[EM] Re: SSD is BeatpathWinner
Markus-- You say: In my opinion, the statement "If p(z)[A,B] > p(z)[B,A], then candidate B must be elected with zero probability" defines a _method_ and not a _criterion_ because: [...] I reply: Fine. You don't have to convince me. If you say that that defines Schulze's method, then it defines Schulze's method. No argument from me. You continue: Therefore, what you call "BeatpathWinner" or "SSD" or "CSSD" are only different tie-breaking strategies for the Schulze method that I proposed in 1997. I reply: Then you're saying that BeatpathWinner is an instance of Schulze's method. How about this method: MajorityBeatpathWinner: X has a majorilty beatpath win against Y if there's a majority beatpath from X to Y, and the strongest beatpath from X to Y is stronger than the strongest beatpath from Y to X. A candidate wins if no one has a majority beatpath win against him/her. [end of MajorityBeatpathWinner definition] This is also an instance of Schulze's method, as you define it above. Schulze's method is a very broad family of methods indeed :-) And that's not even counting the earlier version(s) that used beat-and-tie paths instead of beatpaths. 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] Distance measure--Are issue-position differences additive?
Bart-- You wrote: This doesn't seem possible for more than one dimension-- don't Merrill's models show sincere Borda yeilding slightly higher SU than the CW in two dimensions, and Approval higher than both when there are only three candidates? I reply: I don't know; I'd have to check. But it can be demonstrated that if distance is city-block distance, then the CW always maximizes SU, and that if distance is Euclidean distance, then the CW maximizes SU under the conditions I described, including when the population density is a normal function about some center, in each dimension. Why does the CW maximize SU with city-block distance? Say we start at the median point, the point that's at the voter-median in each dimension. (By "going away from" or "going toward", I mean increasing or decreasing distance to). Say we depart from that point in one of the issue-dimensions. Immediately after departure, we're going away from more voters than we're going toward, in that dimension. With city-block distance, if half of the voters are on the +X side of the central point, and half on the -X side, and if we're on the +X side, and going farther in the +X direction, we're going away from every voter whose X co-ordinate is less than ours, at the same rate at which we're going toward all the voters whose X co-ordinate is more than ours. So, as soon as we've gone any distance in the +X direction, then, continuing in that direction, we're going away from more voters than we're going toward, because we've added some voters who are in the -X direction from us, because we've passed the X co-ordinate of those voters. That's true for any issue-dimension, and it's true for any position away from the voter median point. Excuse that hasty argument. But you see that it's true, that going away from the voter-median point increases the summed distance to the voters. On another day I"ll demonstrate the correctness of my claim about Euclidean distance. By the way, though, I've told why city-block distance is more meaningful in spatial models. I could add that von Neuman & Morgenstern spoke of using hypothetical lotteries to put completely different things on a single common utility scale. That further strengthens the argument for city-block distance. Also, even when Euclidean distance is used, doesn't the relative scale of issue-distances in the various dimensions matter? If so, and if there's an effort to make that right, then doesn't that mean relating the importance of distances in the various issue-dimensions? And if that can be done, why not just add them up? If the various issue-space distances are all just amounts of the same quantity, disutility. Again, these arguments are hasty, and probably not well-worded. 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
Re: [EM] condorcet methods
Curt, --- Curt Siffert <[EMAIL PROTECTED]> wrote: > Operating from the following assumptions: > > 1) There is never a viable reason to select a candidate other than the > Condorcet Winner if a CW exists > 2) Any voting criterion that is inherently incompatible with electing a > Condorcet Winner should be discarded Heh! > 3) All Condorcet "tiebreakers" pass some criteria and fail others > > I am just curious if there is a *set* of Condorcet methods, such that > all popular criteria are met by at least one of the methods. I wonder what criteria you have in mind. The best Condorcet methods seem to be Schulze, Tideman, and Jobst's River method. Some criteria aren't met if winning votes aren't used as the measure of defeat strength. > Then the population could be told that the election will select a > Condorcet Winner if one exists, and if not, one of the tiebreaking > methods would be selected randomly. It would be better if they all met > the Smith or Schwartz criteria. > > It remove the motivation for targetted tactical voting if there was > always a chance the tactical voting would backfire. I think this won't help much... The three methods above behave identically given a three-candidate cycle, and most strategy examples I've seen only use three candidates. 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] condorcet methods
Curt Siffert wrote: Then the population could be told that the election will select a Condorcet Winner if one exists, and if not, one of the tiebreaking methods would be selected randomly. It would be better if they all met the Smith or Schwartz criteria. It remove the motivation for targetted tactical voting if there was always a chance the tactical voting would backfire. I'm not sure what you main by *targeted* tactical voting, but if a candidate has no chance of being the Condorcet winner, then that candidate's chances are improved by creating a cycle if the cycle is resolved randomly. Election-methods mailing list - see http://electorama.com/em for list info
[EM] Schulze's method isn't BeatpathWinner
You've kept insisting that SSD is Schulze's method. And it's true that, as you've been defining Schulze method, SSD is a special case of Schulze's method, which is a classification of methods rather than a method. But SSD isn't a special case of BeatpathWinner. SSD and BeatpathWinner are two dilfferent methods that can give two different outcomes wilth the same ballot-set, as in the example that I posted yesterday. In an example such as that, BeatpathWinner and SSD give different results. There isn't come version of BeatpathWinner that is SSD. So Schulze's method isn't BeatpathWinner. But no one can say that the definition of Schulze's method has lacked variety and changeableness. For instance, you've also defined Schulze's method in a way that uses beat-and-tie-paths instead of beatpaths. Mike Ossipoff _ On the road to retirement? Check out MSN Life Events for advice on how to get there! http://lifeevents.msn.com/category.aspx?cid=Retirement Election-methods mailing list - see http://electorama.com/em for list info
[EM] condorcet methods
Operating from the following assumptions: 1) There is never a viable reason to select a candidate other than the Condorcet Winner if a CW exists 2) Any voting criterion that is inherently incompatible with electing a Condorcet Winner should be discarded 3) All Condorcet "tiebreakers" pass some criteria and fail others I am just curious if there is a *set* of Condorcet methods, such that all popular criteria are met by at least one of the methods. Then the population could be told that the election will select a Condorcet Winner if one exists, and if not, one of the tiebreaking methods would be selected randomly. It would be better if they all met the Smith or Schwartz criteria. It remove the motivation for targetted tactical voting if there was always a chance the tactical voting would backfire. Sorry if this has been discussed, I can't even begin to read every message on this list. :-) Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Sincere methods
On Mar 30, 2005, at 02:53, Gervase Lam wrote: Should I thus read your comment so that you see MinMax (margins) as a sincere method (the best one, or just one good sincere method) whose weaknesses with strategic voting can best be patched by using Raynaud (Margins)? Roughly speaking yes, but not exactly. If you think Margins is an important way to measure closeness to being a Condorcet Winner, then Raynaud(Margins) might be the next best thing. I cannot think of any other reasonable Margins method. Of course, if you are willing to move away from Margins, there are other more simple pairwise methods around that are reasonably 'strategic resistant'. I think margins is one natural sincere voting method. For practical purposes I accept also methods that do not make sense as sincere methods. They may be needed in order to fight against strategic voting. In general think it would be very informative to always mention which sincere method each proposed practical voting method is based on. Or if there is no such complete sincere method in the background, then one should at least mention what (sincere) criteria have been taken as the basis. It seems that often the default value is simply to assume that the (ranking based) methods are Condorcet compatible. Many take also Smith set as granted I guess (I don't). For my taste using only these basic criteria is a bit lean. The main goal of a voting method is anyway to elect the best possible candidate, and defending against strategies is just something that may be needed in order not to let the voting method fail because of the strategic votes. Examples may help to clarify what I mean. (SVM = SIncere Voting Method, PVM = Practical Voting Method, SC = Sincere Criteria) SVM: MinMax (margins), PVM: Raynaud (margins) - the case that we discussed SVM: MinMax (margins), PVM: MinMax (wv) - winning votes used to defend against strategies - I think both margins and winning votes based PVMs (as well as any others) are ok as long as there are god reasons to use them - someone might claim that also winning votes based methods could be used as SVMs (?) SVM: MinMax (margins), PVM: MinMax (margins) - it would be nice if the SVM could be used also as the PVM - I think this case could be feasible in many situations; it all depends on if strategy threats are considered marginal or serious SC: Condorcet, PVM: MinMax (wv) - when Condorcet is used as the SC any defensive means are ok as long as they don't violate Condorcet - if there is a top cycle, any candidate could be elected SC: Condorcet + Smith set, PVM: ... - now the winner (in case of a top cycle) could be anyone within the Smith set SVM: Condorcet + Approval for cycle resolution, PVM: Condorcet + Approval for cycle resolution - this case just demonstrates that there could be also other SVMs than MinMax (margins) - The "sincere target" is thus to elect the most approved candidate if there is no Condorcet winner Selecting a PVM is of course a problem of finding a balance between SVMs and methods that are good in eliminating strategies (= balance between threat of not electing the best candidate because of deviation from the target SVM and threat of not electing the best candidate because of strategic voting). In cases where strategy problems are considered big we end up selecting some strategy eliminating focused PVM. In cases where strategy problems are less threatening we end up selecting a PVM that is close to the SVM. Typically examples of strategic voting are handled as abstract examples that demonstrate that strategic manipulation of the end result is possible. In order to evaluate their real weight I would like to see an estimate on what the probability of each strategic voting case is in real life. One could for example look at some real life presidential election in some real country and then estimate how easy it would be to implement the strategy, how detailed information of the voters' preferences is needed, how many voters (and from which parties) would follow the strategy etc. In my opinion at least large scale public elections are not very easy to manipulate (in ranking based elections). If someone is interested, I would be happy to see examples e.g. on how the "SVM: MinMax (margins), PVM: MinMax (margins)" case (this one should be an easy target) can be fooled in large public elections (with no more exact information than some opinion polls on how voters are going to vote). As a response to your comment, I'm "willing to move away from Margins" in the PVM area if there are good reasons to do so (= to defend against strategies). Also other than margin based methods can be taken as the starting point (SVM) if they are properly justified. I picked the MinMax (margins) up because I think it is too often seen as a no good method although I think it is a good candidate for a SVM and possibly a well working PVM too. I have tried to open a discussion on these topics
[EM] Re: Definite Majority Choice, AWP, AM
From: Jobst Heitzig <[EMAIL PROTECTED]> Subject: [EM] Re: Definite Majority Choice, AWP, AM The following proves that the only immune candidate is the least approved not strongly defeated candidate, assuming no pairwise defeat or approval ties: Let A be that candidate, with approval a. To prove that A is immune, assume that B1 defeats A, with approval b1. We show that there is a beatpath A>...>B1 with all defeats at least as strong as B1>A, that is, with all intermediate candidates having approval at least b1. Because of a>b1, and since B1 does not defeat all more approved ones, there is B2 with approval b2>b1 and B2>B1. If a>b2, also B2 does not defeat all more approved ones, hence there is B3 with approval b3>b2 and B3>B2, and so on until we find some Bk with approval bk>=a and Bk>...>B1. Now either Bk=A or A>Bk, QED. Now assume that B is a candidate other than A, with approval b. We show that B is not immune. If b>a then the defeat A>B has strenght a but all defeats against A have strength below a, hence all beatpaths B>...>A have strength below A, so B is not immune. If, on the other hand, bb, but any defeat B>... has strength b...>C has strength below c, so again B is not immune. QED. This proves that all immune methods, especially RP, River, Beatpath, are equivalent to DMC when defeat strength := approval of defeating candidate, and when no pairwise ties exist. This is a very nice proof, and another interesting and valuable characterization of DMC: When defeat strength is measured by the approval of the defeating candidate, there is only one possible immune method, namely DMC. All of the main competing Condorcet methods collapse into simple little old DMC by the device of measuring defeat strength by approval. And measuring defeat strength by approval in no way decreases any of the strategy resistance or other nice properties of the winning votes versions of those methods. Also, it's very nice to have the great variety of other descriptions and characterizations of this method that we have seen lately. Watch out IRV ! The only thing that worries me is this: what if DMC gets adopted all over the place, and it turns out that Donald gets the credit because he proves that he came up with an equivalent version before we did? I don't really waste any time worrying about such things, but wouldn't that be irony in the extreme? [I don't care. Let him have the credit. It would be worth it!] Forest Election-methods mailing list - see http://electorama.com/em for list info
[EM] Approval Strategies
Mike, thanks for the excellent summary of Approval strategies. I wasn't trying to be all inclusive, because my goal was limited to automatic computation of approval cutoffs for insertion into ranked and rated ballots in some kind of Declared Strategy Voting scheme. This scheme, in turn, was for the purpose of transforming "lottery methods" into deterministic methods. Since lotteries come with winning probabilities for the candidates, I considered these probabilities to be available. The other strategies that you outlined are definitely more useful to the voters who must supply thir own approval cutoffs. Forest Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Election-methods Digest, Vol 9, Issue 87
Date: Fri, 1 Apr 2005 01:25:36 +1000 (EST) From: Chris Benham <[EMAIL PROTECTED]> Subject: [EM] Re: DMC,AWP,AM Forest, You wrote: "I wonder if the following Approval Margins Sort (AMS) is equivalent to your Approval Margins method: 1. List the alternatives in order of approval with highest approval at the top of the list. 2. While any adjacent pair of alternatives is out of order pairwise ... among all such pairs swap the members of the pair that differ the least in approval. ... CB: AMS doesn't seem very "intuitive", especially to the uninitiated, but I like it! (My other worry is that I even understand it.) So how is this method worse than the best of the methods you currently advocate? 1. It's deterministic. 2. It's not quite as easy to describe or motivate as Definite Majority Choice. A perhaps ridiculous question: does the AMS process always stabilize? Not a ridiculous question: it's the pigeon hole principle: there are only finitely many permutations of the alternatives, and you cannot return to any of these after you have left it, because once X and Y have been swapped, they are never swapped back, since only out-of-order pairs get swapped. Forest Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Sincere methods
On Mar 31, 2005, at 03:38, Gervase Lam wrote: Schulze(Margins) (also known as Cloneproof Schwartz Sequential Dropping and Beatpath etc...) is possibly another reasonable method. See the recent "LNHarm performance" thread. Thanks, I'm already familiar with this one. My opinion briefly: nice design, strong against strategies, don't know if meant to be sincere or just strategy proof, linearization of group opinions (if meant to be a sincere method) and Smith set could be discussed. This mailing list is a bit too active with respect to the time I have available so I have not followed the "LNHarm performance" thread in detail, but I'll check if I'll learn more from there. Best Regards, Juho Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: DMC,AWP,AM
Forest, You wrote: > "I wonder if the following Approval Margins Sort (AMS) is equivalent to your Approval Margins method: 1. List the alternatives in order of approval with highest approval at the top of the list. 2. While any adjacent pair of alternatives is out of order pairwise ... among all such pairs swap the members of the pair that differ the least in approval. This method is clone independent and monotonic, and yields a social order that reverses exactly when the ballots are reversed. If AMS and AM are the same, it might be useful to have this alternative description. > AMS is monotonic in a strong sense: if ballots are changed so as to increase alternative X's approval or to give X a victory that it didn't have before, while leaving all of the other approvals and pairwise defeats the same, then X cannot move down in the social order produced by this AMS method. In other words, AMS is monotonic with respect to the entire social order it produces. > After one example it is pretty obvious that AM and AMS are equivalent when there are only three alternatives, since they both yield the CW when there is one, and they both preserve the approval order if the only upward defeat arrow is from the bottom to the top, and they both reverse the closest approval margin pair, otherwise." CB: AMS doesn't seem very "intuitive", especially to the uninitiated, but I like it! (My other worry is that I even understand it.) So how is this method worse than the best of the methods you currently advocate? A perhaps ridiculous question: does the AMS process always stabilize? 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] BeatpathWinner is SSD
Dear Mike, I wrote (29 March 2005): > 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. You wrote (30 March 2005): > SSD and CSSD are two different methods, which can give two > different outcomes with the same ballot-set. So BeatpathWinner > can't be both SSD and CSSD. > > BeatpathWinner is equivalent to CSSD, but not to SSD. > > I mention that for your information, so that, if you want to > be correct, you can leave SSD out of the list of names that > refer to BeatpathWinner or methods equivalent to it. But it > isn't important, and, as I said, I mention it only for your > information. I wrote (30 March 2005): > BeatpathWinner _is_ SSD _is_ CSSD in so far as all of them > share this property: > >If p(z)[A,B] > p(z)[B,A], then candidate B must be >elected with zero probability. > > If you don't agree with this then please post an example > where this is not true. You wrote (30 March 2005): > If sharing a property makes methods the same, then > BeatpathWinner is Approval, because both methods meet WDSC. Of course, the question is what a "criterion" is and what a "method" is. Example: The Borda method chooses that candidate who has the largest Borda score. Of course, it is possible that there is more than one candidate with the same largest Borda score. There are many different proposals how to solve this problem; but nevertheless I would summarize all these proposals under the name "Borda method". I would say that these proposals are only "different tie-breaking strategies for the Borda method". In my opinion, the statement "If p(z)[A,B] > p(z)[B,A], then candidate B must be elected with zero probability" defines a _method_ and not a _criterion_ because: 1. When the number of voters goes to infinity then the probability that there is more than one candidate C who can be elected without contradicting this statement goes to zero. This cannot be said about WDSC. 2. In my opinion, a "criterion" is a "desirable property". But this statement itself is not a desirable property, it only describes a possible way to get compliance with some other desirable properties (e.g. monotonicity, Smith-IIA, Schwartz, resolvability, reversal symmetry). Therefore, what you call "BeatpathWinner" or "SSD" or "CSSD" are only different tie-breaking strategies for the Schulze method that I proposed in 1997. Markus Schulze Election-methods mailing list - see http://electorama.com/em for list info
