Re: [EM] Why I Prefer IRV to Condorcet
--- On Sun, 14/12/08, Kristofer Munsterhjelm wrote: > Juho Laatu wrote: > > --- On Fri, 5/12/08, Kristofer Munsterhjelm > wrote: > > > >> Alright. You may like Minmax for being Minmax, and > >> that's okay; but in my case, I'm not sure > if it > >> would withstand strategy (there's that > "hard to > >> estimate the amount of strategy that will > happen" > >> again), and the Minmax heuristic itself > doesn't seem > >> important enough to trade things like clone > independence and > >> Smith for. > > > > The good points in Minmax are related to behaviour > > with sincere votes. It is not really rigged to > > remove maximum number or amount of strategic threats > > (but to implement one natural sincere utility > > function). The question then is which properties one > > should emphasize (electing the right winner vs. not > > electing a wrong winner due to strategic voting). > > > > All Condoret methods are vulnerable to some very > > basic strategies. Some Condorcet methods try to > > fix some additional threats. One may say that > > differences in the level of vulnerability are not > > that big. And fixing one problem often leads to > > vulnerability on some other area. > > There is probably a Pareto front in this respect. Just like > some methods fail more criteria than others, some methods > would do both worse on sincere votes and resist strategy > less; it would be Pareto-dominated by better methods. But > since there's a Pareto front and not a single objective, > some methods on that front will be better at translating > sincere expression (whatever metric is used to measure > this), while some are much more resistant against strategy. > > If we take that further, some compliances are probably more > "expensive" than others. Intuitively, I think > clone independence is pretty inexpensive (that it alters > situations that is much more likely to be due to strategy > than honest voting), but I have no proof of this, of course; > and similarly intuitively, I think that MDQBR (mutual > dominant quarter burial resistance) would be very expensive, > since so many voters are burying that the dishonest ballot > bundle will collide with a sincere ballot bundle (in the > latter case, the "buriers' candidate" should > win, because there are no buriers and the expression is > sincere). Yes. We may complain when the favourite of the strategists is elected with some set of votes. But we should also always ask the question who should have been elected if we would have a similar set of sincere votes (or if some other group of strategists changed the votes in the reverse direction). > > > One may say that all Condorcet methods are quite > > resistant to strategic voting, espacially in the > > typical environments (large public elections with > > independent decision making and with limited > > information on how others are going to vote). > > That's what it all boils down to. We don't know > whether Condorcet methods are adequately resistant. The Condorcet methods have at least passed one of my tests. I have several times asked the election method experts to give a simple set of strategic rules that voters could apply in Condorcet elections for their benefit. But I have not seen any. The next task would be to point out real life like election examples where strategies are easy and riskless enough so that they could be publicly recommended to voters (in typical large public elections). Also this has been quite difficult to achieve. One could also try to find out strategic opportunities in coming real life Condorcet elections and try to find good strategic advices for voters in them. I haven't seen this either. All this does not prove that Condorcet would not fall in some scenarios, but at least this shows some direction and something about the typical behaviour. (Also methods that are currently widely used do have vulnerabilities.) > The > cover-all-bases approach is to try to have the method pass > as many criteria as possible so that even in the worst case, > the system resists strategy. If the criteria are cheap, > there's little harm (except the waste of work, but > having a margin of safety is probably a good thing, ceteris > paribus). The other approach would be to actually > investigate the kind of strategy that would develop, but > this is difficult: even if we had access to near-unlimited > numbers of experiments, we wouldn't know whether the > dynamics would lead to things like vote management on one > hand, or the initial strategy resistance would discourage > people from building upon them on the other. Real life testing is probably the best thing to do. > > > I say this to present Minmax in a positive light. > > Maybe the fairness of the method is also a > > positive value. Maybe the strategic defences are > > not needed, especially since there is a risk that > > we don't elect the best winner then. Maybe focus > > on the positive properties even encourages sincere > > voting (=let's just pic
Re: [EM] Why I Prefer IRV to Condorcet
Juho Laatu wrote: --- On Fri, 5/12/08, Kristofer Munsterhjelm wrote: Alright. You may like Minmax for being Minmax, and that's okay; but in my case, I'm not sure if it would withstand strategy (there's that "hard to estimate the amount of strategy that will happen" again), and the Minmax heuristic itself doesn't seem important enough to trade things like clone independence and Smith for. The good points in Minmax are related to behaviour with sincere votes. It is not really rigged to remove maximum number or amount of strategic threats (but to implement one natural sincere utility function). The question then is which properties one should emphasize (electing the right winner vs. not electing a wrong winner due to strategic voting). All Condoret methods are vulnerable to some very basic strategies. Some Condorcet methods try to fix some additional threats. One may say that differences in the level of vulnerability are not that big. And fixing one problem often leads to vulnerability on some other area. There is probably a Pareto front in this respect. Just like some methods fail more criteria than others, some methods would do both worse on sincere votes and resist strategy less; it would be Pareto-dominated by better methods. But since there's a Pareto front and not a single objective, some methods on that front will be better at translating sincere expression (whatever metric is used to measure this), while some are much more resistant against strategy. If we take that further, some compliances are probably more "expensive" than others. Intuitively, I think clone independence is pretty inexpensive (that it alters situations that is much more likely to be due to strategy than honest voting), but I have no proof of this, of course; and similarly intuitively, I think that MDQBR (mutual dominant quarter burial resistance) would be very expensive, since so many voters are burying that the dishonest ballot bundle will collide with a sincere ballot bundle (in the latter case, the "buriers' candidate" should win, because there are no buriers and the expression is sincere). One may say that all Condorcet methods are quite resistant to strategic voting, espacially in the typical environments (large public elections with independent decision making and with limited information on how others are going to vote). That's what it all boils down to. We don't know whether Condorcet methods are adequately resistant. The cover-all-bases approach is to try to have the method pass as many criteria as possible so that even in the worst case, the system resists strategy. If the criteria are cheap, there's little harm (except the waste of work, but having a margin of safety is probably a good thing, ceteris paribus). The other approach would be to actually investigate the kind of strategy that would develop, but this is difficult: even if we had access to near-unlimited numbers of experiments, we wouldn't know whether the dynamics would lead to things like vote management on one hand, or the initial strategy resistance would discourage people from building upon them on the other. I say this to present Minmax in a positive light. Maybe the fairness of the method is also a positive value. Maybe the strategic defences are not needed, especially since there is a risk that we don't elect the best winner then. Maybe focus on the positive properties even encourages sincere voting (=let's just pick the best winner). Maybe the Minmax viewpoint to who is best is accurate enough for the purpose. And if there are meninful strategies and counter strategies then I think the method may already have failed. Minmax is not necessarily the ideal utility function (for ranked votes). I think different elections may well have different sincere needs. Different methods may be used for different needs. In Minmax it is quite easy to justify electing Condorcet loser (in some very rare cases) or to fail strict clone compliancy (in some very rare cases). Also mutual majority can be explained away (I already tried this in this mail stream) but here it is easier to give space also to other opinions. This raises the question: for ranked electoral methods, what is the ideal utility function, or more precisely, what is the ideal honest aggregation function? One may argue for Borda being it (Bayesian regret), or Minmax (gives up as little as possible), Kemeny-Young (maximum likelihood, maximize the number of voters that agree with each preference) or Dodgson (minimize ballot differences to CW). In the case of different ideal functions for different needs, the question is displaced to what conditions would make, say, Minmax, optimal. Some more words on trading clone independence and Smith. Note that Minmax doesn't trade them away since it respects them almost always. (And in these cases we can diecuss if it is justified to violate these criteria in these special cases.) A less than 100% compliance with som
Re: [EM] Why I Prefer IRV to Condorcet
Chris Benham wrote: Kristofer, You wrote (Sun.Nov.23): "Regarding number two, simple Condorcet methods exist. Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll partially grant this, though, since the good methods are complex, but I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In MAM, you take all the pairwise contests, sort by strength, and affirm down the list unless you would contradict an earlier affirmed contest. This method is cloneproof, monotonic, etc..." Raynaud isn't Borda-elimination. It is Pairwise Elimination, i.e. eliminate the loser of the most decisive or strongest pairwise result (by one measure or another) until one candidate remains. You may have instead meant to write "Baldwin",though some sources just talk about 2 different versions of Nanson. Simpler and much better than any of those methods are Condorcet//Approval and Smith//Approval and Schwartz//Approval ,in each case interpreting ranking as approval and so not allowing ranking among unapproved candidates. I haven't had the time to reply to the longer posts here yet, but of course, you're right. I meant to say Baldwin, not Raynaud. The difference between the two is that one eliminates the loser, while the other eliminates all below average - somewhat like the difference between Hare and Carey. Nanson's the average, and Baldwin's the loser-elimination, unless I'm mistaken. If you don't like approval cutoffs (implicit or explicit; you probably have no problem with the implicit ones, but I'm using the general "you" here), perhaps Smith//Range would work (or for that matter, UncAAO with range as partial approval, though it's not as simple). One of the problems with Range is that there's a great incentive to equal-rank (bottom or top). Interpreting the ballot as a ranked ballot to determine the Smith (or whatever) set, then breaking ties by whoever has the greatest score, might ameliorate both Range and Condorcet's problems: you can't bury without decreasing your score for the tiebreak, and you can't maximize without throwing some discriminatory power (that's useful for the first stage) away. Though, on the other hand, it might just lead to ballots like: X: 100, Y: 99.999, Z: 99.998, W: 0.003, A: 0.002, B: 0.001, C: 0 But if Smith//Approval is good, then that won't be any worse - well, it might, somewhat, since you can't have "equal scores but different rank" in this version. I guess one of the advantages of implicit Smith//A is that you can't bury disapproved candidates. Smith//Range would lose this advantage. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I Prefer IRV to Condorcet
Kristofer, You wrote (Sun.Nov.23): "Regarding number two, simple Condorcet methods exist. Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll partially grant this, though, since the good methods are complex, but I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In MAM, you take all the pairwise contests, sort by strength, and affirm down the list unless you would contradict an earlier affirmed contest. This method is cloneproof, monotonic, etc..." Raynaud isn't Borda-elimination. It is Pairwise Elimination, i.e. eliminate the loser of the most decisive or strongest pairwise result (by one measure or another) until one candidate remains. You may have instead meant to write "Baldwin",though some sources just talk about 2 different versions of Nanson. Simpler and much better than any of those methods are Condorcet//Approval and Smith//Approval and Schwartz//Approval ,in each case interpreting ranking as approval and so not allowing ranking among unapproved candidates. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
--- On Fri, 5/12/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > Alright. You may like Minmax for being Minmax, and > that's okay; but in my case, I'm not sure if it > would withstand strategy (there's that "hard to > estimate the amount of strategy that will happen" > again), and the Minmax heuristic itself doesn't seem > important enough to trade things like clone independence and > Smith for. The good points in Minmax are related to behaviour with sincere votes. It is not really rigged to remove maximum number or amount of strategic threats (but to implement one natural sincere utility function). The question then is which properties one should emphasize (electing the right winner vs. not electing a wrong winner due to strategic voting). All Condoret methods are vulnerable to some very basic strategies. Some Condorcet methods try to fix some additional threats. One may say that differences in the level of vulnerability are not that big. And fixing one problem often leads to vulnerability on some other area. One may say that all Condorcet methods are quite resistant to strategic voting, espacially in the typical environments (large public elections with independent decision making and with limited information on how others are going to vote). I say this to present Minmax in a positive light. Maybe the fairness of the method is also a positive value. Maybe the strategic defences are not needed, especially since there is a risk that we don't elect the best winner then. Maybe focus on the positive properties even encourages sincere voting (=let's just pick the best winner). Maybe the Minmax viewpoint to who is best is accurate enough for the purpose. And if there are meninful strategies and counter strategies then I think the method may already have failed. Minmax is not necessarily the ideal utility function (for ranked votes). I think different elections may well have different sincere needs. Different methods may be used for different needs. In Minmax it is quite easy to justify electing Condorcet loser (in some very rare cases) or to fail strict clone compliancy (in some very rare cases). Also mutual majority can be explained away (I already tried this in this mail stream) but here it is easier to give space also to other opinions. Some more words on trading clone independence and Smith. Note that Minmax doesn't trade them away since it respects them almost always. (And in these cases we can diecuss if it is justified to violate these criteria in these special cases.) A less than 100% compliance with some criteria may sometimes be useful. Either beneficial or acceptable because some criteria need to be violated in any case. I did'n btw quite like term "Minmax heuristic" since my dictionary defines heuristic in mathematics, science and philosophy as "using or obtained by exploration of possibilities rather than by following set rules". The rules and justifyig explanations of Minmax(margins) are very exact. (Actually most other Condorcet methods are more inclined towards heuristic style exploration, e.g. to find the most strategy resistant methods.) > > One should also ask if the clone criterion is ideal. > > For strategy reasons sufficient independence of > > clones may be necessary to make it safe for > > parties/wings to nominate more than one candidate > > (or to nominate only one). > > > > How about the following situation. Both Democrats > > and Republicans have three clone candidates. All > > votes are sincere. Both parties have 50% support. > > The Democrat candidates have a clear group > > preference order. The Republican candidates are > > badly looped. Is the fact that electing a > > Republican candidate would leave us in a > > situation where majority of the voters are > > not happy but would like to replace this > > candidate with another candidate a sufficient > > reason to elect the best Democrat candidate > > instead. I.e. should we be fully independent of > > clones or should we elect the candidate that > > seems to be the best compromise candidate / > > most agreeable (=least opposition in any > > pairwise comparison)? > > Independence of clones make the method resistant to > nomination (dis)incentives. Or rather, robust independence > of clones (not just "remove clones, then run through > method"), does. This is useful because one of the major > problems with Plurality is that it has a severe nomination > disincentive; if your candidate is similar to some other > candidate, you'll both lose. It's the other way with > Borda. > > I don't quite see what you're saying. The Democrat > candidates have a clear group preference order, whereas the > Republican candidates are looped; so something like: > > 50: D1>D2>D3>R1>R2>R3 > 16: R1>R2>R3>D1>D2>D3 > 17: R2>R3>R1>D1>D2>D3 > 17: R3>R1>R2>D1>D2>D3 > > A cloneproof method would act as if D* and R* are one > candidate (more or less). It may pick R3 instead of R1 > because 18 instead of 16 preferred that one, but it > should
Re: [EM] Why I Prefer IRV to Condorcet
Juho Laatu wrote: --- On Mon, 1/12/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: Then you should advocate Minmax for being Minmax, not for being Condorcet compliant. If you do the latter, then people may argue that the system is inconsistent because it doesn't follow up the implication of Condorcet (Condorcet loser, etc). But to my knowledge, you want to do the former, so I won't comment on this. I don't have any strong promotional interests. I like clarity and clear understanding. In this case there is no need to refer to Condorcet compatibility since Minmax(margins) can be defined well (maybe better) without it. Also the fact that the Condorcet winner vs. Condorcet loser question is tricky may be a reason to describe the method as Minmax. But in general I do not fancy the idea of using verbal tricks to make something look better or worse than it is. I'm thus ok with any definition. Minmax as Minmax sounds good. On the other hand minmax is a mathematical term and adding "margins" there makes it even more complex. For this reason also e.g. "least additional votes", "least interest to change" or "best pairwise result" based names or short abbreviations could be ok (for use outside the EM expert community). Alright. You may like Minmax for being Minmax, and that's okay; but in my case, I'm not sure if it would withstand strategy (there's that "hard to estimate the amount of strategy that will happen" again), and the Minmax heuristic itself doesn't seem important enough to trade things like clone independence and Smith for. I would have two reasons as well, but none of those you mentioned. It's possible to be cloneproof without being Smith and vice versa.. 1. Logical endpoint of mutual majority. A mutual majority set is one that a majority prefers to all else. Now consider a mutual dominant nth set. A mutual dominant nth set is a set that 1/n of all voters prefer to all the others, and where one of the candidates within wins, pairwise. Smith is just mutual dominant set with n->inf. 2. Condorcet for sets. Smith is Condorcet for sets. If a set can beat all those outside the set pairwise, it should win. If the set is of size one, well, that's just Condorcet. The only reason why it should hold for size one, but not, say, size two, is if some other heuristic (like the Minmax metric/utility heuristic) is more important. If it is, see my first paragraph; but if we want this method primarily because it's Condorcet, or because the Condorcet idea itself is a good one, then we should be consistent and take that Condorcet as far as possible. The mutual majority criterion is related to clones. But it can also be seen as a criterion that refers to the majority rule and life after the election. I mean that some majority group may say after the election "we want these candidates to win" and it is difficult to explain that they will not get what they want since they had conflicting opinions within that candidate set on which one of them should win. I'm considering the majority rule interpretation; otherwise, I could just have gone straight for independence of clones. I defined a mutual dominant set above, and for small values of n, one could reasonably expect parties (or those who support them) to wonder, if the method is Condorcet (thus candidates that pairwise beat others are good candidates), and supports majority rule (thus mutual majority etc), why it doesn't elect from the mutual dominant nth set. If you have Smith, you can ensure that it does, no matter how large n is. "Condorcet for sets" sounds a bit "aesthetics based" to me since I don't know what practical real life situation (other than aesthetic observations on the graph that describes the pairwise preferences) could be used to justify this criterion. If that set was one candidate (or a nominated party/grouping) then the basic Condorcet rule would apply, but if the Smith set is just a random set of candidates and there is no single majority group of voters behind this group opinion then it is harder to find the rationale. (The set members may not be clones and there may not be a single set of voters that think that this set is better than others.) I suppose this leads back to clone independence, so I won't address it here, except to say that majority for a set makes sense (Mutual Majority; at least it does to me), and so should Condorcet for a set. One should also ask if the clone criterion is ideal. For strategy reasons sufficient independence of clones may be necessary to make it safe for parties/wings to nominate more than one candidate (or to nominate only one). How about the following situation. Both Democrats and Republicans have three clone candidates. All votes are sincere. Both parties have 50% support. The Democrat candidates have a clear group preference order. The Republican candidates are badly looped. Is the fact that electing a Republican candidate would leave us in a situation where majority of the
Re: [EM] Why I Prefer IRV to Condorcet
--- On Mon, 1/12/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > > There are different kind of criteria. > > If one decides the winner based on one single > > vote a method that would elect the least > > preferred candidate would be bad. Things get > > however more complex with group opinions that > > may contain cycles. Then it is possible that > > some candidate loses to every other candidate > > but still is the most liked one in the sense > > that there is only a very weak interest to > > change that candidate to some other candidate. > > Then you should advocate Minmax for being Minmax, not for > being Condorcet compliant. If you do the latter, then people > may argue that the system is inconsistent because it > doesn't follow up the implication of Condorcet > (Condorcet loser, etc). But to my knowledge, you want to do > the former, so I won't comment on this. I don't have any strong promotional interests. I like clarity and clear understanding. In this case there is no need to refer to Condorcet compatibility since Minmax(margins) can be defined well (maybe better) without it. Also the fact that the Condorcet winner vs. Condorcet loser question is tricky may be a reason to describe the method as Minmax. But in general I do not fancy the idea of using verbal tricks to make something look better or worse than it is. I'm thus ok with any definition. Minmax as Minmax sounds good. On the other hand minmax is a mathematical term and adding "margins" there makes it even more complex. For this reason also e.g. "least additional votes", "least interest to change" or "best pairwise result" based names or short abbreviations could be ok (for use outside the EM expert community). > > I can see two kind of reasoning that people > > may use to justify the use of Smith set as > > a criterion that determines the best winner. > > > > 1) Clone based. Smith set is some sort of an > > approximation of clone candidates. Smith set > > is however wider (wider than the set of > > candidates that are next to each others in > > every ballot). (Note also that candidates > > that are next to each others in every ballot > > need not be clones in the sense that they > > would be ideologically similar.) > > > > 2) Drawing technique based. When drawing a > > graph that represents the results of the > > election one typically draws the Smith set > > candidates at the top of the paper, and all > > the other candidates below that group. Since > > people intuitively model also group opinions > > as linear preference chains this drawing > > technique may give them a false impression of > > the group preferences. The problem is that > > this drawing technique hides the defeats of > > the Smith set members to each others. > > I would have two reasons as well, but none of those you > mentioned. It's possible to be cloneproof without being > Smith and vice versa.. > > 1. Logical endpoint of mutual majority. A mutual majority > set is one that a majority prefers to all else. Now consider > a mutual dominant nth set. A mutual dominant nth set is a > set that 1/n of all voters prefer to all the others, and > where one of the candidates within wins, pairwise. Smith is > just mutual dominant set with n->inf. > > 2. Condorcet for sets. Smith is Condorcet for sets. If a > set can beat all those outside the set pairwise, it should > win. If the set is of size one, well, that's just > Condorcet. The only reason why it should hold for size one, > but not, say, size two, is if some other heuristic (like the > Minmax metric/utility heuristic) is more important. If it > is, see my first paragraph; but if we want this method > primarily because it's Condorcet, or because the > Condorcet idea itself is a good one, then we should be > consistent and take that Condorcet as far as possible. The mutual majority criterion is related to clones. But it can also be seen as a criterion that refers to the majority rule and life after the election. I mean that some majority group may say after the election "we want these candidates to win" and it is difficult to explain that they will not get what they want since they had conflicting opinions within that candidate set on which one of them should win. "Condorcet for sets" sounds a bit "aesthetics based" to me since I don't know what practical real life situation (other than aesthetic observations on the graph that describes the pairwise preferences) could be used to justify this criterion. If that set was one candidate (or a nominated party/grouping) then the basic Condorcet rule would apply, but if the Smith set is just a random set of candidates and there is no single majority group of voters behind this group opinion then it is harder to find the rationale. (The set members may not be clones and there may not be a single set of voters that think that this set is better than others.) One should also ask if the clone criterion is ideal. For strategy reasons sufficient independence of clones ma
Re: [EM] Why I Prefer IRV to Condorcet
Juho Laatu wrote: --- On Thu, 27/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: Minmax may elect the Condorcet loser only when there is no Condorcet winner. And only in situations where all other candidates are worse than the Condorcet loser from the minmax philosophy/utility point of view. The problem is criterion compliance. Isolated, I think passing Condorcet and failing Condorcet loser is a contradiction, because this means you can possibly reverse the election and get a "worst" that is the "best". I know that there are weaknesses to my argument (since others could make the same reasoning about Consistency, for instance, and exclude all Condorcet methods), but I think that inasfar as voting methods are metrics of winners, and the reason for why one is supposed to use this method is because of its criterion compliance (which is really a way of saying certain ways of picking winners/not picking winners is desirable), one should take the reason to its full extent, which a method that fails Condorcet loser doesn't do. There are different kind of criteria. If one decides the winner based on one single vote a method that would elect the least preferred candidate would be bad. Things get however more complex with group opinions that may contain cycles. Then it is possible that some candidate loses to every other candidate but still is the most liked one in the sense that there is only a very weak interest to change that candidate to some other candidate. Then you should advocate Minmax for being Minmax, not for being Condorcet compliant. If you do the latter, then people may argue that the system is inconsistent because it doesn't follow up the implication of Condorcet (Condorcet loser, etc). But to my knowledge, you want to do the former, so I won't comment on this. >> Smith isn't just a hardening criterion. In a sense, it also assures voters that they can vote in a way they want without having to compensate in order to get a candidate from the Smith (or mutual majority, etc) set, if all other voters are honest. In this way, it would be similar to independence of clones: a cloneproof method tells voters that now it matters much less whether candidates are loosely spread or tightly clumped around an area, even if the candidates were clumped/spread apart simply because of the political environment (and through no adverse intent nor strategic nomination). I can see two kind of reasoning that people may use to justify the use of Smith set as a criterion that determines the best winner. 1) Clone based. Smith set is some sort of an approximation of clone candidates. Smith set is however wider (wider than the set of candidates that are next to each others in every ballot). (Note also that candidates that are next to each others in every ballot need not be clones in the sense that they would be ideologically similar.) 2) Drawing technique based. When drawing a graph that represents the results of the election one typically draws the Smith set candidates at the top of the paper, and all the other candidates below that group. Since people intuitively model also group opinions as linear preference chains this drawing technique may give them a false impression of the group preferences. The problem is that this drawing technique hides the defeats of the Smith set members to each others. I would have two reasons as well, but none of those you mentioned. It's possible to be cloneproof without being Smith and vice versa.. 1. Logical endpoint of mutual majority. A mutual majority set is one that a majority prefers to all else. Now consider a mutual dominant nth set. A mutual dominant nth set is a set that 1/n of all voters prefer to all the others, and where one of the candidates within wins, pairwise. Smith is just mutual dominant set with n->inf. 2. Condorcet for sets. Smith is Condorcet for sets. If a set can beat all those outside the set pairwise, it should win. If the set is of size one, well, that's just Condorcet. The only reason why it should hold for size one, but not, say, size two, is if some other heuristic (like the Minmax metric/utility heuristic) is more important. If it is, see my first paragraph; but if we want this method primarily because it's Condorcet, or because the Condorcet idea itself is a good one, then we should be consistent and take that Condorcet as far as possible. One could see Kemeny as a good definition of a good social ordering. That may or may not correlate with the definition of the best single winner. If the concept of a social ordering is to have any use, I think the winner must be first on it. My statement was not quite accurate. I should have said only that the criteria for determining the social ordering and the best winner in some single-winner election may be different. In what situations would the single winner and the social ordering differ? It does, for proportional completion (because that's proportional and thus PR-
Re: [EM] Why I Prefer IRV to Condorcet
Thanks, the referred paper contains a clear explanation of the links between minmax and Schulze. Use of the "minmax criterion" (max interest to change to another candidate) for groups too differs from the basic minmax method in that also other pairwise preferences than those that involve candidate X directly may influence the evaluation of candidate X. My understanding is that the main driver behind the beatpath based methods has been the interest to guarantee independence of clones (well, maybe some aesthetic values too). Unfortunately all the criteria are not compatible with each others, and doing this takes one step away from the "minmax criterion" for individual candidates (that can be used as one possible sincere social utility criterion - at least the margins based version). Using beatpaths to identify clones is also not an exact definition of which candidates are clones, but at least it covers all clones (when defined as "candidates next to each others in every ballot"). In that sense beatpaths may be seen a slight overkill, but maybe a necessary one (?) if one wants independence of clones and the decisions to be based on the pairwise comparison matrix only. Juho --- On Fri, 28/11/08, Markus Schulze <[EMAIL PROTECTED]> wrote: > From: Markus Schulze <[EMAIL PROTECTED]> > Subject: Re: [EM] Why I Prefer IRV to Condorcet > To: [EMAIL PROTECTED] > Date: Friday, 28 November, 2008, 2:41 AM > Hallo, > > Juho Laatu wrote (28 Nov 2008): > > > I didn't quite get this. When evaluating > > candidate X minmax just checks if voters > > would be interested in changing X to some > > other candidate (in one step), while > > methods like Schulze and Ranked Pairs may > > base their evaluation on chains of victories > > leading to X. > > Suppose the MinMax score of a set Y of candidates > is the strength of the strongest win of > a candidate A outside the set Y against > a candidate B inside the set Y. Then the > Schulze method (but not the Ranked Pairs > method) guarantees that the winner is > always chosen from the set with minimum > MinMax score. See section 9 of my paper: > > http://m-schulze.webhop.net/schulze1.pdf > > Because of this reason, the worst pairwise > defeat of the Schulze winner is usually very > weak. And, in most cases, the Schulze winner > is identical to the MinMax winner. This has > been confirmed by Norman Petry and Jobst > Heitzig (with different models): > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html > http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html > > Markus Schulze > > > > 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] Why I Prefer IRV to Condorcet
Hallo, Juho Laatu wrote (28 Nov 2008): > I didn't quite get this. When evaluating > candidate X minmax just checks if voters > would be interested in changing X to some > other candidate (in one step), while > methods like Schulze and Ranked Pairs may > base their evaluation on chains of victories > leading to X. Suppose the MinMax score of a set Y of candidates is the strength of the strongest win of a candidate A outside the set Y against a candidate B inside the set Y. Then the Schulze method (but not the Ranked Pairs method) guarantees that the winner is always chosen from the set with minimum MinMax score. See section 9 of my paper: http://m-schulze.webhop.net/schulze1.pdf Because of this reason, the worst pairwise defeat of the Schulze winner is usually very weak. And, in most cases, the Schulze winner is identical to the MinMax winner. This has been confirmed by Norman Petry and Jobst Heitzig (with different models): http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
--- On Thu, 27/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > > Note that the minmax philosophy is to study paths of > > length one. Minmax philosophy says that voter interest > > to replace the elected candidate with another is more > > relevant than their interest to replace the candidates > > in chain. (Such chains of changes do not typically > > happen in real life after the election.) > > I'm not sure about this. The alternate description of > Minmax as making use of successive eliminations may point at > it involving long paths. At least I think that's partly > the reason Schulze is so similar to Minmax (or > Smith//Minmax). I didn't quite get this. When evaluating candidate X minmax just checks if voters would be interested in changing X to some other candidate (in one step), while methods like Schulze and Ranked Pairs may base their evaluation on chains of victories leading to X. > > Minmax may elect the Condorcet loser only when there > > is no Condorcet winner. And only in situations where > > all other candidates are worse than the Condorcet > > loser from the minmax philosophy/utility point of > view. > > The problem is criterion compliance. Isolated, I think > passing Condorcet and failing Condorcet loser is a > contradiction, because this means you can possibly reverse > the election and get a "worst" that is the > "best". I know that there are weaknesses to my > argument (since others could make the same reasoning about > Consistency, for instance, and exclude all Condorcet > methods), but I think that inasfar as voting methods are > metrics of winners, and the reason for why one is supposed > to use this method is because of its criterion compliance > (which is really a way of saying certain ways of picking > winners/not picking winners is desirable), one should take > the reason to its full extent, which a method that fails > Condorcet loser doesn't do. There are different kind of criteria. If one decides the winner based on one single vote a method that would elect the least preferred candidate would be bad. Things get however more complex with group opinions that may contain cycles. Then it is possible that some candidate loses to every other candidate but still is the most liked one in the sense that there is only a very weak interest to change that candidate to some other candidate. > >> As for Smith, I would like to have that > >> as well, since if the method says Condorcet for a > candidate, > >> it should also say Condorcet for a set (unless > there's > >> some overriding strategy-proofing reason as to why > not). > > > > I don't see that as a requirement even if there > were > > no strategy-proofing needs. The minmax philosophy says > > that voters may have more interest to replace the > > elected Smith set member with another member of the > > set than they have interest to replace someone outside > > of that set with others. > > If that is true, one should advocate Minmax on that the > Minmax philosophy is a good one, and if it meets Condorcet, > that's a bonus as well, but that it's the Minmax > philosophy that is paramount. Yes, I assumed that in this case the society had chosen minmax as a sincere utility function that determines the best winner. > Smith isn't just a hardening criterion. In a sense, it > also assures voters that they can vote in a way they want > without having to compensate in order to get a candidate > from the Smith (or mutual majority, etc) set, if all other > voters are honest. In this way, it would be similar to > independence of clones: a cloneproof method tells voters > that now it matters much less whether candidates are loosely > spread or tightly clumped around an area, even if the > candidates were clumped/spread apart simply because of the > political environment (and through no adverse intent nor > strategic nomination). I can see two kind of reasoning that people may use to justify the use of Smith set as a criterion that determines the best winner. 1) Clone based. Smith set is some sort of an approximation of clone candidates. Smith set is however wider (wider than the set of candidates that are next to each others in every ballot). (Note also that candidates that are next to each others in every ballot need not be clones in the sense that they would be ideologically similar.) 2) Drawing technique based. When drawing a graph that represents the results of the election one typically draws the Smith set candidates at the top of the paper, and all the other candidates below that group. Since people intuitively model also group opinions as linear preference chains this drawing technique may give them a false impression of the group preferences. The problem is that this drawing technique hides the defeats of the Smith set members to each others. > > One could see Kemeny as a good definition of a good > > social ordering. That may or may not correlate with > > the definition of the best single winner. > > If the concept of
Re: [EM] Why I Prefer IRV to Condorcet
Juho Laatu wrote: --- On Tue, 25/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: I'll try to answer very shortly to most of the points. I can comment more if there are some interesting ones. From: Kristofer Munsterhjelm <[EMAIL PROTECTED]> Subject: Re: [EM] Why I Prefer IRV to Condorcet To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Date: Tuesday, 25 November, 2008, 1:37 PM Juho Laatu wrote: --- On Sun, 23/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: Regarding number two, simple Condorcet methods exist. Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll partially grant this, though, since the good methods are complex Minmax is both simple and good. I think at least minmax(margins) is a good solution for many needs. The weakest spot of minmax(margins) could be that it fails mutual majority. That means for example that nominating a set of clones instead of just one candidate could lead (at least in theory) to not winning the election. On the other hand other methods than minmax(margins) may not respect the good idea of mmm to elect the candidate that has the least incentive among voters to be changed to some other of the candidates. the candidates. I think Schulze said that his method was the one that agreed most with Minmax while still being cloneproof. According to Warren, that is true (he refers to simulations made by Petry and Heitzig) - see http://rangevoting.org/SchulzeExplan.html . The claim seems to be about Smith//MinMax. Yes; so we can say it's the method that agrees most with Minmax while being cloneproof and Smith. At the other end of "generalizable methods" you have Kemeny. Kemeny is not cloneproof (it suffers from crowding). I wonder what "Cloneproof Kemeny" would look like, but there have been attempts to move Ranked Pairs closer to Kemeny. See Heitzig's Short Ranked Pairs: http://listas.apesol.org/pipermail/election-methods-electorama.com/2004-November/014208.html Note that the minmax philosophy is to study paths of length one. Minmax philosophy says that voter interest to replace the elected candidate with another is more relevant than their interest to replace the candidates in chain. (Such chains of changes do not typically happen in real life after the election.) I'm not sure about this. The alternate description of Minmax as making use of successive eliminations may point at it involving long paths. At least I think that's partly the reason Schulze is so similar to Minmax (or Smith//Minmax). (Minmax(margins) fails also Smith and Condorcet loser, but those violations can be explained to be intentional and positive.) That's a problem, in my opinion. A voting method also is a metric of who deserves to win. Yes if one sets that as a target. The alternative is to emphasize also other aspects like being free of strategic voting related risks. I think minmax can be seen as an ideal definition (for some needs) of which candidate is best. In that point of view, if the metric says that Condorcet winners are good, but the method can elect Conorcet losers, the metric is self-contradictory. Minmax may elect the Condorcet loser only when there is no Condorcet winner. And only in situations where all other candidates are worse than the Condorcet loser from the minmax philosophy/utility point of view. The problem is criterion compliance. Isolated, I think passing Condorcet and failing Condorcet loser is a contradiction, because this means you can possibly reverse the election and get a "worst" that is the "best". I know that there are weaknesses to my argument (since others could make the same reasoning about Consistency, for instance, and exclude all Condorcet methods), but I think that inasfar as voting methods are metrics of winners, and the reason for why one is supposed to use this method is because of its criterion compliance (which is really a way of saying certain ways of picking winners/not picking winners is desirable), one should take the reason to its full extent, which a method that fails Condorcet loser doesn't do. As for Smith, I would like to have that as well, since if the method says Condorcet for a candidate, it should also say Condorcet for a set (unless there's some overriding strategy-proofing reason as to why not). I don't see that as a requirement even if there were no strategy-proofing needs. The minmax philosophy says that voters may have more interest to replace the elected Smith set member with another member of the set than they have interest to replace someone outside of that set with others. If that is true, one should advocate Minmax on that the Minmax philosophy is a good one, and if it meets Condorcet, that's a bonus as well, but that it's the Minmax philosop
Re: [EM] Why I Prefer IRV to Condorcet
--- On Tue, 25/11/08, Chris Benham <[EMAIL PROTECTED]> wrote: > I agree that resistance to Burying is atractive and IRV's big selling > point versus Condorcet methods. Yes, this may be the strongest selling argument of IRV against Condorcet. But I think this doesn't yet mean that Condorcet methods would in real life be vulnerable to burying. Use of burial may require good understanding of the opinions of others and good coordination, and may include risks, and requires many voters to accept the idea of strategic voting. My hope thus is that these threats would mostly remain theoretical. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
--- On Tue, 25/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: I'll try to answer very shortly to most of the points. I can comment more if there are some interesting ones. > From: Kristofer Munsterhjelm <[EMAIL PROTECTED]> > Subject: Re: [EM] Why I Prefer IRV to Condorcet > To: [EMAIL PROTECTED] > Cc: [EMAIL PROTECTED] > Date: Tuesday, 25 November, 2008, 1:37 PM > Juho Laatu wrote: > > --- On Sun, 23/11/08, Kristofer Munsterhjelm > <[EMAIL PROTECTED]> > > wrote: > > > >> Regarding number two, simple Condorcet methods > exist. Borda-elimination (Nanson or Raynaud) is Condorcet. > Minmax is quite > >> simple, and everybody who's dealt with sports > knows Copeland (with > >> Minmax tiebreaks). I'll partially grant this, > though, since the > >> good methods are complex > > > > Minmax is both simple and good. I think at least > minmax(margins) is a > > good solution for many needs. > > > > The weakest spot of minmax(margins) could be that it > fails mutual > > majority. That means for example that nominating a set > of clones > > instead of just one candidate could lead (at least in > theory) to not > > winning the election. > > > > On the other hand other methods than minmax(margins) > may not respect > > the good idea of mmm to elect the candidate that has > the least > > incentive among voters to be changed to some other of > the candidates. > > I think Schulze said that his method was the one that > agreed most with Minmax while still being cloneproof. > According to Warren, that is true (he refers to simulations > made by Petry and Heitzig) - see > http://rangevoting.org/SchulzeExplan.html . The claim seems to be about Smith//MinMax. > At the other end of "generalizable methods" you > have Kemeny. Kemeny is not cloneproof (it suffers from > crowding). I wonder what "Cloneproof Kemeny" would > look like, but there have been attempts to move Ranked Pairs > closer to Kemeny. See Heitzig's Short Ranked Pairs: > http://listas.apesol.org/pipermail/election-methods-electorama.com/2004-November/014208.html Note that the minmax philosophy is to study paths of length one. Minmax philosophy says that voter interest to replace the elected candidate with another is more relevant than their interest to replace the candidates in chain. (Such chains of changes do not typically happen in real life after the election.) > > (Minmax(margins) fails also Smith and Condorcet loser, > but those > > violations can be explained to be intentional and > positive.) > > That's a problem, in my opinion. A voting method also > is a metric of who deserves to win. Yes if one sets that as a target. The alternative is to emphasize also other aspects like being free of strategic voting related risks. I think minmax can be seen as an ideal definition (for some needs) of which candidate is best. > In that point of view, > if the metric says that Condorcet winners are good, but the > method can elect Conorcet losers, the metric is > self-contradictory. Minmax may elect the Condorcet loser only when there is no Condorcet winner. And only in situations where all other candidates are worse than the Condorcet loser from the minmax philosophy/utility point of view. > As for Smith, I would like to have that > as well, since if the method says Condorcet for a candidate, > it should also say Condorcet for a set (unless there's > some overriding strategy-proofing reason as to why not). I don't see that as a requirement even if there were no strategy-proofing needs. The minmax philosophy says that voters may have more interest to replace the elected Smith set member with another member of the set than they have interest to replace someone outside of that set with others. > >> , but I'll ask whether you think MAM (Ranked > Pairs(wv)) is too complex. In MAM, you take all the pairwise > contests, sort by strength, and affirm down the list unless > you would contradict an > >> earlier affirmed contest. This method is > cloneproof, monotonic, > >> etc... > >> > >> Perhaps you could explain it in that "say A > won. B's supporters are > >> going to say "but some people preferred B to > A!". Then you can say, > >> but more people preferred C to B and A to C". > I'm not sure, there may be better explanations. > > > > Also minmax(margins) is close to this. It has a very > natural > > explanation. (I gave one rough explanation above. > Another one is > > "elect the candidate that needs least additional > votes to win all > > others".)
Re: [EM] Why I Prefer IRV to Condorcet
Chris Benham wrote: Kristopher, All Condorcet methods are vulnerable to Burial. Smith,IRV has in common with IRV but not the other well-known Condorcet methods that a Mutual Dominant Third winner can't be buried. But like all other Condorcet methods it is not absolutely invulnerable to Burial like IRV. 37: A>B 31: B>A 32: C>B B is the CW, but if the A>B voters bury B by changing to A>C then the Smith,IRV winner changes from B to A. For the advantage over IRV of the difference between Smith and Mutual Dominant Third (MDT), we lose Burial Invulnerability and Later-no-Harm and Later-no-Help and Mono-add-Top. So I think the argument that Smith,IRV is really much better than the simpler plain IRV is weak. Likewise the case that Smith,IRV is the best Condorcet method. I wouldn't say Smith,IRV is the best Condorcet method, either, but it may be the closest thing if people are very inclined towards burying candidates (and we want Condorcet). "Is it possible to make a monotonic method that's resistant to burial?" Yes, FPP fills that bill. Other methods have incentives to "bury" only by truncating, not order-reversing. (According to a definition I'm not entirely happy with this qualifiies as "burying"). I have in mind the methods that met Later-no-Help and not Later-no-Harm, such as Bucklin and Approval. It would seem that in order for a method to be completely resistant to burial (including truncation), it must meet both LNHelp and LNHarm. That makes sense, because Burial involves altering the position of those lower down on your ranking to help the candidate that's higher up in your ranking. However, we know from Woodall that we can't have both LNHs, mutual majority, and monotonicity, nor can we have LNH* and Condorcet. Thus a method that's completely resistant would seem to need to be nonmonotonic or fail mutual majority, and in either case fail Condorcet. There is one way out: consider a method that fails LNH* only in such ways that are not conducive to burial. For instance, it may be that if you vote A>B>C, then moving B last would cause C to win (instead of B). This is like Warren's claims about Black (Condorcet else Borda). You gave an example where burial works in Black, so Black is somewhat susceptible to burial, but it's theoretically possible there may be a method that works this way. There's also another caveat in the other direction: consider a method with compulsory full ranking and a fixed number of candidates. It may be susceptible to burial (order reversal) even if LNH* no longer make any sense. - FPTP works, but really just because you can't bury. This can technically be "fixed" by treating FPTP as a ranked voting method where only your first preference matters. Still, it's a bit of a trick, so let me try something a bit more detailed. I wonder if there's a method that meets Condorcet and Dominant Mutual * burial resistance (the lesser the fraction the better), and is also monotonic. Both Smith,IRV and "first preference Copeland" meet Dominant Mutual Third burial resistance, but they're both nonmonotonic. While I'm wishing, having it summable would also be nice. Or, for that matter, do we have a method that meets DMTBR, mutual majority, and monotonicity? Perhaps DAC (since it meets LNHelp), but it has other problems, and it doesn't meet plain DMT. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I Prefer IRV to Condorcet
Kristopher, All Condorcet methods are vulnerable to Burial. Smith,IRV has in common with IRV but not the other well-known Condorcet methods that a Mutual Dominant Third winner can't be buried. But like all other Condorcet methods it is not absolutely invulnerable to Burial like IRV. 37: A>B 31: B>A 32: C>B B is the CW, but if the A>B voters bury B by changing to A>C then the Smith,IRV winner changes from B to A. For the advantage over IRV of the difference between Smith and Mutual Dominant Third (MDT), we lose Burial Invulnerability and Later-no-Harm and Later-no-Help and Mono-add-Top. So I think the argument that Smith,IRV is really much better than the simpler plain IRV is weak. Likewise the case that Smith,IRV is the best Condorcet method. "Is it possible to make a monotonic method that's resistant to burial?" Yes, FPP fills that bill. Other methods have incentives to "bury" only by truncating, not order-reversing. (According to a definition I'm not entirely happy with this qualifiies as "burying"). I have in mind the methods that met Later-no-Help and not Later-no-Harm, such as Bucklin and Approval. Chris Benham Kristofer Munsterhjelm wrote (Tues.Nov.25): As we know, Smith,IRV is resistant to burial (hence my statement of "if you're going to have IRV, have Smith,IRV", since you gain Condorcet compliance). I also think Minmax-elimination is resistant to burial (at least it elects the "right" candidate in your Mutual Dominant Quarter example). However, IRV is nonmonotonic. Is it possible to make a monotonic method that's resistant to burial? Dominant Mutual Third resistance? Dominant Mutual Quarter? It would give very unintuitive results, but might be needed if most of the electorate go "on a burial spree". I know of no method that actually has these properties, though; the method I called "first preference Copeland" was shown to be nonmonotonic as well (incidentally, by you: http://lists.electorama.com/pipermail/election-methods-electorama.com/2007 -January/019135.html ) (FPC is the method that, for each candidate, its penalty is the sum of the first preference votes of the ones that pairwise beat it. Whoever has least penalty wins.) Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
Juho Laatu wrote: --- On Sun, 23/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: Regarding number two, simple Condorcet methods exist. Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll partially grant this, though, since the good methods are complex Minmax is both simple and good. I think at least minmax(margins) is a good solution for many needs. The weakest spot of minmax(margins) could be that it fails mutual majority. That means for example that nominating a set of clones instead of just one candidate could lead (at least in theory) to not winning the election. On the other hand other methods than minmax(margins) may not respect the good idea of mmm to elect the candidate that has the least incentive among voters to be changed to some other of the candidates. I think Schulze said that his method was the one that agreed most with Minmax while still being cloneproof. According to Warren, that is true (he refers to simulations made by Petry and Heitzig) - see http://rangevoting.org/SchulzeExplan.html . At the other end of "generalizable methods" you have Kemeny. Kemeny is not cloneproof (it suffers from crowding). I wonder what "Cloneproof Kemeny" would look like, but there have been attempts to move Ranked Pairs closer to Kemeny. See Heitzig's Short Ranked Pairs: http://listas.apesol.org/pipermail/election-methods-electorama.com/2004-November/014208.html (Minmax(margins) fails also Smith and Condorcet loser, but those violations can be explained to be intentional and positive.) That's a problem, in my opinion. A voting method also is a metric of who deserves to win. In that point of view, if the metric says that Condorcet winners are good, but the method can elect Conorcet losers, the metric is self-contradictory. As for Smith, I would like to have that as well, since if the method says Condorcet for a candidate, it should also say Condorcet for a set (unless there's some overriding strategy-proofing reason as to why not). , but I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In MAM, you take all the pairwise contests, sort by strength, and affirm down the list unless you would contradict an earlier affirmed contest. This method is cloneproof, monotonic, etc... Perhaps you could explain it in that "say A won. B's supporters are going to say "but some people preferred B to A!". Then you can say, but more people preferred C to B and A to C". I'm not sure, there may be better explanations. Also minmax(margins) is close to this. It has a very natural explanation. (I gave one rough explanation above. Another one is "elect the candidate that needs least additional votes to win all others".) Kemeny is also quite simple, I suppose. It's merely "Find the ordering where most people agree with the preferences". However, it's not in polytime; finding the winner, asymptotically, is very hard (though linear programming tricks can be used, that makes the method extremely complex). I don't think Kemeny is Smith, either. I don't claim that Minmax(margins) would be the best Condorcet method for all needs. I rather claim that there are many kind of elections and there are many alternative targets. Minmax (margins) emphasizes small opposition (in favour of any other single candidate) against the elected candidate. This justification focuses on the performance with sincere votes. Also other good criteria that describe which candidate would be the best may be used.. Another direction is to look for a method that is most resistent to straegic voting. (Many of the best known criteria emphasize this viewpoint.) If the environment where the method will be used in plagued with widespread strategic voting then it makes sense to emphasize the "strategy free" oriented criteria a bit. If the voters are expected to be predominantly sincere then one has the luxury to focus on criteria that aim at electing the best winner. The problem is that we don't know how strategic people, or parties are going to be. This depends on the nation and people; when New York briefly had STV, the parties almost immediately turned to vote management, but other countries with STV have been free of vote management. I think Ireland is one of the latter. One way to deal with this is to make the method maximally safe against strategy. However, for some types of strategy this makes the method return worse results were the voters honest. Say there's an election where the "unaugmented winner" is X. If the method is strategy-hardened, the winner will be Y instead. Then there may be an instance in which people truly wanted X, but also another instance where the people truly wanted Y but some employed strategy. The method can't read people's minds and thus can't know which is the case, which means that any case of the former would lead to a worse result if the method
Re: [EM] Why I Prefer IRV to Condorcet
Chris Benham wrote: Greg, I've come to the strong view that truncation (e.g. bullet voting) without order-reversal shouldn't really qualify as a (insincere) "strategy". I don't see any point or use in us trying to distinguish between: truncation because the voter is sincerely ambivalent or has no preference among the unranked candidates, truncation because the voter's preferences among the unranked candidates are too weak for her to be bothered recording, or truncation because the voter fears being stung by later-harm or is deliberately concealing a clear pairwise preference in a diabolical scheme to thwart the election of a shining sincere Condorcet winner. I agree that resistance to Burying is atractive and IRV's big selling point versus Condorcet methods. As we know, Smith,IRV is resistant to burial (hence my statement of "if you're going to have IRV, have Smith,IRV", since you gain Condorcet compliance). I also think Minmax-elimination is resistant to burial (at least it elects the "right" candidate in your Mutual Dominant Quarter example). However, IRV is nonmonotonic. Is it possible to make a monotonic method that's resistant to burial? Dominant Mutual Third resistance? Dominant Mutual Quarter? It would give very unintuitive results, but might be needed if most of the electorate go "on a burial spree". I know of no method that actually has these properties, though; the method I called "first preference Copeland" was shown to be nonmonotonic as well (incidentally, by you: http://lists.electorama.com/pipermail/election-methods-electorama.com/2007 -January/019135.html ) (FPC is the method that, for each candidate, its penalty is the sum of the first preference votes of the ones that pairwise beat it. Whoever has least penalty wins.) Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I Prefer IRV to Condorcet
Greg, I've come to the strong view that truncation (e.g. bullet voting) without order-reversal shouldn't really qualify as a (insincere) "strategy". I don't see any point or use in us trying to distinguish between: truncation because the voter is sincerely ambivalent or has no preference among the unranked candidates, truncation because the voter's preferences among the unranked candidates are too weak for her to be bothered recording, or truncation because the voter fears being stung by later-harm or is deliberately concealing a clear pairwise preference in a diabolical scheme to thwart the election of a shining sincere Condorcet winner. I agree that resistance to Burying is atractive and IRV's big selling point versus Condorcet methods. Chris Benham Greg Dennis wrote (Sat.Nov.22): Perhaps intuitiveness is a bit in the eyes of the beholder, but I'll tell you the strategies I find intuitive: - Burying a candidate with strong first choice support - Bullet voting for a candidate with strong first choice support - A compromise in which you switch your first choice vote to a candidate who has stronger first choice support. -snip- ...I have grown to believe resistance to burying essential. -snip- Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
--- On Sun, 23/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > Regarding number two, simple Condorcet methods exist. > Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax > is quite simple, and everybody who's dealt with sports > knows Copeland (with Minmax tiebreaks). I'll partially > grant this, though, since the good methods are complex Minmax is both simple and good. I think at least minmax(margins) is a good solution for many needs. The weakest spot of minmax(margins) could be that it fails mutual majority. That means for example that nominating a set of clones instead of just one candidate could lead (at least in theory) to not winning the election. On the other hand other methods than minmax(margins) may not respect the good idea of mmm to elect the candidate that has the least incentive among voters to be changed to some other of the candidates. (Minmax(margins) fails also Smith and Condorcet loser, but those violations can be explained to be intentional and positive.) > , but > I'll ask whether you think MAM (Ranked Pairs(wv)) is too > complex. In MAM, you take all the pairwise contests, sort by > strength, and affirm down the list unless you would > contradict an earlier affirmed contest. This method is > cloneproof, monotonic, etc... > > Perhaps you could explain it in that "say A won. > B's supporters are going to say "but some people > preferred B to A!". Then you can say, but more people > preferred C to B and A to C". I'm not sure, there > may be better explanations. Also minmax(margins) is close to this. It has a very natural explanation. (I gave one rough explanation above. Another one is "elect the candidate that needs least additional votes to win all others".) I don't claim that Minmax(margins) would be the best Condorcet method for all needs. I rather claim that there are many kind of elections and there are many alternative targets. Minmax (margins) emphasizes small opposition (in favour of any other single candidate) against the elected candidate. This justification focuses on the performance with sincere votes. Also other good criteria that describe which candidate would be the best may be used.. Another direction is to look for a method that is most resistent to straegic voting. (Many of the best known criteria emphasize this viewpoint.) If the environment where the method will be used in plagued with widespread strategic voting then it makes sense to emphasize the "strategy free" oriented criteria a bit. If the voters are expected to be predominantly sincere then one has the luxury to focus on criteria that aim at electing the best winner. There are thus different kind of environments and different kind of needs. One should pick the best method for each need and environment. Somewhere it may be e.g. FPTP or minmax(margins), somewhere something else. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
Greg wrote: I have written up my reasons for preferring IRV over Condorcet methods in an essay, the current draft of which is available here: http://www.gregdennis.com/voting/irv_vs_condorcet.html I welcome any comments you have. I'll try to do so, then. Note that I support Condorcet. Regarding reason number one, it is true that if there are minor parties that make no difference, IRV will act as if they didn't exist. That is; as long as they get a smaller share of the votes than any of those who would matter, they are excluded. However, as soon as a former minor third party grows large enough, it destabilizes IRV. You can see this in the Yee diagrams for IRV, where the borders near candidates become noisy (and this noise some times travels well into the regions of the candidates themselves). This may be what you're conceding regarding center squeeze, but the problem is not only the third party's, it's all the participants', since the destabilization turns IRV a lot more random (because of the amplifying nature of the elimination). IRV may elect Condorcet winners, but if you accept that electing Condorcet winners is a good thing, then simple tweaks will make IRV even better: one may check for a Condorcet winner (among the remaining candidates) after each elimination, or eliminate the one of the two bottom rated that loses the pairwise contest between the two. Also, the picture may be false: if we were to count Plurality elections as Condorcet elections, one of the two major parties would undoubtedly be the Condorcet winner according to the ballots, but this is merely because of strategy. Regarding number two, simple Condorcet methods exist. Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll partially grant this, though, since the good methods are complex, but I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In MAM, you take all the pairwise contests, sort by strength, and affirm down the list unless you would contradict an earlier affirmed contest. This method is cloneproof, monotonic, etc... Perhaps you could explain it in that "say A won. B's supporters are going to say "but some people preferred B to A!". Then you can say, but more people preferred C to B and A to C". I'm not sure, there may be better explanations. Even if so, this does provide a hard choice, though. I'll grant that, since as far as Condorcet methods have momentum as election methods, Schulze has the most. I wonder if there are simpler heuristics for Schulze than beatpaths. Schulze's mentioned the Schwartz set heuristic (which I think would be hard to explain) and the arborescence heuristic (which I don't know what is). There's also the observation that voters may not need to know the method. Some counties in New Zealand use Meek STV, which basically uses a convergence algorithm to determine the weights of the ballots after a candidate is elected. That's quite complex, yet they still use it. Regarding the third and fourth, I'll again say that some Condorcet methods are more resistant to burial than others. The IRV modifications I talked about earlier resists burial - Chris Benham showed that the "check for a Condorcet winner" modification passes "mutual dominant third burial resistance", meaning that you can't bury a candidate that would be in the honest mutual dominant third set. Unfortunately, the modification is also nonmonotonic (like IRV is). While I'll have to grant this, I'll say that pushover isn't that unintuitive. Imagine a runoff; now stack the deck against your opponent by making the method elect those who would split your opponent's vote. The randomness or chaos of IRV, as mentioned in the first point response, may make this more difficult than one would expect, but to the extent that is true, IRV suffers from the chaos itself. Also, you use examples to show that by demanding core support, IRV gets rid of unknowns. However, IRV can fail to elect candidates with significant core support. Warren has an example of that at http://rangevoting.org/CoreSupp.html . Regarding number five, I would think that IRV would limit Condorcet rather than making it feasible. Consider the case where IRV is passed but nothing significant happens to the distribution of power. Then we say "Hey, IRV is bad, but give us a chance, try Condorcet". The voters may readily say "you got your chance, and election methods don't seem to matter anyway, we just get two party rule". In addition, if IRV doesn't do anything, we're still left with a two party regime, and those parties will be very interested in blocking Condorcet. To the extent applicable, the Australian House of Representatives election may show whether IRV supports multiple parties: in this case, it doesn't seem to do so (the House usually being populated by three parties, but the National
Re: [EM] Why I Prefer IRV to Condorcet
--- On Sat, 22/11/08, Greg <[EMAIL PROTECTED]> wrote: > Perhaps intuitiveness is a bit in the eyes of the beholder, > but I'll > tell you the strategies I find intuitive: > > - Burying a candidate with strong first choice support Yes. This is close to the case that I discussed. I didn't assume strong first choice support but just any strength (e.g. being close to a Condorcet winner). > - Bullet voting for a candidate with strong first choice > support Yes. (Also any other strength ok, or one could bullet vote one's own not-so-strong favourite.) > - A compromise in which you switch your first choice vote > to a > candidate who has stronger first choice support. Yes. (Again strong first choice support typical but not necessary.) > > From anecdotal personal experience, I actually think > burying might be > the most intuitive of them all. Yes, may be. > Almost every university > election I > voted for as an undergraduate used IRV. After each one, > there was > often a person here or there who claimed to have voted for > one > front-runner and buried the other front-runner on their > ballot, not > aware that this had no effect on the outcome. Now, as I go > around > teaching IRV to people, there's often some guy who > thinks he's clever > who brings up the idea of burying (though he doesn't > know the term > "bury"), thinking he's discovered some sort > of flaw; that is, until I > correct him. One problem (or actually a good thing) with strategies is that if there are strategies they may not always be rational. In such a situation hopefully we can recommend sincere voting to all voters as a better alternative to confused use of various strategies. > > It is from this personal experience that I have grown to > believe > resistance to burying essential. Again, this is purely > anecdotal, and > empirical research in this area would be helpful. It is very difficult to defend against widespread irrational use of strategies. Recommending sincere voting may be a good approach. (Maybe people will learn after spoiling some election and electing some clearly unwanted candidate as a result of burying all the reasonable competitors :-) .) Juho > > Greg > > > On Sat, Nov 22, 2008 at 5:53 AM, Juho Laatu > <[EMAIL PROTECTED]> wrote: > > Yes, it is not intuitive to abandon one's > favourite. What is then intuitive? Burying as a Condorcet > strategy is certainly not intuitive (quite difficult to > understand even to experts). Burying in the sense of ranking > the strongest competitor of one's favourite potential > winner last may be intuitive to many. > > > > Since in Condorcet there are some situations where > burying is a working strategy, this property (if advertised) > may encourage people to (irrationally) bury (or rank the > competitors last) even more generally. In IRV voters may > also intuitively bury although that doesn't make much > sense. > > > > In Condorcet one would thus have to trust > "political advisers" to tell when to bury (to make > the strategy rational). Similarly in the example that I gave > the voters would maybe have to be reminded that it could be > wise to compromise this time. > > > > > > > > Although all the three factions are large the B > supporters may see C as a spoiler. If C would not > participate both B and C supporters would be happier with > the outcome. (C thus spoils the result also from the C > supporters' point of view.) > > > > In the example B and C could be candidates of the same > party. Then nominating also C (the more extreme of the two > potential candidates) was maybe a mistake. > > > > Juho > > > > > > > > --- On Sat, 22/11/08, Greg > <[EMAIL PROTECTED]> wrote: > > > >> From: Greg <[EMAIL PROTECTED]> > >> Subject: Re: [EM] Why I Prefer IRV to Condorcet > >> To: [EMAIL PROTECTED] > >> Cc: election-methods@lists.electorama.com > >> Date: Saturday, 22 November, 2008, 10:04 AM > >> Yes, this is as intuitive as it comes in terms of > IRV > >> strategy, but I > >> still find it ultimately counter-intuitive for the > average > >> voter. > >> Candidate C has a the second-most number of first > choices, > >> which > >> likely corresponds to the second-biggest campaign > >> (second-most amount > >> of money, volunteers, name recognition, exposure, > ads, > >> etc). The > >> thought of abandoning C in favor of B, who will > probably > >> have a > >> smaller campaign (less money, fewer volunteers, &g
Re: [EM] Why I Prefer IRV to Condorcet
Perhaps intuitiveness is a bit in the eyes of the beholder, but I'll tell you the strategies I find intuitive: - Burying a candidate with strong first choice support - Bullet voting for a candidate with strong first choice support - A compromise in which you switch your first choice vote to a candidate who has stronger first choice support. >From anecdotal personal experience, I actually think burying might be the most intuitive of them all. Almost every university election I voted for as an undergraduate used IRV. After each one, there was often a person here or there who claimed to have voted for one front-runner and buried the other front-runner on their ballot, not aware that this had no effect on the outcome. Now, as I go around teaching IRV to people, there's often some guy who thinks he's clever who brings up the idea of burying (though he doesn't know the term "bury"), thinking he's discovered some sort of flaw; that is, until I correct him. It is from this personal experience that I have grown to believe resistance to burying essential. Again, this is purely anecdotal, and empirical research in this area would be helpful. Greg On Sat, Nov 22, 2008 at 5:53 AM, Juho Laatu <[EMAIL PROTECTED]> wrote: > Yes, it is not intuitive to abandon one's favourite. What is then intuitive? > Burying as a Condorcet strategy is certainly not intuitive (quite difficult > to understand even to experts). Burying in the sense of ranking the strongest > competitor of one's favourite potential winner last may be intuitive to many. > > Since in Condorcet there are some situations where burying is a working > strategy, this property (if advertised) may encourage people to > (irrationally) bury (or rank the competitors last) even more generally. In > IRV voters may also intuitively bury although that doesn't make much sense. > > In Condorcet one would thus have to trust "political advisers" to tell when > to bury (to make the strategy rational). Similarly in the example that I gave > the voters would maybe have to be reminded that it could be wise to > compromise this time. > > > > Although all the three factions are large the B supporters may see C as a > spoiler. If C would not participate both B and C supporters would be happier > with the outcome. (C thus spoils the result also from the C supporters' point > of view.) > > In the example B and C could be candidates of the same party. Then nominating > also C (the more extreme of the two potential candidates) was maybe a mistake. > > Juho > > > > --- On Sat, 22/11/08, Greg <[EMAIL PROTECTED]> wrote: > >> From: Greg <[EMAIL PROTECTED]> >> Subject: Re: [EM] Why I Prefer IRV to Condorcet >> To: [EMAIL PROTECTED] >> Cc: election-methods@lists.electorama.com >> Date: Saturday, 22 November, 2008, 10:04 AM >> Yes, this is as intuitive as it comes in terms of IRV >> strategy, but I >> still find it ultimately counter-intuitive for the average >> voter. >> Candidate C has a the second-most number of first choices, >> which >> likely corresponds to the second-biggest campaign >> (second-most amount >> of money, volunteers, name recognition, exposure, ads, >> etc). The >> thought of abandoning C in favor of B, who will probably >> have a >> smaller campaign (less money, fewer volunteers, etc), I >> think will >> strike the average voter as counter-intuitive. In these >> respects, this >> scenario is quite unlike the standard spoiler scenario, >> where the >> incentive is to intuitively switch one's vote from the >> smaller to the >> bigger campaign. Nevertheless, I would agree that it's >> something to be >> on the lookout for as IRV spreads. >> >> Greg >> >> >> On Sat, Nov 22, 2008 at 2:00 AM, Juho Laatu >> <[EMAIL PROTECTED]> wrote: >> > Here's one IRV example with three strong >> candidates and where voters do have some incentive to >> compromise. >> > >> > 45: A>B>C >> > 10: B>A>C >> > 15: B>C>A >> > 30: C>B>A >> > >> > We have one centrist candidate (B) between two others. >> > >> > According to this poll it seems that B will be >> eliminated first, and then A would win since some B >> supporters prefer A to C. >> > >> > If sufficient number of C supporters would abandon >> their favourite and vote B>C>A, then C would be >> eliminated first and the centrist candidate B would be >> elected. >> > >> > Based on this poll it seems that if C voters don't >>
Re: [EM] Why I Prefer IRV to Condorcet
Yes, it is not intuitive to abandon one's favourite. What is then intuitive? Burying as a Condorcet strategy is certainly not intuitive (quite difficult to understand even to experts). Burying in the sense of ranking the strongest competitor of one's favourite potential winner last may be intuitive to many. Since in Condorcet there are some situations where burying is a working strategy, this property (if advertised) may encourage people to (irrationally) bury (or rank the competitors last) even more generally. In IRV voters may also intuitively bury although that doesn't make much sense. In Condorcet one would thus have to trust "political advisers" to tell when to bury (to make the strategy rational). Similarly in the example that I gave the voters would maybe have to be reminded that it could be wise to compromise this time. Although all the three factions are large the B supporters may see C as a spoiler. If C would not participate both B and C supporters would be happier with the outcome. (C thus spoils the result also from the C supporters' point of view.) In the example B and C could be candidates of the same party. Then nominating also C (the more extreme of the two potential candidates) was maybe a mistake. Juho --- On Sat, 22/11/08, Greg <[EMAIL PROTECTED]> wrote: > From: Greg <[EMAIL PROTECTED]> > Subject: Re: [EM] Why I Prefer IRV to Condorcet > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Saturday, 22 November, 2008, 10:04 AM > Yes, this is as intuitive as it comes in terms of IRV > strategy, but I > still find it ultimately counter-intuitive for the average > voter. > Candidate C has a the second-most number of first choices, > which > likely corresponds to the second-biggest campaign > (second-most amount > of money, volunteers, name recognition, exposure, ads, > etc). The > thought of abandoning C in favor of B, who will probably > have a > smaller campaign (less money, fewer volunteers, etc), I > think will > strike the average voter as counter-intuitive. In these > respects, this > scenario is quite unlike the standard spoiler scenario, > where the > incentive is to intuitively switch one's vote from the > smaller to the > bigger campaign. Nevertheless, I would agree that it's > something to be > on the lookout for as IRV spreads. > > Greg > > > On Sat, Nov 22, 2008 at 2:00 AM, Juho Laatu > <[EMAIL PROTECTED]> wrote: > > Here's one IRV example with three strong > candidates and where voters do have some incentive to > compromise. > > > > 45: A>B>C > > 10: B>A>C > > 15: B>C>A > > 30: C>B>A > > > > We have one centrist candidate (B) between two others. > > > > According to this poll it seems that B will be > eliminated first, and then A would win since some B > supporters prefer A to C. > > > > If sufficient number of C supporters would abandon > their favourite and vote B>C>A, then C would be > eliminated first and the centrist candidate B would be > elected. > > > > Based on this poll it seems that if C voters don't > compromise (or if C will not withdraw) then from C > supporters' point of view the worst candidate (A) will > be elected. > > > > - This situation could be reasonably common (or > plausible) in real life > > - B is a Condorcet winner ((that IRV would not elect)) > > - B seems to be politically closer to C than to A > > - C is not a weak candidate since with few more > "core" voters or second place support it could > beat A (if the strong centrist candidate B will be > eliminated first) > > > > C supporters could be optimistic and hope for a change > in opinions before the election day. I mean that in real > elections many voters may be optimistic and fighting > spirited and believe rather in those earlier polls that gave > their favourite more votes than this poll etc. > > > > The strategy of the C voters is not very > "intuitive" in the sense that it is never natural > to abandon one's favourite (it could be easier e.g. to > rank the strongest competitor last even if that would be an > irrational strategy). But on the other hand it is quite > straight forward to see from the poll results (maybe voiced > out by media) that indeed it makes sense for the C > supporters to give up and abandon C if people will vote as > indicated in this poll. The voters will thus have a dilemma, > whether to vote sincerely or whether to compromise. > > > > Juho > > > > > > > > --- On Sat, 22/11/08, Greg > <[EMAIL PROTECTED]> wrote: > > > >&
Re: [EM] Why I Prefer IRV to Condorcet
Yes, this is as intuitive as it comes in terms of IRV strategy, but I still find it ultimately counter-intuitive for the average voter. Candidate C has a the second-most number of first choices, which likely corresponds to the second-biggest campaign (second-most amount of money, volunteers, name recognition, exposure, ads, etc). The thought of abandoning C in favor of B, who will probably have a smaller campaign (less money, fewer volunteers, etc), I think will strike the average voter as counter-intuitive. In these respects, this scenario is quite unlike the standard spoiler scenario, where the incentive is to intuitively switch one's vote from the smaller to the bigger campaign. Nevertheless, I would agree that it's something to be on the lookout for as IRV spreads. Greg On Sat, Nov 22, 2008 at 2:00 AM, Juho Laatu <[EMAIL PROTECTED]> wrote: > Here's one IRV example with three strong candidates and where voters do have > some incentive to compromise. > > 45: A>B>C > 10: B>A>C > 15: B>C>A > 30: C>B>A > > We have one centrist candidate (B) between two others. > > According to this poll it seems that B will be eliminated first, and then A > would win since some B supporters prefer A to C. > > If sufficient number of C supporters would abandon their favourite and vote > B>C>A, then C would be eliminated first and the centrist candidate B would be > elected. > > Based on this poll it seems that if C voters don't compromise (or if C will > not withdraw) then from C supporters' point of view the worst candidate (A) > will be elected. > > - This situation could be reasonably common (or plausible) in real life > - B is a Condorcet winner ((that IRV would not elect)) > - B seems to be politically closer to C than to A > - C is not a weak candidate since with few more "core" voters or second place > support it could beat A (if the strong centrist candidate B will be > eliminated first) > > C supporters could be optimistic and hope for a change in opinions before the > election day. I mean that in real elections many voters may be optimistic and > fighting spirited and believe rather in those earlier polls that gave their > favourite more votes than this poll etc. > > The strategy of the C voters is not very "intuitive" in the sense that it is > never natural to abandon one's favourite (it could be easier e.g. to rank the > strongest competitor last even if that would be an irrational strategy). But > on the other hand it is quite straight forward to see from the poll results > (maybe voiced out by media) that indeed it makes sense for the C supporters > to give up and abandon C if people will vote as indicated in this poll. The > voters will thus have a dilemma, whether to vote sincerely or whether to > compromise. > > Juho > > > > --- On Sat, 22/11/08, Greg <[EMAIL PROTECTED]> wrote: > >> From: Greg <[EMAIL PROTECTED]> >> Subject: Re: [EM] Why I Prefer IRV to Condorcet >> To: election-methods@lists.electorama.com >> Date: Saturday, 22 November, 2008, 3:06 AM >> Thanks, Chris. I'll correct the errors and rephrase some >> things I >> didn't say correctly. >> >> On the Compromise strategy, I think some compromises are >> more >> intuitive than others. I think it's intuitive to >> abandon a more weakly >> supported candidate, e.g. Nader, in favor of a major >> candidate, as is >> common in FPTP. But it strikes me as more >> counter-intuitive, at least >> for the average voter, to abandon a candidate with strong >> core support >> in favor of a more weakly supported candidate, as could >> happen under >> IRV. Then there's the issue as to whether the result of >> the >> strategizing is a better or worse result overall . . . but >> that's a >> tricky topic for another time. >> >> >> > Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST) >> > From: Chris Benham <[EMAIL PROTECTED]> >> > Subject: [EM] Why I Prefer IRV to Condorcet >> > >> > Greg, >> > I generally liked your essay. I rate IRV as the best >> of the single-winner methods that >> > meet Later-no-Harm, and a good method (and a vast >> improvement on FPP). >> > >> > But I think you made a couple of technical errors. >> > >> > "However, because bullet voting can help and >> never backfire against one's top choice under >> > Condorcet, expect every campaign with a shot at >> winning to encourage its supporters to >> > bullet vote. " >> > >> > Bullet vo
Re: [EM] Why I Prefer IRV to Condorcet
Here's one IRV example with three strong candidates and where voters do have some incentive to compromise. 45: A>B>C 10: B>A>C 15: B>C>A 30: C>B>A We have one centrist candidate (B) between two others. According to this poll it seems that B will be eliminated first, and then A would win since some B supporters prefer A to C. If sufficient number of C supporters would abandon their favourite and vote B>C>A, then C would be eliminated first and the centrist candidate B would be elected. Based on this poll it seems that if C voters don't compromise (or if C will not withdraw) then from C supporters' point of view the worst candidate (A) will be elected. - This situation could be reasonably common (or plausible) in real life - B is a Condorcet winner ((that IRV would not elect)) - B seems to be politically closer to C than to A - C is not a weak candidate since with few more "core" voters or second place support it could beat A (if the strong centrist candidate B will be eliminated first) C supporters could be optimistic and hope for a change in opinions before the election day. I mean that in real elections many voters may be optimistic and fighting spirited and believe rather in those earlier polls that gave their favourite more votes than this poll etc. The strategy of the C voters is not very "intuitive" in the sense that it is never natural to abandon one's favourite (it could be easier e.g. to rank the strongest competitor last even if that would be an irrational strategy). But on the other hand it is quite straight forward to see from the poll results (maybe voiced out by media) that indeed it makes sense for the C supporters to give up and abandon C if people will vote as indicated in this poll. The voters will thus have a dilemma, whether to vote sincerely or whether to compromise. Juho --- On Sat, 22/11/08, Greg <[EMAIL PROTECTED]> wrote: > From: Greg <[EMAIL PROTECTED]> > Subject: Re: [EM] Why I Prefer IRV to Condorcet > To: election-methods@lists.electorama.com > Date: Saturday, 22 November, 2008, 3:06 AM > Thanks, Chris. I'll correct the errors and rephrase some > things I > didn't say correctly. > > On the Compromise strategy, I think some compromises are > more > intuitive than others. I think it's intuitive to > abandon a more weakly > supported candidate, e.g. Nader, in favor of a major > candidate, as is > common in FPTP. But it strikes me as more > counter-intuitive, at least > for the average voter, to abandon a candidate with strong > core support > in favor of a more weakly supported candidate, as could > happen under > IRV. Then there's the issue as to whether the result of > the > strategizing is a better or worse result overall . . . but > that's a > tricky topic for another time. > > > > Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST) > > From: Chris Benham <[EMAIL PROTECTED]> > > Subject: [EM] Why I Prefer IRV to Condorcet > > > > Greg, > > I generally liked your essay. I rate IRV as the best > of the single-winner methods that > > meet Later-no-Harm, and a good method (and a vast > improvement on FPP). > > > > But I think you made a couple of technical errors. > > > > "However, because bullet voting can help and > never backfire against one's top choice under > > Condorcet, expect every campaign with a shot at > winning to encourage its supporters to > > bullet vote. " > > > > Bullet voting can "backfire against one's top > choice under Condorcet" because Condorcet > > methods, unlike IRV, fail Later-no-Help. > > > > > http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf > > > > In this 1996 Douglas Woodall paper, see "Election > 6" and the accompanying discussion on > > page 5/6 of the pdf (labelled on the paper as > "Page 13"). > > > > Quoting again from your paper: > > "As mentioned, every voting system is > theoretically vulnerable to strategic manipulation, and IRV > > is no exception. However, under IRV, there is no > strategy that can increase the likelihood of > > electing one's first choice beyond the opportunity > offered by honest rankings. While there are > > strategies for increasing the chances of less > preferred candidates under IRV, like push-over, > > they are counter-intuitive." > > > > The Push-over strategy is certainly not limited to > improving the chance of electing a "lower > > [than first] choice". Say sincere is: > > > > 49: A? > > 27: B>A > > 24: C>B > > > > B is the IRV winner
Re: [EM] Why I Prefer IRV to Condorcet
Thanks, Chris. I'll correct the errors and rephrase some things I didn't say correctly. On the Compromise strategy, I think some compromises are more intuitive than others. I think it's intuitive to abandon a more weakly supported candidate, e.g. Nader, in favor of a major candidate, as is common in FPTP. But it strikes me as more counter-intuitive, at least for the average voter, to abandon a candidate with strong core support in favor of a more weakly supported candidate, as could happen under IRV. Then there's the issue as to whether the result of the strategizing is a better or worse result overall . . . but that's a tricky topic for another time. > Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST) > From: Chris Benham <[EMAIL PROTECTED]> > Subject: [EM] Why I Prefer IRV to Condorcet > > Greg, > I generally liked your essay. I rate IRV as the best of the single-winner > methods that > meet Later-no-Harm, and a good method (and a vast improvement on FPP). > > But I think you made a couple of technical errors. > > "However, because bullet voting can help and never backfire against one's top > choice under > Condorcet, expect every campaign with a shot at winning to encourage its > supporters to > bullet vote. " > > Bullet voting can "backfire against one's top choice under Condorcet" because > Condorcet > methods, unlike IRV, fail Later-no-Help. > > http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf > > In this 1996 Douglas Woodall paper, see "Election 6" and the accompanying > discussion on > page 5/6 of the pdf (labelled on the paper as "Page 13"). > > Quoting again from your paper: > "As mentioned, every voting system is theoretically vulnerable to strategic > manipulation, and IRV > is no exception. However, under IRV, there is no strategy that can increase > the likelihood of > electing one's first choice beyond the opportunity offered by honest > rankings. While there are > strategies for increasing the chances of less preferred candidates under IRV, > like push-over, > they are counter-intuitive." > > The Push-over strategy is certainly not limited to improving the chance of > electing a "lower > [than first] choice". Say sincere is: > > 49: A? > 27: B>A > 24: C>B > > B is the IRV winner, but if? 4-21 (inclusive) of the A voters change to C or > C>? then the winner > changes to A. > > But as you say the strategy isn't "intuitive" , and backfires if too many of > the A supporters try it. > Some IRV opponents claim to like Top-Two Runoff, but that is more vulnerable > to Push-over > than IRV (because the strategists can support their sincere favourite in the > second round). > > The quite intuitive strategy that IRV is vulnerable to is Compromise, like > any other method that > meets Majority. But voters' incentive to compromise (vote one's front-runner > lesser-evil in first > place to reduce the chance of front-runner greater-evil winning) is generally > vastly vastly less > than it is under FPP. > > (There are methods that meet both Majority and Favourite Betrayal, and in > them compromisers > can harmlessly vote their sincere favourites in equal-first place.) > > But some Condorcet advocates are galled? by the Compromise incentive that can > exist where > there is a sincere CW who is not also a sincere Mutual Dominant Third winner. > > 49: A>B > 02: B>A > 22: B > 27: C>B > > On these votes B is the CW, but IRV elects A.? If the C>B voters change to B > then B will be > the voted majority favourite, so of course IRV like Condorcet methods and FPP > will elect B. > > Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
For some light on the question as to whether or not IRV's failures of the Condorcet Criterion are apt to be rare: http://zesty.ca/voting/sim/ FWS Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
#1 - If your target is to elect Condorcet winners methods that meet Condorcet criterion could be considered. #2 - There are also simple Condorcet methods like "elect the one that needs least additional votes to win all others". - It is also a fact that in many countries few voters actually know and care about the internal details of the method. IRV and Condorcet may look quite similar to them. #3 - I don't think _rational_and_successful_use_ of Condorcet strategies is intuitive to the regular voters. - Some voters may however follow proposed strategies even if they are irrational (also in IRV). - IRV has its problematic scenarios too (like you shortly mentioned). - In large public elections with independent decision making, inaccurate poll information, changing opinions, and less than 100% penetration of strategic voters many strategic vulnerabilities of Condorcet become difficult to apply (or are not probable). Many strategies are easier to carry out on paper and with exaggerated votes and exaggerated voter behaviour than in real life. Each example should be analysed in detail but I'll skip that for now. #4 - One simple approach for A and B would be to sling mud on C too. C seems to be a potential winner (maybe even a sincere Condorcet winner) so one should definitely not let him just hide (if mud is generally used). - I think all candidates want all kind of support (core or other), also in Condorcet although only IRV requires strong core support. - Hiding candidates may be seen as weak candidates, and therefore also Condorcet candidates need clear statements and a profile. - Also in IRV candidates should try to please all the voters to get second preferences (they are important too although first preferences are a must). - No big difference between candidate behaviour. In IRV candidates with limited first place support are not likely to be successful. #5 - Yes, the methods could pave the way for each others. IRV leads in the U.S.. so it may help more. #6 - I don't see a big difference between IRV+STV and Condorcet+STV. Ranking based single winner methods should be a good enough stepping stone for ranking based multi winner methods. Political will may be more important than the internal details of the methods. (- Legal battles might be another thing, and that is a risk in the U.S.) (- Also other good multi winner methods than STV exist.) #7 - Yes, IRV seems to be ahead in the U.S. - People may be familiar with runoffs, but also with tournaments Many of the reasons didn't say that IRV is a better method than Condorcet but focused on other benefits of IRV (or on how it can help Condorcet). Strategic vulnerabilities seemed to be the central point when comparing the actual methods. The vulnerabilities of the two methods are different. I don't think Condorcet is essentially more vulnerable in typical public elections. Also performance with sincere votes should have some weight. Electing a "wrong" candidate with sincere votes doesn't look nice. If election of Condorcet winners is the target then one could try to guarantee that. In some places voters are happy to vote as told by strategists and use whatever tricks there might be. In some places strategic voting is not considered to be good behaviour. Also individuals are different. One could use methods with suitable resistance against strategies or methods that pick good winners depending on the expected strategic behaviour level of the environment. (One could also change the method to a better one if one sees that fears of widespread strategic voting did not materialize, or the other way around.) IRV and Condorcet promoters could indeed cooperate more. IRV is not that bad, and Condorcet certainly neither. The disagreeing promoters (trying to kill the campaigns of each others) may actually be one of the biggest problems slowing down progress in the U.S. Condorcet has also the problem that it has different variants and no consensus on which one is the best. The serial elimination process of IRV may be appealing to the voters (looks like a good fight where some super hero remains last) but due to its semi-random nature (see e.g. the Yee diagrams) it can't be considered to be optimal. IRV is however an improvement when compared to many methods in use today. I tried to be brief. Ask for clarifications if I was too brief somewhere. Juho --- On Wed, 19/11/08, Greg <[EMAIL PROTECTED]> wrote: > From: Greg <[EMAIL PROTECTED]> > Subject: [EM] Why I Prefer IRV to Condorcet > To: [EMAIL PROTECTED] > Date: Wednesday, 19 November, 2008, 11:28 PM > I have written up my reasons for preferring IRV over > Condorcet methods > in an essay, the current draft of which is available here: > http://www.gregdennis.com/voting/irv_vs_condorcet.html > > I welcome any comments you have. > > Thanks, > Greg > &
[EM] Why I Prefer IRV to Condorcet
Greg, I generally liked your essay. I rate IRV as the best of the single-winner methods that meet Later-no-Harm, and a good method (and a vast improvement on FPP). But I think you made a couple of technical errors. "However, because bullet voting can help and never backfire against one's top choice under Condorcet, expect every campaign with a shot at winning to encourage its supporters to bullet vote. " Bullet voting can "backfire against one's top choice under Condorcet" because Condorcet methods, unlike IRV, fail Later-no-Help. http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf In this 1996 Douglas Woodall paper, see "Election 6" and the accompanying discussion on page 5/6 of the pdf (labelled on the paper as "Page 13"). Quoting again from your paper: "As mentioned, every voting system is theoretically vulnerable to strategic manipulation, and IRV is no exception. However, under IRV, there is no strategy that can increase the likelihood of electing one's first choice beyond the opportunity offered by honest rankings. While there are strategies for increasing the chances of less preferred candidates under IRV, like push-over, they are counter-intuitive." The Push-over strategy is certainly not limited to improving the chance of electing a "lower [than first] choice". Say sincere is: 49: A 27: B>A 24: C>B B is the IRV winner, but if 4-21 (inclusive) of the A voters change to C or C>? then the winner changes to A. But as you say the strategy isn't "intuitive" , and backfires if too many of the A supporters try it. Some IRV opponents claim to like Top-Two Runoff, but that is more vulnerable to Push-over than IRV (because the strategists can support their sincere favourite in the second round). The quite intuitive strategy that IRV is vulnerable to is Compromise, like any other method that meets Majority. But voters' incentive to compromise (vote one's front-runner lesser-evil in first place to reduce the chance of front-runner greater-evil winning) is generally vastly vastly less than it is under FPP. (There are methods that meet both Majority and Favourite Betrayal, and in them compromisers can harmlessly vote their sincere favourites in equal-first place.) But some Condorcet advocates are galled by the Compromise incentive that can exist where there is a sincere CW who is not also a sincere Mutual Dominant Third winner. 49: A>B 02: B>A 22: B 27: C>B On these votes B is the CW, but IRV elects A. If the C>B voters change to B then B will be the voted majority favourite, so of course IRV like Condorcet methods and FPP will elect B. Chris Benham Greg wrote (Wed.Nov.19, 2008): I have written up my reasons for preferring IRV over Condorcet methods in an essay, the current draft of which is available here: http://www.gregdennis.com/voting/irv_vs_condorcet.html I welcome any comments you have. Thanks, Greg Make the switch to the world's best email. Get Yahoo!7 Mail! http://au.yahoo.com/y7mail Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
Hi Greg, --- En date de : Mer 19.11.08, Greg <[EMAIL PROTECTED]> a écrit : > De: Greg <[EMAIL PROTECTED]> > Objet: [EM] Why I Prefer IRV to Condorcet > À: [EMAIL PROTECTED] > Date: Mercredi 19 Novembre 2008, 15h28 > I have written up my reasons for preferring IRV over > Condorcet methods > in an essay, the current draft of which is available here: > http://www.gregdennis.com/voting/irv_vs_condorcet.html > > I welcome any comments you have. > > Thanks, > Greg I want to comment on the first point/reason. I'll quote from the page. >First and foremost, IRV eliminates the most common type of Condorcet >failure --- the "spoiler" scenario --- where the presence of a candidate >with little core support causes a Condorcet winner with strong core >support to lose. I don't understand what kind of scenario you're referring to. I thought I did, and was going to say that good Condorcet methods don't behave in that way. But then I noticed the term "core support," which puzzles me in the context of Condorcet spoilers. >Admittedly, there is another situation similar to the spoiler problem --- >the "center squeeze" scenario -- in which IRV may fail to elect the >Condorcet winner. In this scenario, the presence of a candidate with >strong core support causes a Condorcet winner with little core support to >lose. Fortunately, despite the theoretical possibility of this scenario, >the empirical evidence suggests that it is vanishingly rare in practice. >Despite the hundreds of public IRV elections that are conducted worldwide >every year, the actual concrete examples of it occurring in practice are >few and far between. A problem with using IRV elections to judge whether IRV suffers from a center squeeze effect, is that it overlooks the possibility that IRV's nomination incentives deter would-be Condorcet winners from running (due to the fact that everyone knows they would not win). You can make the argument that plurality also has very good Condorcet efficiency since it is never observed to fail to elect a Condorcet winner. Even adding the ability to rank lower preferences would probably not change this, since with no real change to the method there is also no real change to the nomination incentives. >Lacking sufficient examples of real elections in which IRV has failed to >elect the Condorcet winner, a few IRV critics have resorted to using top- >two runoff elections in which the Condorcet winner lost as evidence of >IRV's center-squeeze problem. However, top-two runoff and instant runoff >are different systems that can produce different results, so >this "evidence" is hardly convincing. Actually some of us will argue that top-two runoff seems likely to have better Condorcet efficiency (in the abstract sense) than IRV. I can see an argument for both sides. But I would agree that they are different systems with different incentives. I have a few problems with #4... Partly that I find the arguments speculative wrt candidate behavior, and partly that I don't see an inherent advantage in knowing where candidates stand if everything is still going to come down to competing blocs of core support that probably dislike each other. Mostly, and related, it's that if we agree that we can't trust voters to give us meaningful lower preferences, then I lose most of my enthuasism for voting methods. If we can only trust first preferences, and candidates that get a lot of first preferences, how much room do we really have to make improvements? We can stray from plurality hardly at all. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I Prefer IRV to Condorcet
I have written up my reasons for preferring IRV over Condorcet methods in an essay, the current draft of which is available here: http://www.gregdennis.com/voting/irv_vs_condorcet.html I welcome any comments you have. Thanks, Greg Election-Methods mailing list - see http://electorama.com/em for list info
