Re: [EM] Majority winner set
JanetRAnderson wrote: I'm still grasping for a counting method which is easily explained to the public. Let me try this out with you. Using IRV, eliminate all but the two top candidates, in order from least to most. A look at the real life current returns in Florida shows, better than most mathematical formulas, how critical the order of transfer becomes in a close election. Would this be an improvement over the current definition of IRV? Janet Is this any different from IRV as currently defined? I think the general consensus, even among those on this list who don't agree on much else, is that the root of most of IRV's problems is the fact that it uses transfers at all. Bart
Re: [EM] Majority winner set
Markus Schulze wrote: Suppose that this given voter would have approved Nader and disapproved Gore and Bush if he had no information about the voting behaviour of the other voters. Then I am saying that this voter votes insincerely when he approves Nader and Gore and disapproves only Bush after he has got additional information about the voting behaviour of the other voters. You seem to consider it to be an advantage of Approval Voting that he can't express both preferences. I consider it to be a disadvantage of Approval Voting that he can't express both preferences. From my own perspective as a voter, I consider it an advantage NOT to be able to express all preferences. Here's why: If I can express all preferences, then I must assume that other voters can do likewise. Now typically, I will consider some preferences to be more important than others. By being able to express all preferences, all I am really gaining is the right to express preferences I consider unimportant, in addition to the important ones. In exchange for this slight gain, I must accept that other voters' slight preferences can cancel out my important ones. By restricting the ability to express preferences, you encourage voters to focus on the distinctions they consider important, leaving less important ones for other voters to decide (who may be more interested in these). This closely mirrors the social contract we call common courtesy, where individuals willingly accept a slight inconvenience when it provides a greater benefit to another -- such as holding a door open for someone carrying an armload of packages. The expectation is that we, or someone we care about, will benefit from this social contract at some time or another. Immediate reciprocity is not nessary or expected. The fact that he can't express both preferences means that he can influence the election result only when he has very exact information about the voting behaviour of the other voters. When his information I think you know better than this. The behavior of approval voting in the complete absence of polling information is well known. Its average-case performance w/resp. to individual expectations is nearly as good as the Condorcet methods, and certainly better than IRV. Approval's worst-case behavior is actually better than Condorcet's, at least where excluding extremely unpopular candidates is concerned. isn't exact enough then he will probably approve all potential winners resp. disapprove all potential winners so that his vote has no influence on the election result. I don't know what you mean by this statement, but your conclusion makes no sense. Bart Is this really what you want? That a person who doesn't have exact information about the voting behaviour of the other voters should not be able to influence the result of the elections? Markus Schulze
Re: [EM] Majority winner set
you wrote (2 Dec 2000): This, along with small party members' tendency to vote for a lesser- evil in 1st place, and the parties reluctance to run more than 1 candidate, should be mentioned whenever someone talks about IRV's "track record". However, I would like to know whether you would consider a change from Alternative Voting to Plurality in Australia to be a step forward or a step backward. Come on, Markus, that's like asking someone which they like, Bush or Gore. Changing from IRV to Plurality would be a step sideways. You wrote (2 Dec 2000): As you suggested, a version of IIAC could be written about sincere ratings. In fact, we often hear IIAC spoken of as if it is about sincere ratings, and 2 ballotings, one of which has a candidate who isn't in the other balloting. When people refer to that "version", they never define it. It would obviously be much wordier and more complicated than the version that I quote, and which is almost surely Arrow's version: Deleting a loser from the ballots and then recounting those ballots should never change who wins. Arrow presumes that every voter always casts his complete opinion of the candidates on the ballot. He calls this presumption "Unrestricted Domain Criterion." This criterion says that the election method must not restrict the opinion that a given voter can cast. That's odd, because in the versions that I've heard of, Arrow stipulates rank balloting, not ratings balloting. Therefore, to your opinion, Arrow is one of the "head-up-the-ass academics" One thing Arrow is, is a mystery man about whose impossibility theorem many many legends and rumors and tales have been woven. If you want to say that Arrow is one of those academics who are accurately described by my characterization, I'll take your word for that. who doesn't use your "universally accepted" theory. It isn't a theory. And it isn't mine. But you're 1/3 right, because it's universally accepted by everyone but you and your you-know-whats that what voters vote is ballots of the type that are called for by the voting system in use. They don't vote ratings in rank balloting elections, for instance. You wrote (2 Dec 2000): But what are you saying? That the person who doesn't vote Gore over Bush because he wants to vote Nader over Gore is voting insincerely?. He can't express both preferences. As I said, not doing the impossible can't be counted as an act, and so it also isn't an insincere act. Suppose that this given voter would have approved Nader and disapproved Gore and Bush if he had no information about the voting behaviour of the other voters. Then I am saying that this voter votes insincerely when he approves Nader and Gore and disapproves only Bush after he has got additional information about the voting behaviour of the other voters. And I'm saying that that isn't relevant to sincerity, which is about voting a false preference or avoidably declining to vote a sincere one (as described in my definition). Look, if I was going to vote for Gore in the election, believing that I needed him as a lesser-evil, and then I heard that Nader actually could have a win, and that information induces me to change my vote from Gore to Nader, do you claim that I'm voting insincerely when I vote for my favorite because I've found out that I might be able to help him win? Maybe, according to you, sincere voting is possible only in a 0-info election, or by someone who votes according to principle and couldn't care less about optimizing his outcome. You seem to consider it to be an advantage of Approval Voting that he can't express both preferences. Excuse me, Markus; would you post the date of the archived posting in which I said that? I consider it to be a disadvantage of Approval Voting that he can't express both preferences. Yes, according to popular belief, you improve the situation when you let people express more preferences. You've just re-stated that very common popular belief. Actually, however, rank balloting only makes things worse when it forces people to rank someone else over their favorite. When rank balloting is counted by any but the few best ways, it creates a strategic mess, and yes: It's not as good as Approval. Does that answer your question? The fact that he can't express both preferences means that he can influence the election result only when he has very exact information about the voting behaviour of the other voters. Wrong. Vote for all the candidates whose merit is above the average, and you maximize your utility expectation when there's zero information about other people's preferences. Also, many, probably including you, have an exaggerated notion of how much, on the average, people's expression of preferences will be shored in Approval. Actually, since typically a voter will vote for about half of the candidates, it turns out that he'll be expressing about half of his pairwise preferences. If he voted for exactly half of
Re: [EM] Majority winner set
Markus's definition of sincere Approval voting says that reversing or falsifying preferences among candidates other than the incumbant is sincere. Nonsense. Besides, it seems real funky to have different sincerity definitions for different methods. To my opinion, "sincerity" must be defined in such a manner that there is a unique (but not necessarily deterministic) way of voting "sincerely" for a voter with a given opinion. Though everyone has a right to their opinion, you'd have a difficult time convincing others to share that one. Likewise, sincere means that you're not misrepresenting your preferences, but it certainly doesn't say anything about whether or not your voting is influences by strategic considerations. As was pointed out, a sincere ranking can be a strategic vote, if it's done after a strategic calculation when other ways of voting were considered. Mike wrote (24 Nov 2000): A voter votes sincerely if he doesn't vote a preference that isn't a sincere preference or leave unvoted a sincere preference that the balloting system would have allowed him to vote in addition to the preferences that he actually did vote. To my opinion, this is only a necessary but not a sufficient condition for "sincerity." To my opinion, it is also necessary that the voting behaviour of a "sincere" voter does not depend on his information about the voting behaviour of the other voters. I answered this mistaken claim earlier in this message. Say I sincerely believe that candidate X is corrupt. So I spread the word everywhere that he's corrupt, so that he won't win. I'm doing it for a strategic purpose, with an intent to change the outcome of the election. But I also sincerely believe that it's true. Am I acting insincerely? Mike wrote (1 Dec 2000): Markus wrote (30 Nov 2000): I doubt that those who don't promote Approval Voting will agree to your definition of "sincerity." I'm reasonably sure that Brams Fishburn have said, in their book _Approval Voting_, that, for Approval, they define sincere voting as voting without reversing a preferences, without falsifying a preference. Brams and Fishburn are well known supporters of Approval Voting. I'd misunderstood that sentence, and thought that you'd said "promote" instead of "don't promote". But what are you saying? That the person who doesn't vote Gore over Bush because he wants to vote Nader over Gore is voting insincerely?. He can't express both preferences. As I said, not doing the impossible can't be counted as an act, and so it also isn't an insincere act. Mike wrote (1 Dec 2000): Their definition means the same thing that my definition means when it's applied to Approval. My definition agrees with how Brams Fishburn would define sincere voting for Approval, and it also agrees with how we'd all define sincere voting with rank balloting and Plurality. When Approval Voting is used then the optimal strategy looks as follows: 1. Approve all those candidate you prefer to the expected winner. 2. Disapprove all those candidate to which you prefer the expected winner. 3. Approve the expected winner when rather a less preferred than a more preferred candidate is elected. Otherwise disapprove him. #3 isn't clear. It should say "Vote for the expected winner when the other of the 2 frontrunners is someone whom you like less." This is a better way of saying what you said: Vote for whichever of the likely 2 frontrunners you prefer to the other, and vote for everyone whom you like better than him. That's one way of saying that you should vote for the candidate you'd vote for in Plurality, and for everyone whom you like more. But the person who likes mathematics might want to be more elaborate, and take into account estimates of frontrunner probabilities for the various pairs of candidates, to calculate strategy for Plurality or Approval. I emphasize that that isn't necessary, and that one can do fine in Approval by voting for the candidate he'd vote for in Plurality and for everyone whom he likes better--for his favorite of the 2 expected frontrunners and for everyone whom he likes better. Due to Mike's definition of "sincerity," a voter who uses this strategy votes "sincerely." To my opinion, this voter votes "insincerely" at least in those cases where he would have voted in a different manner when he had no information about the voting behaviour of the oher voters. Did you say that with the purpose of convincing anyone or influencing anyone? Then you didn't say it sincerely. It was an insincere statement :-) Mike _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
Re: [EM] Majority winner set
I'm still grasping for a counting method which is easily explained to the public. Let me try this out with you. Using IRV, eliminate all but the two top candidates, in order from least to most. A look at the real life current returns in Florida shows, better than most mathematical formulas, how critical the order of transfer becomes in a close election. Would this be an improvement over the current definition of IRV? Janet - Original Message - From: "MIKE OSSIPOFF" [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, December 02, 2000 10:11 AM Subject: Re: [EM] Majority winner set Markus's definition of sincere Approval voting says that reversing or falsifying preferences among candidates other than the incumbant is sincere. Nonsense. Besides, it seems real funky to have different sincerity definitions for different methods. To my opinion, "sincerity" must be defined in such a manner that there is a unique (but not necessarily deterministic) way of voting "sincerely" for a voter with a given opinion. Though everyone has a right to their opinion, you'd have a difficult time convincing others to share that one. Likewise, sincere means that you're not misrepresenting your preferences, but it certainly doesn't say anything about whether or not your voting is influences by strategic considerations. As was pointed out, a sincere ranking can be a strategic vote, if it's done after a strategic calculation when other ways of voting were considered. Mike wrote (24 Nov 2000): A voter votes sincerely if he doesn't vote a preference that isn't a sincere preference or leave unvoted a sincere preference that the balloting system would have allowed him to vote in addition to the preferences that he actually did vote. To my opinion, this is only a necessary but not a sufficient condition for "sincerity." To my opinion, it is also necessary that the voting behaviour of a "sincere" voter does not depend on his information about the voting behaviour of the other voters. I answered this mistaken claim earlier in this message. Say I sincerely believe that candidate X is corrupt. So I spread the word everywhere that he's corrupt, so that he won't win. I'm doing it for a strategic purpose, with an intent to change the outcome of the election. But I also sincerely believe that it's true. Am I acting insincerely? Mike wrote (1 Dec 2000): Markus wrote (30 Nov 2000): I doubt that those who don't promote Approval Voting will agree to your definition of "sincerity." I'm reasonably sure that Brams Fishburn have said, in their book _Approval Voting_, that, for Approval, they define sincere voting as voting without reversing a preferences, without falsifying a preference. Brams and Fishburn are well known supporters of Approval Voting. I'd misunderstood that sentence, and thought that you'd said "promote" instead of "don't promote". But what are you saying? That the person who doesn't vote Gore over Bush because he wants to vote Nader over Gore is voting insincerely?. He can't express both preferences. As I said, not doing the impossible can't be counted as an act, and so it also isn't an insincere act. Mike wrote (1 Dec 2000): Their definition means the same thing that my definition means when it's applied to Approval. My definition agrees with how Brams Fishburn would define sincere voting for Approval, and it also agrees with how we'd all define sincere voting with rank balloting and Plurality. When Approval Voting is used then the optimal strategy looks as follows: 1. Approve all those candidate you prefer to the expected winner. 2. Disapprove all those candidate to which you prefer the expected winner. 3. Approve the expected winner when rather a less preferred than a more preferred candidate is elected. Otherwise disapprove him. #3 isn't clear. It should say "Vote for the expected winner when the other of the 2 frontrunners is someone whom you like less." This is a better way of saying what you said: Vote for whichever of the likely 2 frontrunners you prefer to the other, and vote for everyone whom you like better than him. That's one way of saying that you should vote for the candidate you'd vote for in Plurality, and for everyone whom you like more. But the person who likes mathematics might want to be more elaborate, and take into account estimates of frontrunner probabilities for the various pairs of candidates, to calculate strategy for Plurality or Approval. I emphasize that that isn't necessary, and that one can do fine in Approval by voting for the candidate he'd vote for in Plurality and for everyone whom he likes better--for his favorite of the 2 expected frontrunners and for everyone whom he likes better. Due to Mike's definition of "sincerity,&qu
Re: [EM] Majority winner set
Dear Craig, dear Martin, dear Mike, Craig wrote (1 Dec 2000): Markus wrote (30 Nov 2000): I suggest the following definition of sincere voting in Approval Voting: A voter votes "sincerely" when he approves all those candidates he prefers to the incumbent and disapproves all those candidates to which he prefers the incumbent. Ahh. I was halfway into writing a message against this when I realised that it's actually quite a good definition. The incumbent represents a perceived utility value of zero (no change) while the other candidates are above or below that value. I'm assuming that whether or not he votes for the incumbent does not effect the sincerity of the vote (?). I agree. Craig wrote (1 Dec 2000): Does this mean, however, that if the incumbent is no longer running, and the incumbent is more liked by a voter than any of the candidates (00 pres election?), then that voter cannot cast a sincere vote? Even when the incumbent doesn't run for re-election the vNM utility of the incumbent is a good guess for what a given voter can expect from the new winner. When the incumbent doesn't run for re-election and a given voter strictly prefers the incumbent to every running candidate, then -to my opinion- this voter disapproves all candidates when he votes sincerely. Martin wrote (1 Dec 2000): Is there not a difference between voting insincerely and voting strategically? For example, if I like Alice and Bob equally in a plurality system, then a cross-mark for Alice, and a cross-mark for Bob are both sincere votes. Suppose I use a dice to initially decide, and pick Alice. then I get info from polls and discover that the race is between Bob and Charlie, and change my vote. This, by Mr. Schulze's requirement, is insincere. But if in the same case the dice happens to pick Bob, then presumably this would be a sincere vote? But to have the sincerity of my vote effectively decided by a dice seems, well... odd at least. Don't like it. To my opinion, "sincerity" must be defined in such a manner that there is a unique (but not necessarily deterministic) way of voting "sincerely" for a voter with a given opinion. Example: When FPP is used then the unique way of voting sincerely is to make a cross-mark for that candidate who is the favorite candidate due to this voter's sincere opinion. Of course it is possible that a given voter has no unique favorite candidate. In this case he will randomly or arbitrarily decide which of his favorite candidates gets his cross-mark. But who gets his cross-mark must not change when this given voter gets additional information about the voting behaviour of the other voters. Mike wrote (24 Nov 2000): A voter votes sincerely if he doesn't vote a preference that isn't a sincere preference or leave unvoted a sincere preference that the balloting system would have allowed him to vote in addition to the preferences that he actually did vote. To my opinion, this is only a necessary but not a sufficient condition for "sincerity." To my opinion, it is also necessary that the voting behaviour of a "sincere" voter does not depend on his information about the voting behaviour of the other voters. Mike wrote (1 Dec 2000): Markus wrote (30 Nov 2000): I doubt that those who don't promote Approval Voting will agree to your definition of "sincerity." I'm reasonably sure that Brams Fishburn have said, in their book _Approval Voting_, that, for Approval, they define sincere voting as voting without reversing a preferences, without falsifying a preference. Brams and Fishburn are well known supporters of Approval Voting. Mike wrote (1 Dec 2000): Their definition means the same thing that my definition means when it's applied to Approval. My definition agrees with how Brams Fishburn would define sincere voting for Approval, and it also agrees with how we'd all define sincere voting with rank balloting and Plurality. When Approval Voting is used then the optimal strategy looks as follows: 1. Approve all those candidate you prefer to the expected winner. 2. Disapprove all those candidate to which you prefer the expected winner. 3. Approve the expected winner when rather a less preferred than a more preferred candidate is elected. Otherwise disapprove him. Due to Mike's definition of "sincerity," a voter who uses this strategy votes "sincerely." To my opinion, this voter votes "insincerely" at least in those cases where he would have voted in a different manner when he had no information about the voting behaviour of the oher voters. Markus Schulze
Re: [EM] Majority winner set
Markus said: I assume that the voters vote vNM utilities and that the election method takes from the reported vNM utilities the information it needs to calculate the winner because I define the criteria in terms of reported vNM utilities. Yes, you define the criteria in terms of a form input that the voting system doesn't actually receive. That's why you can't apply your system to Approval or single-winner Cumulative. Mike Ossipoff _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
RE: [EM] Majority winner set
Markus wrote (in part): I suggest the following definition of sincere voting in Approval Voting: A voter votes "sincerely" when he approves all those candidates he prefers to the incumbent and disapproves all those candidates to which he prefers the incumbent. Ahh. I was halfway into writing a message against this when I realised that it's actually quite a good definition. The incumbent represents a perceived utility value of zero (no change) while the other candidates are above or below that value. I'm assuming that whether or not he votes for the incumbent does not effect the sincerity of the vote (?). Does this mean, however, that if the incumbent is no longer running, and the incumbent is more liked by a voter than any of the candidates (00 pres election?), then that voter cannot cast a sincere vote?
RE: [EM] Majority winner set
Mike wrote (in part): Take another look at my definition of sincere voting. It doesn't say that sincere voting must be nonstrategic. With a rank method the only sincere ballot is a sincere ranking of all the candidates. Why do you have to rank all the candidates in order for it to be a sincere ballot? In fact, I think that the opposite could be true (see below). In Plurality, the only sincere ballot is one that votes for one's sincere favorite. But in Approval, I'm not sure what you'd want to call a sincere ballot. I think that a sensible definition of sincere voting, encompassing all voting methods, is as follows; A voter votes sincerely where no candidate x is voted below another candidate y, if the voter actually prefers x to y. In situations where a voter does not prefer one candidate to another, and is allowed by the method to express the equality of those candidates on the ballot without compromising the validity of that vote or preventing the voter for expressing other sincere preferences, then the vote must show those candidates as equal on the ballot. This definition would mean that in a rank ballot with three candidates A,B,C, and the voter preferring A to B and C, but not having a preference between B and C, then voting A first, and not numbering the others, is the only sincere vote possible. If you add candidate D, whom the voter likes less than all the other candidates, then there are five (or seven) sincere ways of voting; A1 A1,B2 A1,C2 A1,B2,C3 (with or without D4) A1,C2,B3 (with or without D4) In a cumulative voting situation, it would allow a voter to give two candidates the same number of votes, even if that voter prefers one candidate to another, but doesn't allow a voter to give a different number of votes to two candidates liked the same. I could extrapolate to the other methods, but I won't bother at the moment. The definition is broad enough to define a wide range of voting choices as sincere, and also allows for a distinction between sincere strategic voting and insincere strategic voting. Whether this is a good thing or not, I don't know, but I think the definition is intuitively correct, as well as applicable to all methods situations.
Re: [EM] Majority winner set
Dear Markus: You wrote: Of course, it is possible that a given voter makes strategical considerations and gets to the conclusion that voting _sincerely_ is the best _strategy_. But nevertheless it makes sense to differ between sincere voters and insincere voters. When a given voter makes strategical considerations and gets to the conclusion that he cannot get any advantage by voting insincerely, then this is a desirable situation. When a given voter makes strategical considerations and gets to the conclusion that it is advantageous to vote insincerely, then this is not a desirable situation. To me there are degrees of undesirability, depending on the type of strategy used and on the effects of that strategy: 1) I consider it worse if voters actually reverse preferences, than to either express a preference where there is none or abstain where there is a preference. 2) I consider it worse if the insincere strategy worsens the outcome. It is still undesirable if insincere strategy tends to improve the outcome, but less so -- this just means that strategy provides a means to compensate for a system's shortcomings. It's perhaps undesirable that this is necessary, but it's better than not compensating for the shortcomings. 3) I consider it worse if the needed strategy is overly obscure or complex, or misleading in the sense that some voters are fooled into using it incorrectly or lulled into falsely thinking it unnecessary Depending on the above, insincere strategy can be more important or less important than other concerns -- do you agree? If not, it seems to me that the only option is the raffle method, where each voter chooses a single name, and one of these ballots is selected randomly (which does this violate -- non-dictatorship, or non-imposition?) In other words: It is not a problem that a given voter makes strategical considerations after he has got additional information about the voting behaviour of the other voters. But it is a problem when this given voter changes his own voting behaviour because of these strategical considerations. But if there weren't a chance of this happening, there would be no strategical consideration. I suggest the following definition of sincere voting in Approval Voting: A voter votes "sincerely" when he approves all those candidates he prefers to the incumbent and disapproves all those candidates to which he prefers the incumbent. It might work where the incumbent is the obvious front-runner -- at least it gives the voter the flexibility of whether or not to vote for the incumbent -- but there are situations where it wouldn't make sense: 1) There is no incumbent, or 2) The incumbent has no particular advantage over one or more other candidates.
RE: [EM] Majority winner set
Take another look at my definition of sincere voting. It doesn't say that sincere voting must be nonstrategic. With a rank method the only sincere ballot is a sincere ranking of all the candidates. Why do you have to rank all the candidates in order for it to be a sincere ballot? In fact, I think that the opposite could be true (see below). Maybe. Then my definition could be greatly shortened. I'd felt that not expressing a sincere preference when there voting system gives no reason not to is an insincere nonvoting of that preference, an insincere statement that the candidates are equally good. But yes, there's a case for saying the only insincere ballot is one which votes an unfelt pairwise preference. That's because not voting either over the other could be interpreted as not saying anything about their relative merit, rather than saying that they're equally good. That sounds just as valid, and would simplify my definition. Anyway, I claim that in Approval, when it's impossible to vote 2 preferences on the same ballot, it isn't insincere to not combine them, because not doing the impossible doesn't count as an act of any kind, and so it isn't an insincere act. Hence the way I worded my definition. But if we agree that the only insincere vote is one which votes an unfelt preference, then my definition can be much shortened. In Plurality, the only sincere ballot is one that votes for one's sincere favorite. But in Approval, I'm not sure what you'd want to call a sincere ballot. I think that a sensible definition of sincere voting, encompassing all voting methods, is as follows; A voter votes sincerely where no candidate x is voted below another candidate y, if the voter actually prefers x to y. In situations where a voter does not prefer one candidate to another, and is allowed by the method to express the equality of those candidates on the ballot without compromising the validity of that vote or preventing the voter for expressing other sincere preferences, then the vote must show those candidates as equal on the ballot. Ok, you've removed the insincere label from not voting a felt preference, and, as I said, there seems to be a perfectly valid case for regarding it that way. Where I simply referred to voting a preference that isn't a sincere preference, you allow the voter to do that under conditions where he rates the candidates equal, but voting them so would interfere with voting other preferences. I've got to check out how that will act differently from my wording. If you already know, tell me. Maybe when I study your example, that will answer my question. Of course anytime two or more different definitions are reasonable, but only some of them act with all criteria all methods in keeping with how the criteria are intended, then there's a case for using one of those definitions. I don't know yet how these different definitions would act differently. So far I don't know if there are situations where voting 2 candidates equal would interfere with the voting of some preference. Again, a study of your example might show a situation like that. Mike Ossipoff This definition would mean that in a rank ballot with three candidates A,B,C, and the voter preferring A to B and C, but not having a preference between B and C, then voting A first, and not numbering the others, is the only sincere vote possible. If you add candidate D, whom the voter likes less than all the other candidates, then there are five (or seven) sincere ways of voting; A1 A1,B2 A1,C2 A1,B2,C3 (with or without D4) A1,C2,B3 (with or without D4) In a cumulative voting situation, it would allow a voter to give two candidates the same number of votes, even if that voter prefers one candidate to another, but doesn't allow a voter to give a different number of votes to two candidates liked the same. I could extrapolate to the other methods, but I won't bother at the moment. The definition is broad enough to define a wide range of voting choices as sincere, and also allows for a distinction between sincere strategic voting and insincere strategic voting. Whether this is a good thing or not, I don't know, but I think the definition is intuitively correct, as well as applicable to all methods situations. _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
Re: [EM] Majority winner set
Dear Markus-- You said: you say that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "inadequate," "vague," "sloppy," "dishonest," "absurd," "faulty," "incorrect," "poor," "silly," "contradictory," "incoherent," "useless," "garbage" and "mumbojumbo." But on the other side, your concept has similar ingredients. First: Your definitions of SFC, GSFC, WDSC, SDSC, FBC, SARC and defensive strategies use "sincere preferences." Of course they do, because those criteria are about people being able to vote sincerely without a penalty, to whaterver degree that can be guaranteed. Since unpenallized sincere voting is the goal, it's odd that you think I shouldn't talk about sincere voting. Second: Your definition of "sincerity" is implausible. You wrote (24 Nov 2000): A voter votes sincrely if he doesn't vote a preference that isn't a sincere preference or leave unvoted a sincere preference that the balloting system would have allowed him to vote in addition to the preferences that he actually did vote. Example: Suppose that Approval Voting is used. Suppose that the sincere opinion of a given voter is A B C D E and that this voter decides to approve A, B, C and D. The day before election day, this voter hears that candidate E has no chances to win and that only candidate B and candidate C have realistic chances to win. Therefore, this given voter decides to approve only candidate A and candidate B. Due to your definition of "sincerity," this given voter votes "sincerely." But (1) in so far as this voter changes his voting behaviour after he has got additional information about the voting behaviour of the other voters and (2) in so far as this given voter changes his voting behaviour because of strategical considerations, it is clear that this given voter votes strategically. Therefore your definition of "sincerity" isn't suitable to differ between sincere voters and strategical voters. Take another look at my definition of sincere voting. It doesn't say that sincere voting must be nonstrategic. With a rank method the only sincere ballot is a sincere ranking of all the candidates. In Plurality, the only sincere ballot is one that votes for one's sincere favorite. But in Approval, I'm not sure what you'd want to call a sincere ballot. Obviously the 2 kinds of insincerity are voting a false preference, and not voting a sincere preference when there's no reason why you couldn't have voted it. Hence my definition. With rank balloting and Plurality, the only sincere vote is one that doesn't strategize. Though you'd like it to, that statement would have no meaning with Approval. Maybe that doesn't sound like what "sincere" means to you, but that's how I define it. My definition complies with your expectations with rank balloting Plurality, and it's general enough that it applies to Approval too, even though sincerity in Approval isn't as easy to discuss as you'd like it to be. Again: When you really think that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "inadequate," "vague," "sloppy," "dishonest," "absurd," "faulty," "incorrect," "poor," "silly," "contradictory," "incoherent," "useless," "garbage" and "mumbojumbo" then please explain why you think that your "universally accepted" concept that criteria should be defined on sincere opinions and election methods should be defined on casted ballots Wrong. I never said that all criteria should be defined in terms of sincere ballots. I said that some work only if defined that way. And I never said that even that is universally accepted. And yes I did and do say that election methods defined on cast ballots is universally accepted by everyone but you your head-up-the-ass academics. Most would agree with me that it's preposterous and silly to add your contrafactual assumption about balloting. might be better. Actually the fact that you define criteria and election methods on different inputs Wrong, voting systems have the same input in my voting system definitions and my criterion definitions: Actual ballots. But there's no reason why a criterion can't speak of voters' sincere preferences as well as their votes. That isn't a voting system input, but it's part of the overall configuration that makes up an example. Remember, Markus, that my criteria are about allowing penalty-free sincere voting to the extent possible. Therefore it's odd that you don't think I should mention sincere voting in criteria. The Condorcet Criterion too can be stated in terms of your not having to do other than vote sincerely as long as there's a SCW and everyone else votes sincerely. Have we cleared that up? Sincere preferences aren't part of a voting system's input, in any of my definitions of
Re: [EM] Majority winner set
Dear Mike, you say that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "inadequate," "vague," "sloppy," "dishonest," "absurd," "faulty," "incorrect," "poor," "silly," "contradictory," "incoherent," "useless," "garbage" and "mumbojumbo." But on the other side, your concept has similar ingredients. First: Your definitions of SFC, GSFC, WDSC, SDSC, FBC, SARC and defensive strategies use "sincere preferences." Second: Your definition of "sincerity" is implausible. You wrote (24 Nov 2000): A voter votes sincrely if he doesn't vote a preference that isn't a sincere preference or leave unvoted a sincere preference that the balloting system would have allowed him to vote in addition to the preferences that he actually did vote. Example: Suppose that Approval Voting is used. Suppose that the sincere opinion of a given voter is A B C D E and that this voter decides to approve A, B, C and D. The day before election day, this voter hears that candidate E has no chances to win and that only candidate B and candidate C have realistic chances to win. Therefore, this given voter decides to approve only candidate A and candidate B. Due to your definition of "sincerity," this given voter votes "sincerely." But (1) in so far as this voter changes his voting behaviour after he has got additional information about the voting behaviour of the other voters and (2) in so far as this given voter changes his voting behaviour because of strategical considerations, it is clear that this given voter votes strategically. Therefore your definition of "sincerity" isn't suitable to differ between sincere voters and strategical voters. Again: When you really think that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "inadequate," "vague," "sloppy," "dishonest," "absurd," "faulty," "incorrect," "poor," "silly," "contradictory," "incoherent," "useless," "garbage" and "mumbojumbo" then please explain why you think that your "universally accepted" concept that criteria should be defined on sincere opinions and election methods should be defined on casted ballots might be better. Actually the fact that you define criteria and election methods on different inputs makes it significantly more difficult to check whether a given election method meets a given criterion. Example: It hasn't yet been demonstrated whether PC resp. Smith//PC meets SDSC. You claim that I "endlessly repeated" the same questions. You claim that you are "real tired of that repetition." But you apparently neglect that you have never answered any of my questions. Although I have invited you several times to explain why you think that your concept might be better, you have never answered. However, I doubt that those who don't promote Approval Voting will agree to your definition of "sincerity." However, I don't have the impression that your statements have anything to do with majority winner sets or beat path GMC. Markus Schulze
Re: [EM] Majority winner set
Markus Schulze wrote: Dear Mike, you wrote (29 Nov 2000): I'm sorry! Because Markus had been repeating things, I must have not thoroughly read one of the paragraphs in his most recent posting. I thought that I did, but I must have missed that sentence, where he stated that the assumption is that the voters report vN-M utilities, sincere or not, and then the voting system takes from those that information that it needs, and would normally get from its own balloting procedure. So I take back the statement that Markus didn't explain it. But my criticisms of those assumptions mostly still remain valid. My answers to some of Markus's statements are different based on what I've just noticed, though. I still say that it's a contrafactual assumption. Why assume that people vote ratings, and that the voting system takes from them the information that it needs, when we could instead just say that the voting system collects the kind of input that it actually does collect when in actual use?? I assume that the voters vote vNM utilities and that the election method takes from the reported vNM utilities the information it needs to calculate the winner because I define the criteria in terms of reported vNM utilities. Markus Schulze I don't see any problem with this, so long as you don't assume that this is the final word in the behavior of the voting system in question. Many voting system analyses start with sincere vNM utilities, and then try to determine the likely effects of strategy. Actually, "sincere vNM utilities" is redundant. I'm not sure what "insincere vNM utilities" could even mean. Anything reported by a voter would be a rating, not a utility, whether sincere or not. I think utilities are mainly useful in thought exercises and computer models, where you can simply generate the numbers and assume they represent utilities. The voters don't "report" these -- the modeler "just knows them", without necessarily even assuming that the hypothetical voters are able to report them accurately. Maybe you mean "report" in a different way -- that the simulator generating the utilities reports them, for example. As to criteria, it seems to me that criteria based on utilities, and criteria based on votes as cast are both useful, but there needs to be an understanding of which is which. Maybe some criteria are more applicable to utilities, and others to votes-as-cast. For example, monotonicity by its definition seems to apply to votes-as-cast. There is probably a sincere analog using utilities, but I don't know how it would be useful. Something like IIA could apply to either, but would have different meanings in either case (and probably should have different names in either case). One might comment on the stability of the system itself -- for example, would additional absentee ballots for Gore cause Bush to win -- while the other might comment on the type or degree of strategy needed to vote most effectively.
Re: [EM] Majority winner set
Markus said: The concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters presumes that every voter casts (not necessarily sincerely) his von Neumann-Morgenstern utilities and that the used election method takes from the reported von Neumann- Morgenstern utilities that information that this election method needs to calculate the winner. That presumption is incorrect. What each voter casts depends on the balloting used by the particular method in use. If the method is Cardinal Ratings, then you can call someone's ratings his sincere or insincere vN-M utilities. And then maybe you can bend the meanings a lot and say that when, in Plurality, someone votes for Gore, then he's voting a set of insincere vN-M utilities, when he gives Gore 1 and everyone else zero. But there's no way that you can call a ranking a set of sincere or insincere vN-M utilities. You claim that this concept was "faulty" because some election methods depend on LESS than the reported von Neumann-Morgenstern utilities. But when you re-think your statement then you will observe that this concept is problematic only when the used election method depends on MORE than just the reported von Neumann- Morgenstern utilities. No, it's problematic anyway. You didn't say that the voter casts something that could be derived from his sincere or insincere vN-M utilities. You said that he casts his sincere or insincere vN-M utilities. With rank methods he in no way can be said to do that. This isn't complicated. You say it isn't problematic because, if we know the vN-M utilities that the voter would like to represent, then from that we can determine how he would vote a ranking, or any other type of balloting. But that's got nothing to do with your earlier claim that the voter votes his sincere or insincere vN-M utilities. He doesn't necessarily. You claim is obviously incorrect. Again: When you really think that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "inadequate," "vague," "sloppy," "dishonest," "absurd," "faulty," "poor," "silly," "contradictory," "useless," "garbage" and "mumbojumbo" ...don't forget "crap". then you are invited to introduce your own concept I'm not going to claim credit for a concept that isn't mine, for specifying balloting in method definitions. However, I'm going to introduce you to the universally accepted concept for that: When defining a method, we tell how voters can indicate preferences or ratings, by marking their ballot, and we specify a count rule for determining the winner from those ballots. That's what you yourself did when you specified that your method uses rank-ballots. and to explain why you think that your own concept might be better. Now I'm going to explain to you why that's better: It applies to more diverse methods, with their different balloting systems, than does your suggestion to define methods as receiving a set of sincere or insincere vN-M utilities from each voter, a suggestion that is quite inapplicable to rank methods. This isn't rocket science, Markus: The fact that you can make a ranking by ordering the candidates according to someone's vN-M utilities for them does not mean that the voter who votes a ranking is casting his vN-M utilities, sincere or otherwise. Nobody hinders you from introducing your own concept. You're too kind, but I'm willing to use the same balloting concept for method definitions that everyone else uses when defining methods. However, I don't have the impression that your statements have anything to do with majority winner sets or beat path GMC. Actually, at this point, you're right. When I said that Plurality meets BPGMC, as you define it, you at first claimed that it doesn't, because of your claim that methods (or just Plurality?) should be evaluated according to what their count rule would do if it were applied to rank ballots. You abandoned that when I asked you to apply it to some well-known methods. Then you started repeating that methods are defined in terms of an input of vN-M utilities. You say you don't have the impression that that has anything to do with my claim that Plurality passes BPGMC? Neither do I :-) I agree that what you've been saying has nothing to do with my claim that Plurality meets BPGMC, and that it doesn't in any way answer that claim. You know what, Markus? I would expect that people are real tired of that repetition. I'm not going to be a party to continuing to send them that repetition. When I reply to those endlessly repeated statements, then I'm partly at fault for their being posted, and I prefer to not be part of the cause of that repetition being posted. Repeat the statements again if you want to, but for me to keep replying to them would be inconsiderate of the other people on this list. Mike Ossipoff And so let me summarize and conclude it in
Re: [EM] Majority winner set
Markus said: I have already said in a different context (23 Sep 2000) that I use the concept that election methods are defined on the reported von Neumann-Morgenstern utilities of the voters. Excuse me, but I didn't notice anything about von Neumann-Morgenstern utilities in your definition of "Schulze's method", for example. But in your reply (23 Sep 2000) you wrote that this concept was "funny," "incomplete," "undefined," "vague" and "not precise." Now you write that this concept was also "sloppy" and "dishonest." Maybe the reason why I said "undefined" and "vague" was because you referred to those purported definitions in the same vague way as you do now, and because you haven't given us a definition of the type to which you vaguely refer. If you didn't refuse to read scientific literature When did I say I was unwilling to read scientific literature? then you would observe that the concept that election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is widely used and that e.g. Gibbard and Hylland use this concept for their impossibility theorems. You say that someone else defines methods in that way, but you don't define your own method in that way. I have to admit that it isn't clear to me how someone else's way of defining some other method is relevant to the issues we've been discussing. For instance, how does it save your BPGMC criterion from its faults that I described? I've asked you twice to show that Approval, Cardinal Ratings, Plurality, and single-winner Cumulative pass or fail the Condorcet Criterion , if we assume that each voter votes a ranking and we have to apply those methods' count rules to rankings. I've explained that your failure to do that shows that the limited applicability of our approach makes it a poor approach of limited questionable usefulness. I've pointed out the silliness of judging a method by what its count rule does with some other method's balloting, when the method we're judging doesn't use that balloting. When you think that this concept is "vague," "sloppy" and "dishonest" I'm not saying that the concept to which you refer so vaguely is vague or sloppy or dishonest. Your reference to it is certainly vague, and your attempt to save BPGMC by requiring the tested method's count rule to be used with a different method's balloting system, with which it may not be usable--that was sloppy. Or, if it wasn't pure sloppiness, maybe it was bias in favor of the way you want to define BPGMC--that's what I meant by "a little bit less than honest with us." then you are invited to introduce your own concept and to explain why you think that your own concept might be better. But unless you have done this, The concept to which you refer is a way of defining a method. All of us here and elsewhere who have defined methods have defined them in some way. I daresay that most of us have defined them in terms of a way in which voters are allowed to express their preferences or ratings of the candidates, and a count rule for counting those expressed preferences or ratings. Explain why that's better than what you've vaguely referred to? Look, if you want to introduce here a way of defining methods that's new here, then you first must define it much better than you have. Then you must show why it's better. It isn't on me to show that it isn't better--least of all now, when it hasn't been defined, but has only been vaguely referred to. For instance, after you define your idea much more clearly than you' have defined it, then you should write definitions for Plurality, Approval, IRV, Tideman(wv) and BeatpathWinner, using the form that you propose for method definitions. But I am NOT asking you to do that, because it doesn't sound like something that would be useful. I'm saying that if you want to discuss the issue of whether your way is better, then you must do as I suggested in the 3 preceding paragraphs. you have to live with the fact that the concept that election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is widely used. Fine, I'll take your word for that, that someone else, somewhere else, defines voting systems in a different way that you refer to vaguely. But I'm not asking you for a more precise specification about that. I doubt that it would be useful. I merely state that you've referred to it vaguely, and I'm willing to leave it at that and take your word for it that someone defines methods in that sort of a way. However, I don't have the impression that your statements have anything to do with majority winner sets or beat path GMC. This has been about a problem of BPGMC. Markus Schulze _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
Re: [EM] Majority winner set
Markus said: you wrote (28 Nov 2000): Excuse me, but I didn't notice anything about von Neumann- Morgenstern utilities in your definition of "Schulze's method", for example. In my definition of the Schulze method, I talk about the number of voters who strictly prefer candidate X to candidate Y. When you know the von Neumann-Morgenstern utilities of the voters, then you also know how many voters strictly prefer candidate X to candidate Y. Therefore the Schulze method can also be defined in terms of von Neumann-Morgenstern utilities. Look, I don't care how you find out people's sincere preferences, but what you're saying is that you define "Schulze's method" in terms of sincere preferences. It makes no sense to define a method that way, since the method's actual input consists of votes, not preferences, and those votes are what the method must act on. You've contradicted yourself about whether you define BPGMC in terms of preferences or votes. And now you say you define "Schulze's method" in terms of sincere preferences, which is entirely absurd, because a method can only act on votes. By all means define your criterion in terms of sincere preferences, with a stipulation of sincere voting, but a voting system must be defined in terms of votes rather than preferences. You wrote (28 Nov 2000): How does it save your BPGMC criterion from its faults that I described? In my definition of beat path GMC, I talk about the number of voters who strictly prefer candidate X to candidate Y. No, a voting systek must be defined in terms of how it acts on people's actual votes, not on their preferences. When you know the von Neumann-Morgenstern utilities of the voters, then you also know how many voters strictly prefer candidate X to candidate Y. Therefore beat path GMC can also be defined in terms of von Neumann-Morgenstern utilities. No. For the reasons I stated above. Again: When you think that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "vague," "sloppy," "dishonest," "faulty," "poor," "silly" and "useless" then you are invited to introduce your own concept and to explain why you think that your own concept might be better. Nobody hinders you from introducing your own concept. Again: I didn't say that the concept that you hinted about is any of those things. I didn't criticize it at all. But, from your demonstration of its use so far, I must say that it's an entirely inadequate way to define a voting system, if it's used as you describe. That's because you speak of using the utilities to determine people's sincere preferences, and defining the method in terms of those sincere preferences. What you forgot to explain was: How does the voting system find out the voters' von Neumann-Morgenstern utilities? The only input available to the voting system is the voters' actual votes. There's no need for me to introduce a new concept for what input to refer to when defining voting systems. All of us define them in terms of people's votes. The voting system specifies a way that voters may express their preferences in the balloting, and a count rule for choosing a winner based on those ballots. That's how voting systems are defined, by everyone who defines a voting system. As I said, I don't have any argument with your claim that someone else does it differently. That's their business, and it's fine with me. I have no idea how it would be done, but I'm not asking you to explain it. However what you've said so far about how it's done wouldn't work: You said that we define a voting system in terms of sincere preferences rather than in terms of votes. That's absurd. You said that the vN-M utilities are used to determine people's sincere preferences, but you didn't explain how the voting system determines those utilities. Mike Ossipoff _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
Re: [EM] Majority winner set
Dear Mike, you wrote (28 Nov 2000): Markus wrote (28 Nov 2000) Mike wrote (28 Nov 2000): Excuse me, but I didn't notice anything about von Neumann- Morgenstern utilities in your definition of "Schulze's method", for example. In my definition of the Schulze method, I talk about the number of voters who strictly prefer candidate X to candidate Y. When you know the von Neumann-Morgenstern utilities of the voters, then you also know how many voters strictly prefer candidate X to candidate Y. Therefore the Schulze method can also be defined in terms of von Neumann-Morgenstern utilities. Look, I don't care how you find out people's sincere preferences, but what you're saying is that you define "Schulze's method" in terms of sincere preferences. It makes no sense to define a method that way, since the method's actual input consists of votes, not preferences, and those votes are what the method must act on. You've contradicted yourself about whether you define BPGMC in terms of preferences or votes. And now you say you define "Schulze's method" in terms of sincere preferences, which is entirely absurd, because a method can only act on votes. By all means define your criterion in terms of sincere preferences, with a stipulation of sincere voting, but a voting system must be defined in terms of votes rather than preferences. It isn't clear to me why you believe that the Schulze method and beat path GMC were defined in terms of SINCERE preferences. In so far as I wrote that I use "the concept that criteria and election methods are defined on the REPORTED von Neumann-Morgenstern utilities of the voters" it is clear that I am talking about the REPORTED von Neumann-Morgenstern utilities of the voters and not about the SINCERE von Neumann-Morgenstern utilities of the voters. You wrote (28 Nov 2000): From your demonstration of its use so far, I must say that it's an entirely inadequate way to define a voting system, if it's used as you describe. That's because you speak of using the utilities to determine people's sincere preferences, and defining the method in terms of those sincere preferences. Again: It isn't clear to me why you believe that the Schulze method and beat path GMC were defined in terms of SINCERE preferences. You wrote (28 Nov 2000): You said that we define a voting system in terms of sincere preferences rather than in terms of votes. That's absurd. You said that the vN-M utilities are used to determine people's sincere preferences, but you didn't explain how the voting system determines those utilities. Again: It isn't clear to me why you believe that the Schulze method and beat path GMC were defined in terms of SINCERE preferences. Again: When you think that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "vague," "sloppy," "dishonest," "faulty," "poor," "silly," "useless" and "contradictory" then you are invited to introduce your own concept and to explain why you think that your own concept might be better. Nobody hinders you from introducing your own concept. You wrote (28 Nov 2000): There's no need for me to introduce a new concept. Then you have to live with the fact that the concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is widely used. Markus Schulze
Re: [EM] Majority winner set
Dear Mike, you wrote (28 Nov 2000): Ok. So now you're saying that, when Schulze's method is used, voters report their vN-M utilities. You'd previously given the impression that the voters report pairwise preferences, via a ranking. Which is it? Yes, you'll say that someone could rank the candidates in order of their vN-M utilities for that voter. Fine, but the voter reports pairwise preferences, via a ranking, with your method, yes? You can call that reporting the order of his vN-M utilities, or we could just as well call it reporting pairwise preferences that may or may not be sincere. So now, unless you're really changing that, we're back to you saying that, actually, with your method, voters report pairwise preferences, via a ranking. You call it reporting pairwise preferences which may be insincere, and I'd say it would make more sense to say that people are simply casting pairwise votes with their ranking, but now that I know what you mean, it doesn't matter which way we say it. Good, because that's what I thought--people report pairwise preferences in your method, which means they cast pairwise votes. Now that we know what you mean, it's evident that it doesn't do anything to save BPGMC. All this mumbojumbo about vN-M utilities, and what it still amounts to is that your method, like all rank methods, is defined in terms of the rankings that people vote. Sometimes you say that your BPGMC is defined in terms of preferences and sometimes you say it's defined in terms of votes. Now I realize that when you say "preferences" you mean preferences that may be insincere, and so we can assume that by pairwise prefereces you mean pairwise votes. Fine. We're now back to this: Plurality meets your BPGMC. You say it doesn't, because you say that Plurality should be tested by applying its count rule to rankk balloting, which Plurality doesn't use, by calling top-rankedness a Plurality vote. You never answered about how you'd apply that notion to Approval, Cardinal Ratings, and single-winner Cumulative, and it's evident now that you aren't going to, because of course you know that it can't be applied to them. And all that garbage about vN-M utilities was just an attempt to use big words to try to cover up the fact that you can't defend your faulty definition of BPGMC. The concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters presumes that every voter casts (not necessarily sincerely) his von Neumann-Morgenstern utilities and that the used election method takes from the reported von Neumann- Morgenstern utilities that information that this election method needs to calculate the winner. You claim that this concept was "faulty" because some election methods depend on LESS than the reported von Neumann-Morgenstern utilities. But when you re-think your statement then you will observe that this concept is problematic only when the used election method depends on MORE than just the reported von Neumann- Morgenstern utilities. Again: When you really think that the well known and widely used concept that criteria and election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is "inadequate," "vague," "sloppy," "dishonest," "absurd," "faulty," "poor," "silly," "contradictory," "useless," "garbage" and "mumbojumbo" then you are invited to introduce your own concept and to explain why you think that your own concept might be better. Nobody hinders you from introducing your own concept. However, I don't have the impression that your statements have anything to do with majority winner sets or beat path GMC. Markus Schulze
Re: [EM] Majority winner set
Dear Mike, I have already said in a different context (23 Sep 2000) that I use the concept that election methods are defined on the reported von Neumann-Morgenstern utilities of the voters. But in your reply (23 Sep 2000) you wrote that this concept was "funny," "incomplete," "undefined," "vague" and "not precise." Now you write that this concept was also "sloppy" and "dishonest." If you didn't refuse to read scientific literature then you would observe that the concept that election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is widely used and that e.g. Gibbard and Hylland use this concept for their impossibility theorems. When you think that this concept is "vague," "sloppy" and "dishonest" then you are invited to introduce your own concept and to explain why you think that your own concept might be better. But unless you have done this, you have to live with the fact that the concept that election methods are defined on the reported von Neumann-Morgenstern utilities of the voters is widely used. However, I don't have the impression that your statements have anything to do with majority winner sets or beat path GMC. Markus Schulze
Re: [EM] Majority winner set
Dear Mike, you wrote (21 Nov 2000): Plurality doesn't have rank balloting. Plurality isn't just a count rule to be applied to rank-ballots. Plurality, like any voting system, is a combination of a balloting system and a count rule. I don't agree with you that the ballot design is a part of the election method. To my opinion, the ballot design --especially questions like (1) how the candidates have to be sorted on the ballot, (2) whether there should be party affiliations, (3) whether there should be write-in options, (4) whether there should be a NOTA option, (5) what should be done when NOTA is chosen or (6) whether the ballots should be counted by hand or by computer-- is a part of the electoral law but not of the election method itself. However, I don't have the impression that your statements have anything to do with majority winner sets or beat path GMC. Markus Schulze
Re: [EM] Majority winner set
Markus said: you wrote (21 Nov 2000): Plurality doesn't have rank balloting. Plurality isn't just a count rule to be applied to rank-ballots. Plurality, like any voting system, is a combination of a balloting system and a count rule. I don't agree with you that the ballot design is a part of the election method. To my opinion, the ballot design --especially questions like (1) how the candidates have to be sorted on the ballot, (2) whether there should be party affiliations, (3) whether there should be write-in options, (4) whether there should be a NOTA option, (5) what should be done when NOTA is chosen or (6) whether the ballots should be counted by hand or by computer-- is a part of the electoral law but not of the election method itself. I reply: I didn't say that the shape, size color of the ballot, and the order of the candidates on the ballot, and whether there should be party affiliations, and whether there should be write-in options, and whether the ballots should be counted by hand or by computer-- is part of the voting system. Also, adding NOTA to the alternatives isn't part of the voting system either, as you said. Those things are details of balloting, but they aren't part of the intrinsic balloting system any more than they're part of the voting system. Now I'll tell you something that _is_ the intrinsic balloting system: The basic rules for how voters may express preferences for candidates, disregarding size shape of ballot, which candidates are allowed on the ballot, in what order the candidates are listed, etc. Either you're real sloppy today, or you're being a little less than honest with us , if you're claiming that the basic rules governing how voters may express preferences for candidates isn't part of the voting system. Has it occurred to you why they call it a _voting_ system? "Doo...oing" :-) Markus continues: However, I don't have the impression that your statements have anything to do with majority winner sets or beat path GMC. I reply: Wrong. My initial comment was that your definition of Beatpath GMC was worded in such a way that no method can pass it. Then you changed your definition from being about preferences to being about votes. Then I told you that, by your new definition, Plurality meets Beatpath GMC. Then, wanting to be nice, I said that it isn't just Beatpath GMC, but also Condorcet needs the fix that I described. Then I began using Condorcet's Criterion as an example, because it's a simpler criterion, and a much more widely-used one than Beatpath GMC. But the discussion was still about Beatpath GMC, and whether or not it's met by Plurality, and whether your newest statements about BPGMC make any sense. By the way, you never did say whether Condorcet's Criterion, according to your way of looking at it, as met by Approval. While you're at it, you can tell me whether it's met by Cardinal Ratings and single-winner Cumulative. As I said, the fact that you can't answer that shows that your definitions of CC BPGMC don't work. Look, it just fortuitously happens that a ranking reveals a 1st choice, and so you can call that 1st choice the Plurality vote. But it isn't always the case that a balloting system for one type of voting system can be counted by another voting system's count rule. To base a criterion's definition on an attempt to do that is silly. If you wanted CC BPGMC to mean what you're saying they mean, then you ought to say what you mean when you write the definition. You should say, for example: "If we have the voters rank the candidates, and then we count those rank ballots according to a certain voting system's count rule, then..." If you don't say what you mean when you write the definition, then people have no way of knowing what you man. Anyway, don't bother rewriting your BPGMC definition in that way, because it wouldn't make any sense, as I've already explained. Mike Ossipoff Markus Schulze _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
Re: [EM] Majority winner set
Dear Mike, you wrote (24 Nov 2000): Ok, that was what I'd thought, but the other day you posted a definiton in terms of people preferring one candidate to another, and the natural interpretation of that is felt preferences, sincere preferences. But I recognize that BPGMC is in terms of voted preferences, and therefore I agree that BeatpathWinner meets BPGMC. And so does Plurality. I'm not just picking on BPGMC. The usual definitions of the Condorcet Criterion have the same problem. When CC is defined in terms of sincere preferences, as it often is, then no method meets it. When it's defined in terms of voted preferences, then Plurality meets it. FPP violates Condorcet and beat path GMC. Example: 40 voters vote A B C. 35 voters vote B C A. 25 voters vote C B A. Due to the Condorcet criterion, candidate B must be elected. Due to beat path GMC, candidate B must be elected. But the FPP winner is candidate A. In the example above, I didn't make any presumptions about whether the voters vote sincerely or strategically. In the example above, I didn't make any presumptions about the sincere opinions of the voters. Did I? Markus Schulze
Re: [EM] Majority winner set
Bart Ingles wrote: Markus Schulze wrote: FPP violates Condorcet and beat path GMC. Example: 40 voters vote A B C. 35 voters vote B C A. 25 voters vote C B A. Due to the Condorcet criterion, candidate B must be elected. Due to beat path GMC, candidate B must be elected. But the FPP winner is candidate A. In the example above, I didn't make any presumptions about whether the voters vote sincerely or strategically. In the example above, I didn't make any presumptions about the sincere opinions of the voters. Did I? Uh, yes, you presume the voters will vote sincerely in FPP, in order for A to win. My mistake, I can't say that you presume sincere voting for FPP, since you don't specify whether the rankings are sincere. On the other hand, the example is not sufficient to show A as the FPP winner.
Re: [EM] Majority winner set
Markus Schulze wrote: FPP violates Condorcet and beat path GMC. Example: 40 voters vote A B C. 35 voters vote B C A. 25 voters vote C B A. Due to the Condorcet criterion, candidate B must be elected. Due to beat path GMC, candidate B must be elected. But the FPP winner is candidate A. In the example above, I didn't make any presumptions about whether the voters vote sincerely or strategically. In the example above, I didn't make any presumptions about the sincere opinions of the voters. Did I? Uh, yes, you presume the voters will vote sincerely in FPP, in order for A to win.
Re: [EM] Majority winner set
Markus wrote: Beat path GMC is defined in terms of voted preferences. Beat path GMC is met e.g. by Schulze(wv) I reply: Ok, that was what I'd thought, but the other day you posted a definiton in terms of people preferring one candidate to another, and the natural interpretation of that is felt preferences, sincere preferences. But I recognize that BPGMC is in terms of voted preferences, and therefore I agree that BeatpathWinner meets BPGMC. And so does Plurality. I'm not just picking on BPGMC. The usual definitions of the Condorcet Criterion have the same problem. When CC is defined in terms of sincere preferences, as it often is, then no method meets it. When it's defined in terms of voted preferences, then Plurality meets it. So here's how I define the Condorcet Criterion: If there's a sincere CW, and if everyone votes sincerely, then the sincere CW should win. Sincere Voting: A voter votes sincrely if he doesn't vote a preference that isn't a sincere preference or leave unvoted a sincere preference that the balloting system would have allowed him to vote in addition to the preferences that he actually did vote. (By "preference", I mean "pairwise preference") [end of definition] A similar fix could fix BPGMC, as well as Condorcet Loser, Mutual Majority Criterion, etc., which share that problem. Mike Ossipoff _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
Re: [EM] Majority winner set
Dear Mike, you wrote (21 Nov 2000): It seems to me that no method can meet that criterion. Say, for instance, that the method is BeatpathWinner, defined in terms of actual voted preferences. Maybe the voter believe that they have a situation where they need defensives truncation, and so they don't vote all of the preferences that they feel. (It's also possible that some voters merely might not have time to rank all of the candidates, or don't feel like expressing preferences for disliked candidates over more disliked ones-- there are some voters who might feel that way). Then those people's preferences won't translate into actual voted preferences on the BeatpathWinner ballots. BeatpathWinner is defined in terms of voted preferences rather than felt preferences, and your criterion is defined in terms of felt preferences. You told me that a criterion shouldn't be defined in that way. Of course you could specify that if some voters have certain sincere preferences and vote sincerely, then a certain result must happen. In that way your criterion would be meetable, without being met by Plurality, as it would be if you merely defined it in terms of voted preferences. Beat path GMC is defined in terms of voted preferences. Beat path GMC is met e.g. by Schulze(wv): http://www.fortunecity.com/meltingpot/harrow/124/methods.html Markus Schulze
Re: [EM] Majority winner set
Markus defined Beatpath GMC as follows: "X Y" means that an absolute majority of the voters strictly prefers candidate X to candidate Y. "There is a majority beat path from X to Y" means that (1) X Y or (2) there is a set of candidates C[1],...,C[n] with X C[1] ... C[n] Y. If there is a majority beat path from candidate A to candidate B and no majority beat path from candidate B to candidate A, then candidate B must not be elected. I reply: It seems to me that no method can meet that criterion. Say, for instance, that the method is BeatpathWinner, defined in terms of actual voted preferences. Maybe the voter believe that they have a situation where they need defensives truncation, and so they don't vote all of the preferences that they feel. (It's also possible that some voters merely might not have time to rank all of the candidates, or don't feel like expressing preferences for disliked candidates over more disliked ones--there are some voters who might feel that way). Then those people's preferences won't translate into actual voted preferences on the BeatpathWinner ballots. BeatpathWinner is defined in terms of voted preferences rather than felt preferences, and your criterion is defined in terms of felt preferences. You told me that a criterion shouldn't be defined in that way. Of course you could specify that if some voters have certain sincere preferences and vote sincerely, then a certain result must happen. In that way your criterion would be meetable, without being met by Plurality, as it would be if you merely defined it in terms of voted preferences. Mike Ossipoff _ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
[EM] Majority winner set
I'm proposing a majority winner set method. It could go with a new criteria (which would be failed by margin systems, and either passed or failed by winning votes systems depending on the specific wording). Definition of majority winner set: The set of candidates who pairwise beat all candidates outside the Smith set, and pairwise beat at least one candidate inside the Smith set by an absolute majority Where this set contains at least one candidate, and is smaller than the Smith set, all candidates not in the majority winner set are eliminated. The majority winner set becomes the new Smith set, and the test is reapplied. eg Smith Set AB 55 - 45 BC 47 - 35 CA 51 - 35 -Majority Winner Set consists of A C -A is eliminated -Majority Winner Set consists of C Also handy for resolving draws. Consider the same as above, but with CA 50-50. Majority winner set consists of A. Comments?
RE: [EM] Majority winner set
Martin wrote: Isn't there another majority winner set consisting of A B? And another for B C? Or do I misunderstand your 'absolute majority'? Yes, I think so. Absolute majority means majority of all votes cast (ie over 50%). B is not included in the majority winner set. However, I should clarify that the majority winner set is those candidates who are in the Smith set, and pairwise beat another member of the Smith set by an absolute majority. This removes the contradiction in my original message. If B defeated C by 52 - 48, then the majority winner set would consist of all three candidates A,B,C, and another method is needed to decide between them - probably Minmax(wv) for want of a better alternative. LAYTON Craig wrote: I'm proposing a majority winner set method. It could go with a new criteria (which would be failed by margin systems, and either passed or failed by winning votes systems depending on the specific wording). Definition of majority winner set: The set of candidates who pairwise beat all candidates outside the Smith set, and pairwise beat at least one candidate inside the Smith set by an absolute majority Where this set contains at least one candidate, and is smaller than the Smith set, all candidates not in the majority winner set are eliminated. The majority winner set becomes the new Smith set, and the test is reapplied. eg Smith Set AB 55 - 45 BC 47 - 35 CA 51 - 35 -Majority Winner Set consists of A C -A is eliminated -Majority Winner Set consists of C Also handy for resolving draws. Consider the same as above, but with CA 50-50. Majority winner set consists of A. Comments?
