1. Each voter marks one candidate as "directly supported" and arbitrarily many additional ones as "approved". 2. This is transformed automatically into an individual ranking by placing the approved over the unapproved ones and completing the ranking by means of the directly supported candidate's published ranking. This step is the stroke of genius that I never would have thought of. It gives the voter more control than mere candidate proxy. 3. After booths have closed, direct support, approval, and pairwise comparisons are counted. 4. A numbered list of voters grouped by directly supported candidates in order of decreasing direct support is constructed like this: 001-0821461: supporters of C 0821462-1318964: supporters of F ... Then each candidate submits in a sealed envelope a number between 1 and the number of voters. The envelopes are opened in public, and the numbers are added modulo the number of voters, giving the number of the "proposing voter". 5. The published ranking of the proposing voter's directly supported candidate becomes the "proposing order". 6. Only now the approval values and the matrix of pairwise defeats are published, and the winner is the topmost candidate in the proposing order who pairwise defeats all more approved candidates. Essentially, this is "Random Ballot from Forest's set P", but without the need to specify individual rankings, and with no "real" randomization but instead with a sophisticated pseudo-random procedure which is under complete deterministic control by the candidates... I'm quite curious about your thoughts! Great! It's much better than Majority Choice Approval at no extra cost. And remember that with any more complicated ballot, most voters will just copy candidate cards, anyway. Forest Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] LNHarm performance: from B to A
Hello, --- [EMAIL PROTECTED] wrote: > I suggest that (for the sake of completeness) you should also > indicate in how many cases ranking the additional candidate A > changed the winner from one of the other unranked candidates > to candidate A. I found these numbers, although I got them by just running the simulations over again, as that seemed like less work. There were 400,000 CDTT trials, and 200,000 each of Schulze(wv) and Schulze(margins), and I'm again dividing them to be out of 100,000: CDTT,MMPO,FPP: 13.75 LNHarm, 1177 LNHelp, 1315 wins moved from B to A. Schulze(wv): 211.5 LNHarm, 742.5 LNHelp, 1545 wins moved from B to A. Schulze(marg): 284.5 LNHarm, 672 LNHelp, 1254.5 wins moved from B to A. Possibly this information could be used to compare the likelihood of different effects from adding the A preference. For instance, in Schulze(margins), harming an earlier preference seemed to be 22.68% as likely as moving the win from B to A, while under CDTT,MMPO,FPP it happened 1.046% as often, and under Schulze(wv), 13.7% as often. Or, you could compare the chances of harming another candidate to the chances of helping another candidate. The former was 1.17% as likely under CDTT, 28.5% as likely under Schulze(wv), and 42.3% as likely under Schulze(margins). For comparison, these were the original results: >CDTT,MMPO,FPP: 13.7 LNHarm, 1177.5 LNHelp. >Schulze(wv): 193 LNHarm, 750 LNHelp. >Schulze(marg): 306 LNHarm, 675.5 LNHelp. >Schulze(opp): 291.5 LNHarm, 838.5 LNHelp. Kevin Venzke __ Découvrez le nouveau Yahoo! Mail : 250 Mo d'espace de stockage pour vos mails ! Créez votre Yahoo! Mail sur http://fr.mail.yahoo.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: K>D>>B > 5: K>>D>B > 4: K>>B>D > 18: D>K>>B > 5: D>>K>B > 1: D>>B>K > 25: B>>K>D > 23: B>>D>K > Kerry is a Condorcet winner. > > Altered preferences > 19: K>D>>B > 5: K>>D>B > 4: K>>B>D > 18: D>K>>B > 5: D>>K>B > 1: D>>B>K > 21: B>>K>D > 23: B>>D>K > 4: B>D>>K (these are sincerely B>>K>D) > There is a cycle now, K>B>D>K 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 D>>K>B 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] Democratic Fair Choice
Dear Folks! Under the working title "Democratic Fair Choice", I described on our Wiki a detailed voting procedure composed from ideas by Forest (most) and me (some): http://wiki.electorama.com/wiki/Imagine_Democratic_Fair_Choice I tried to make it more interesting by writing it as a fictitious television show reporting on an actual election -- hope you have some fun reading it. In short, this is what I suggest: 0. Each candidate simultaneously publishes a ranking of all candidates. 1. Each voter marks one candidate as "directly supported" and arbitrarily many additional ones as "approved". 2. This is transformed automatically into an individual ranking by placing the approved over the unapproved ones and completing the ranking by means of the directly supported candidate's published ranking. 3. After booths have closed, direct support, approval, and pairwise comparisons are counted. 4. A numbered list of voters grouped by directly supported candidates in order of decreasing direct support is constructed like this: 001-0821461: supporters of C 0821462-1318964: supporters of F ... Then each candidate submits in a sealed envelope a number between 1 and the number of voters. The envelopes are opened in public, and the numbers are added modulo the number of voters, giving the number of the "proposing voter". 5. The published ranking of the proposing voter's directly supported candidate becomes the "proposing order". 6. Only now the approval values and the matrix of pairwise defeats are published, and the winner is the topmost candidate in the proposing order who pairwise defeats all more approved candidates. Essentially, this is "Random Ballot from Forest's set P", but without the need to specify individual rankings, and with no "real" randomization but instead with a sophisticated pseudo-random procedure which is under complete deterministic control by the candidates... I'm quite curious about your thoughts! Yours, Jobst Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] median rating / lower quartile
I would just like to point out that median rating is to range voting as Bucklin is to Borda. This was noted back in the days when we first considered Majority Choice Approval (Bucklin based on CR ballots of resolution 3), and were exploring to see if there might be any fruitful generalization to higher resolution CR ballots. Since "Social Utility" is not a method, but is one probe for gauging a method, why not publish both Mean SU, and Median SU, as well as standard deviations and interquartile distances for the performance of various methods in simulations? Forest Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] (oops) Smith//Truncation set
Markus, --- Kevin Venzke <[EMAIL PROTECTED]> wrote: > I don't remember you mentioning this set again. I wonder if that's because the > Smith//Truncation set is not necessarily a subset of the Smith set. I immediately realize why you might not need to mention the Smith//Truncation set again: Schulze(wv) always elects from this set. Kevin Venzke __ Découvrez le nouveau Yahoo! Mail : 250 Mo d'espace de stockage pour vos mails ! Créez votre Yahoo! Mail sur http://fr.mail.yahoo.com/ Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] LNHarm performance; majority rule definitions
Dear Markus, --- [EMAIL PROTECTED] wrote: > I suggest that (for the sake of completeness) you should also > indicate in how many cases ranking the additional candidate A > changed the winner from one of the other unranked candidates > to candidate A. That will be easy enough to find. The only unranked candidate would be B, though. I'll post some statistics later. >Then I proposed the following criterion in 1997: > > If p(wv)[A,B] > V/2 and p(wv)[B,A] < V/2, > then candidate B must be elected with zero > probability. > >Steve Eppley proposed the following criterion in 2000: > > If d[A,B] > V/2 and p(wv)[B,A] < V/2, > then candidate B must be elected with zero > probability. That's interesting. The CDTT contains each candidate who is not disqualified by your criterion. My failed attempt to improve on the CDTT contained each candidate not disqualified by Steve Eppley's version of the criterion. (I posted this before, but the latter wasn't monotonic: Suppose majority-strength defeats are A>B>C>A and D>B. Eppley's criterion says B can't win. But adding some preferences for A so that a majority votes A>D results in B no longer being disqualified, which is harmful to A.) It seems that the CDTT is mostly equivalent to the "Smith//Truncation set" you defined: http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-May/001483.html Except that you wanted it to be somewhat easier to reach a "majority." I don't remember you mentioning this set again. I wonder if that's because the Smith//Truncation set is not necessarily a subset of the Smith set. Kevin Venzke __ Découvrez le nouveau Yahoo! Mail : 250 Mo d'espace de stockage pour vos mails ! Créez votre Yahoo! Mail sur http://fr.mail.yahoo.com/ Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM]CNTT,QLTD ? (enquiry from John Hodges)
Chris, --- Chris Benham <[EMAIL PROTECTED]> wrote: > Participants, > I've had a request from John Hodges, who used to > subscribe and contribute to EM. > > > could you ask the EM folk for an evaluation of the > properties of CNTT,QLTD? In short, it satisfies Condorcet and Smith but fails everything that Bucklin fails. Since you're not eliminating non-Smith members, it doesn't satisfy "Local IIA." > in terms of criterion compliances,but John thinks that > CNTT,QLTD might have compensating practical > advantages. I don't think so; you'd have to keep track of the Bucklin matrix in addition to the pairwise one. And if you eliminated non-Smith members, you'd have to reconsider each ballot. It also seems to me that Bucklin is easier to explain than QLTD, while satisfying the same criteria. Kevin Venzke __ Découvrez le nouveau Yahoo! Mail : 250 Mo d'espace de stockage pour vos mails ! Créez votre Yahoo! Mail sur http://fr.mail.yahoo.com/ Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] James--CP, AERLO, ATLO, defensive strategy definiltion
Dear Mike, you wrote (27 March 2005): > I told Markus that I was going to define majority > rule soon. My definition of majority wishes is > similar, and I guess that I'd better state that > definition now, instead of being vague about what > I mean by majority wishes and majority rule. > > If a majority prefer X to Y, that's a majority > pairwise preference (MPP). The strength of that > MPP is measured by the number of voters who prefer > X to Y. > > An MPP for X over Y is outdone if there is a sequence > of MPPs from Y to X, consisting of MPPs that are all > at least as strong as the MPP of X over Y. > > To violate majority wishes means to elect someone who > has an MPP against him that isn't outdone. > > Protecting majority wishes means avoiding a violation > of majority wishes. > > [end of definition of protecting majority wishes] > > Majority rule: > > X has a majority pairwise vote against Y if a majority > vote X over Y. > > Substituting majority pairwise vote for majority pairwise > preference in the definitions above leads to a definiltion > of majority rule instead of majority wishes. > > Well, it's better to say it explicitly: > > X has a majority pairwise vote (MPV) against Y if a > majority vote X over Y. > > An MPV's strength is measured by the number of people > who vote X over Y. > > An MPV for X over Y is outdone if there's a sequence of > MPVs from Y to X consisting of MPVs that are all at least > as strong as the one for X over Y. > > Violating majority rule means electing someone who has > an MPV against him that isn't outdone. > > [end of definition of violating majority rule] Such criteria have already been proposed in the past. Suppose V is the number of voters. Suppose d[X,Y] is the number of voters who strictly prefer candidate X to candidate Y. Suppose p(z)[X,Y] is the strength of the strongest path from candidate X to candidate Y when the strength of a pairwise defeat is measured by "z" (e.g. "z" = "margins", "z" = "winning votes", "z" = "votes against"). Then I proposed the following criterion in 1997: If p(wv)[A,B] > V/2 and p(wv)[B,A] < V/2, then candidate B must be elected with zero probability. Steve Eppley proposed the following criterion in 2000: If d[A,B] > V/2 and p(wv)[B,A] < V/2, then candidate B must be elected with zero probability. Markus Schulze Election-methods mailing list - see http://electorama.com/em for list info
[EM]CNTT,QLTD ? (enquiry from John Hodges)
Participants, I've had a request from John Hodges, who used to subscribe and contribute to EM. > could you ask the EM folk for an evaluation of the properties of CNTT,QLTD? That stands for "Condorcet(Net) Top Tier, Quota-Limited Trickle-Down", which means "order the candidates using the QLTD method and then elect the highest-ordered member of the Smith set". QLTD is a Bucklin-like method invented by Woodall. Quoting from one of his papers: > My first serious attempt to find a rule that would rival AV resulted in what I call Quota-Limited Trickle-Down (QLTD). Although this has now been superseded by DAC, I describe it here because it is simpler. One starts by crediting every candidate with all their first-preference votes. If no candidate exceeds the quota (of half the number of votes cast), then one gradually adds in the second-preference votes, then the third-preference votes, and so on, until some candidate reaches the quota. For example, it may be that if one credits every candidate with all their first-preference votes, all their second-preference votes and 0.53 times their number of third-preference votes, then exactly one candidate is brought up to the quota; that candidate is then declared elected. > > > The method fails both Clone-Winner and Clone-Loser. Methods like CNTT,DSC and CNTT,DAC seem to be better in terms of criterion compliances,but John thinks that CNTT,QLTD might have compensating practical advantages. Chris Benham Find local movie times and trailers on Yahoo! Movies. http://au.movies.yahoo.com Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] James: Part II, strategy terms
Hi Mike, Replies follow on the subject of strategy terms... > > >Apparently we aren't interested in the same distinctions, that's all. > >By the way, I often use the word "bury" or "burial", meaning to vote a >candidate lower than you would if you voted your preferences and didn't >falsify any preferences. I use that term in that way when I speak of >favorite-burial. You want to give a different meaning to "bury", a >meaning >not supported by the usual meaning of that word. Fine. But you've got to >distinguish between how you like to define things and how others should >define things. Blake has defined the "burying strategy", in the context of voting strategy, in a particular way. I have produced a slightly modified version of his definition, but I think that his basic concept is what's important, rather than my slight tinkering with it. Others beside myself have made use of his terms. "Burying" means one thing in the context of funereal services. In the context of voting strategy, it has been given a definition by Blake, and I (and others) find that definition quite useful. > I wrote: >Your strategic analysis centers on what strategy voters should use to >promote the election of the candidate whom they regard to be the sincere >CW. > you replied: >No, in regards to my criteria and strategy definitions, I'm not >interested >in what strategy voters should use. I'm interested in what strategies >they >should need in order to protect the win of a CW, or to protect majorilty >rule. That sounds like pretty much the same thing to me. > >Excuse me, James. Give me a grounding in the basics :-) Read Blake's EMR page at Condorcet.org. I don't subscribe to all of his definitions, and I don't agree with him on all controversial issues (e.g. margins vs. wv), but I think that some of his terms (e.g. burying, compromising, push-over, crowding) form a useful basis for understanding strategic possibilities in different methods. > >I assume that next you're going to tell me where you believe that I go >wrong >in terms of the basics. > >You continue: > >, and perhaps to start from a place that doesn't >presuppose the normativeness of a particular algorithm. > >I reply: > > > >Well, give me a grounding in this basic: I have no idea what "normative" >means. It isn't that I haven't loooked it up. But the definition that I >find >when I look up "normative" is one that couldn't be consistent with its >use >in voting system discussion. I've begun to accept the fact that >"normative" >is intranslatable, rather like the German word "gar" "Normative" often stands in contrast to "positive". A positive judgement is a judgement about how things are, while a normative judgement is a judgement about how things should be... specifically what rules and organizational systems should be used. In this context, I meant to say that by incorporating the concept of the CW into your strategy criteria, you are already assuming that Condorcet methods are normative, i.e. that they should be used. I happen to agree that they should be used, but I think that basic strategy terms should be established independently from this conclusion. > >Oh, ok, so that's what it means to pre-suppose the normativeness of a >particualr algorithm: "definiltions that seem to be somewhat loaded, >rather >than starting somewhere a bit more flexible." > >Thanks for the precise clarification of what you meant. Your definitions are loaded. That is, obviously designed to support methods that you have already decided to advocate. When you had your "technical evaluation of election methods" page on electionmethods.org, you made no mention of the fact that IRV passes later-no-help/later-no-harm and is therefore immune to the burying strategy, because you had already decided that you didn't want to promote IRV. > >I don't claim to be able to tell you what compromising-compression means, That's too bad, since I gave you the date of the posting where I defined it. That's 3/29/04. But anyway, here's the direct link: http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-March/012515.html In that post (one year ago tomorrow) I discussed the difference between your criteria and Blake's criteria in some depth. Hence, it's closely related to our current discussion, and I request that you read it. > >As I said in the message to which you're replying, your definitions make >reference to the intentiions, beliefs and hopes of the voters using the >strategy. Maybe that would be a good thing for you to keep in mind. Yes, it is. > >There's nothing wrong with telling what you think. But you forgot to tell >why you think it. >Basically, you're saying that it would be helpful to work from your >definitions. I think of them more as Blake's terms than mine. My definitions are only a slightly modified version of his definitions, and I'm open to the possibility that his
