Re: [EM] Andrew: Sincere methodsd
Dear Mike! Although I don't believe in measurable individual utilities in the first place, here's some thoughts on the even more questionable notion of social utility: In replying to Andrew, you stated a seemingly trivial truth: That's CR. If voters have no wish to maximize their own utility expectation, and only want to rate truly in order to maximize social utility, then CR is what maximizes social utility. But that depends heavily on how you choose to define social utility. You seem to take for granted that social utility should be measured by the sum, or equivalently by the arithmetic mean, of the individual utilities. But there is absolutely no reason to believe that this is a good measure of social utility! I suggest to see this as a problem of descriptive statistics: You want to summarize an unknown distribution (that of the true individual utilities) by using some statistics of the empirical distribution (that of the expressed individual utilities), and this statistics you call social utility then. Welfare statistics, for example, usually measures the mean income not by the arithmetic mean but by the median or some other quantile of the income distribution, in order to avoid giving the high incomes to much weight. The median is a simpler, more accurate, and more robust measure of social utility than the sum! It has the additional advantage that we need not assume that utilities possess an additive scale. (Perhaps it corresponds to the median voter theorem for single-peaked one-dimensional preferences in some way?) I would even go so far and suggest to use an even lower quantile to measure social utility, since the goal to get the most utility for the most people implies that it is more important to give some additional utility to the many who possess few instead of giving much additional utility to the few who possess much already. So I suggest to measure social utility by the LOWER QUARTILE of the individual utilities (= that utility value where one quarter of the voters is below and three quarters of the voters are above). Perhaps this will even make CR a somewhat more strategy-resistant method since we use a much more robust measure of social utility. Yours, Jobst Election-methods mailing list - see http://electorama.com/em for list info
[EM] Is an approval cutoff option necessary?
I'm starting to think that an approval cutoff option may be too complicated for a public DMC proposal. It now seems to me that a graded ballot with C as the lowest passing grade is fairly intuitive and with 8 approved ranks leaves sufficient room for voter expression. But mainly, 16 ranks (0 -- 15) mean that approval can be quickly measured using the most significant of the 4 bits. Any comments? BTW, I tested a simple explanation of DMC (fixed LPG = C) on my father and he seemed to actually grasp the basic idea. I'll use Russ's can he still explain it a week later test and tell you what happens ... Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Sincere methods
Hello Gervase, On Mar 24, 2005, at 03:00, Gervase Lam wrote: Date: Wed, 23 Mar 2005 09:15:52 +0200 From: Juho Laatu Subject: [EM] Sincere methods I already gave some support to seeing MinMax (margins) (least additional votes) as one potential sincere method (criticism received too). If you want something a bit more strategic resistant, Reynaud(Margins) might be a good step up. I haven't unfortunately studied the characteristics of this method well enough to comment if it is the best. (I'll try to do my homework better and study all the proposed methods a bit more than I have been able to do so far.) Comment on the use of terms strategic and sincere: A method that has been made strategy resistant is by definition different from the corresponding sincere method (=method that elects the best candidate based on our selected criteria when all the votes are sincere, i.e. without the need to care about strategic votes). Should I thus read your comment so that you see MinMax (margins) as a sincere method (the best one, or just one good sincere method) whose weaknesses with strategic voting can best be patched by using Raynaud (Margins)? Best Regards, Juho Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM]Definite Majority Choice, AWP, AM
Hello Chris, I have one generic comment on evaluation of different voting methods. Examples that include both sincere votes and altered votes nicely demonstrate the possibilities of strategic voting, but when the voting method gets a pile of ballots to be counted, no knowledge of which votes are sincere is available. I'll modify one of the examples to show what I mean. On Mar 24, 2005, at 18:11, Chris Benham wrote: The first is copied from a Sep.22,04 James G-A post. 3 candidates: Kerry, Dean, and Bush. 100 voters. Sincere preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 25: BKD 23: BDK Kerry is a Condorcet winner. Altered preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 21: BKD 23: BDK 4: BDK (these are sincerely BKD) There is a cycle now, KBDK The voting method sees only the altered votes. Although the sincere CW would be K, a voting method that elects K is not necessarily good. In this case votes 4: BDK were altered. But as well it could have been that those votes were sincere and for example votes 4: KBD were altered. Lets say that the sincere votes of those K supporters are 4: KDB. If that was the case, then the sincere CW would have been D. Since the voting method can not know which votes are sincere and which not, I guess it should behave as the votes given in the election were the sincere votes. I can't find any good examples where the voting method would be able to identify some votes as insincere. Maybe in the case that all ballots that have X in the first place are identical one could guess that X supporters have agreed some strategy. But of course that could as well be their sincere uniform opinion. So, it looks to me that in the example above the voting methods should behave as if there was a sincere cycle and not favour K any more than the others. The best voting methods or voting organizers can do in this situation is to try to discourage strategic voting. Best Regards, Juho ((P.S. One possible deviation to this main rule is a voting method that is known to require some certain strategy from the voters (to give the best results). In this case one could assume in the result counting process of the voting method that all voters have voted according to this known strategy and results should therefore be calculated using this assumption. In this case the voting method of course could give unwanted results if all or majority of voters voted sincerely. Maybe one should redefine sincerity in this case = sincere votes are those that follow the recommended/expected voting practice and do that in the light of voter's sincere preferences.)) --end of message-- Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Quartiles for CR
Date: Fri, 25 Mar 2005 09:25:46 +0100 From: Jobst Heitzig [EMAIL PROTECTED] Subject: Re: [EM] Andrew: Sincere methodsd ... The median is a simpler, more accurate, and more robust measure of social utility than the sum! It has the additional advantage that we need not assume that utilities possess an additive scale. (Perhaps it corresponds to the median voter theorem for single-peaked one-dimensional preferences in some way?) I would even go so far and suggest to use an even lower quantile to measure social utility, since the goal to get the most utility for the most people implies that it is more important to give some additional utility to the many who possess few instead of giving much additional utility to the few who possess much already. So I suggest to measure social utility by the LOWER QUARTILE of the individual utilities (= that utility value where one quarter of the voters is below and three quarters of the voters are above). So this means that perhaps we should look at the set of CR values for each candidate, and the candidate who has the highest number q such that the number of his CR values that are above q are at least three times the number of CR values below q ... that candidate should be the winner according to social utility considerations. [If two candidates have the same q, then the one with the higher ratio should win.] I like this because, it tends to be the lower quartile of the population that has the greatest actual need, while the richest quartile can readily buy whatever they think they need. Average utility would make more sense if the benefits actually averaged out, i.e. if they actually got spread around, but under modern Bush style capitalism the trickle down leaks have been effectively caulked. On a related note: I like methods that make use of CR ballots but satisfy the following property: If all of the CR ballots are transformed by different affine transformations, the winner of the method will not be changed. I suppose that we could call this Affine Invariance. DSV methods that infer approval cutoffs for CR ballots from estimated winning probabilities satisfy this affine invariance property. Note that the above quartile method would not satisfy this invariance, but it would satisfy another one: If the same order preserving transformation is applied to all ballots, then the winner is unchanged. If we use Rob's strategy A, or Joe Weinstein's above median probability approval cutoff for a DSV strategy, then both of these invariances are satisfied. Forest Election-methods mailing list - see http://electorama.com/em for list info
[EM] median rating / lower quartile
So I suggest to measure social utility by the LOWER QUARTILE of the individual utilities (= that utility value where one quarter of the voters is below and three quarters of the voters are above). Perhaps this will even make CR a somewhat more strategy-resistant method since we use a much more robust measure of social utility. Given sincere votes, this may be interesting, but if votes are not necessarily sincere, it would be quite possible for all candidates to receive a social utility of 0. That is, the lower quartile feature makes the method into a kind of 3/4 supermajority method. However, scoring candidates by the median rather than the mean might be an improvement on standard cardinal ratings. Has this been discussed before? my best, James Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] median rating / lower quartile
James, You wrote: Given sincere votes, this may be interesting, but if votes are not necessarily sincere, it would be quite possible for all candidates to receive a social utility of 0. That is, the lower quartile feature makes the method into a kind of 3/4 supermajority method. However, scoring candidates by the median rather than the mean might be an improvement on standard cardinal ratings. Has this been discussed before? Yes. I once happened to stumble across an archived message, originally posted by Rob Lanphier, in which he suggested just this. It wasn't long before he shot down his own idea in a follow-up message. http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-April/001603.html http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-April/001607.html my best, James 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] median rating / lower quartile
Fan de Condorcet wrote: James, You wrote: Given sincere votes, this may be interesting, but if votes are not necessarily sincere, it would be quite possible for all candidates to receive a social utility of 0. That is, the lower quartile feature makes the method into a kind of 3/4 supermajority method. However, scoring candidates by the median rather than the mean might be an improvement on standard cardinal ratings. Has this been discussed before? Yes. I once happened to stumble across an archived message, originally posted by Rob Lanphier, in which he suggested just this. It wasn't long before he shot down his own idea in a follow-up message. http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-April/001603.html http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-April/001607.html Some other problems with Median Ratings: * It adds a complication to the vote counting: If there are c candidates and r possible ratings, there need to be c*r entries in the summation array, rather than just c (as in standard Cardinal Ratings). * The previous problem is minor if you choose a reasonably small value of r. But by doing so, you introduce another problem: Ballots based on a 0-100 scale: A=74, B=42, ... A=61, B=87, ... A=61, B=59, ... A=23, B=25, ... A=97, B=72, ... Median ratings: A=61, B=59 The same ballots rounded for a 0-10 scale: A=7, B=4, ... A=6, B=9, ... A=6, B=6, ... A=2, B=3, ... A=10, B=7, ... Median ratings: A=6, B=6 * It fails Neutrality of Spoiled Ballots. A=1, B=4 A=2, B=4 A=8, B=4 A=9, B=4 With these ballots, the median ratings are A=5 and B=4, so A wins. However, if the ballot (A=0, B=0) is added, then the median ratings become A=2 and B=4, so B wins. Election-methods mailing list - see http://electorama.com/em for list info
[EM] Social utility is more important than median utility
Jobst-- You wrote: The median is a simpler, more accurate, and more robust measure of social utility than the sum! I reply: Probably so. You continued: It has the additional advantage that we need not assume that utilities possess an additive scale. True, but there's a good reason for judging a method by the sum of the utilities by which all the voters rate the winner: We discuss voting systems in the hope that one of the better ones will be enacted and used in some future elections. Maybe you or I will be one of those voters at that time, or maybe it will be a relative or descendant or ours. We don't know what kind of examples those future elections will be like, or which voters in those examples we or our descendants or relatives will be. But we maximize our utility expectation, or that of our descendants or relatives, in that future election if we advocate a voting system that does very well by social utility, the sum of the voters' utilities. That's a good reason to judge methods by SU, and I claim that it's completely compellling. By the way, in Merrill's simulations, Approval did significantly better than IRV. If distances in issue-space are measured by city-block distance, then the CW always maximizes SU in spatial models. If distance in issue-space is measured by Euclidean distance, then the CW maximizes SU under the conditions assumed in all spatial simulations. If, for any line through come central point in issue space, the voter population density distribution is the same in both directions along that line from the central point, then, even with Euclidean distance, the CW maximizes SU. The condition in the above paragraph is met, for instance, if the voters are normally distributed about a central point in each issue dimension, as is routinely assumed in spatial model simulations. Mike Ossipoff _ Dont just search. Find. Check out the new MSN Search! http://search.msn.click-url.com/go/onm00200636ave/direct/01/ Election-methods mailing list - see http://electorama.com/em for list info
[EM] How would Median CR work?
How would Median CR work? What would be the exact wording of its balloting and count rules? And, for me more important, would it keep CR's compliance with FBC and WDSC? ...and would it keep CR's social optimization advantage, that if people vote to maximize their utility expectation, then, with a few plausible approximations, CR maximizes the number of voters who will be pleasantly surprised by the outcome--the number of voters for whom the outcome will be better than their pre-election expectation for the election? Mike Ossipoff _ FREE pop-up blocking with the new MSN Toolbar get it now! http://toolbar.msn.click-url.com/go/onm00200415ave/direct/01/ Election-methods mailing list - see http://electorama.com/em for list info
[EM] Early discussion of wv on EM
Yes, judging by the archives, Rob started EM in February '96. But a posting from Steve in EM's 1st month, February '96, shows that the Single-Winner Committee had been operating for some time before that. I include, in this posting, below, a copy of a May '96 posting of mine to EM. But you needn't depend on my re-posting those postings, links being posted to them. Just check out the earliest EM archives for yourself. Before I get to the posting, though, I point out that, even if we only have the EM archives, and not those of the Single-Winner Committee, those archives show that I was advocating wv (sometimes referred to there as votes-for, and described as measuring defeat strength by the voted support for the defeat), well before my first mention of GMC. And they show that I was advocating wv by its general advantages and justifications, the fact that it records and counts the number of people who voted against a candidate, which reassures the lesser-of-2-evils voter who needs to register his vote against someone so badly that he'll give up voting for those he really likes. I told how ww, for that reason, makes it easier to ensure that some gsreater-evil will lose, just by voting someone else over him, because those votes are kept and not deleted by subtraction, as happens in Margins. I told how that's why wv honors majority rule and Margins doesn't. Thsoe general arguments for wv are in those eary EM archives. And they're found on days that were long before my first mention of GMC. Buit, though it isn't true, what if during the same days when I was making those general wv advocacy arguments, I'd also been saying A good thing about wv is that it makes PC meet GMC. Would that somehow negate the general arguments? No, it would merely mean that I was stating an additional thing I liked about wv. I wanted to mention that, but I re-emphasize that the archives show that I was stating those general arguments for wv long before I mentioned GMC. In fact, those general wv advocacy arguments can be found in the 2nd month of the EM archives, March '96. If we had the archives of the Single-Winner Committee, postings much earlier than those could be found. I mention all this and re-post the May '96 posting below, in reply to questions about early advocacy of wv. Here's the May 10th, 1996 posting. Part of it is from me, and part of it is someone whom I was quoting and replying to: Condorcet proposed scoring the candidates according to their worst defeat. He wasn't specific about how to measure that defeat, probably since no one was considering the possibility of short rankings. My proposal is a version of Condorcet's method, as proposed by Condorcet. My proposal is consistent with what Condorcet proposed. One of the possibilities implied by his proposal. I've posted often here about why votes-against is the desirable way to measure defeats. [...meaning that that wv advocacy began well before May '96] [Someone had said]: I find this scheme artificial. While circular Voting systems are proposed by people, not picked from trees. [I reply below. For the rest of this posting, I trust that it will be clear which part is from me and which part is from the person to whom I was replying] Is majority rule artificial too? Most would agree that it's natural. Condorcet's method carries out majority rule where your random method your votes-for method wouldn't. When I say Condorcet's method, I'm referring to my votes-against version of it. [I mention Condorcet a few times below, and, from the above-quoted sentence, those references to Condorcet or Condorcet's method refer to wv Condorcet, in this posting and others, including the March posting that I'm going to re-post] In Steve's many-candidate example, there could be a majority ranking Clinton over Dole, and Condorcet's method would count that. A method counting votes-for would ignore it, and would work more like MPV, making anti-Dole votes sorry they didn't vote Clinton in 1st place. Look, in the U.S., this November, millions of progressives are going to cast a vote-against, for which they're quite willing to give up the opportunity to cast a vote for their favorite. Condorcet's method lets them cast that reliably-counted vote-against, while still voting their favorite in 1st place, and while still ranking Clinton as low as they want to--provided that they merely rank him over the candidate they want to defeat. Votes-against are artificial? Tell that to the Democrat-voting progressives--but they'll do it anyway. ties are logically possible, I am not sure that they are probable nor do I know what they would mean. I am inclined I've repeatedly showed you that the common practice of truncation will cause circular ties even when there's a candidate who, when compared separately to each one of lthe others, is preferred to him by more voters than vice-versa. Trunction can take victory away from Condorcet winners, in your methods,
[EM] 1996 March 24 advocacy of wv
The way to choose a single-winner method is on the basis of what standards you want, what you want from a single-winner method. Since you're into electoral reform, I needn't tell you what the lesser-of- 2-evils problem is, and you don't need me to tell you that the lesser-of-2- evils problem completely dominates the voting of progressives, who virtually always will tell you that they vote for a lesser-evil, abandoning their favorite, because that's the necessary pragmatic voting strategy. That's what we want to get rid of, that need for defensive strategic voting in order to make a lesser-evil beat someone worse. Condorcet's method is the one that gets rid of that problem. Not Copeland, but Condorcet. I talk about a situation with Dole, Clinton Nader. I'll avoid repeating it too much now, since you've already heard it. But defensive strategy means having to vote Clinton equal to or over Nader because that's the only way to ensure that Clinton will keep Dole from winning. Plurality makes people do that. So will Copeland, under commonly expected conditions. So how does Condorcet avoid that problem? That's easy quick to tell: Condorcet counts votes-against. That means that the fact that you've voted Clinton over Dole counts as your vote against Dole, even though you didn't rank Clinton in 1st place. That's it. That's the whole story. *** In particulat, that means that a candidate with a majority againsts him can't win unless every candidate has a majority against them. That can't be said of Copeland. Copeland will often pick someone who has a majority against him even if he's the only candidate with a majority against him. So much for majority rule in Copeland. *** And what does it take for everyone to have a majority against them, in Condorcet? It requires 1 of 2 things: 1. The risky devious offensive strategy of order-reversal cheating has been attempted on a scale sufficient to change the election result, and the simple countermeasure to it hasn't been used. Bruce I have agreed that that devious offensive strategy won't be used on that scale. 2. There's a natural circular tie, in which the electorate's collective preferences are circular, and these circular collective preferences are so strong, and so free of abstention, every candidate has a majority preferring somoene else to him. This is a chaotic situation, an extremely indecisive situation in which there's no good case to be made for picking any particular candidate, where there's no really right solution. So then, in situations that are at all plausible, and where it matters, Condorcet guarantees that a candidate with a majority agsinst him can't win. That can't be said of any other method. In particular, it certainly can't be said of Copeland. *** What that means to the voter is that if you're part of that majority (Clinton voters + Nader voters) who rank Clinton over Dole, even though they don't all rank Clinton in 1st place, you, the rest of that Clinton + Nader majority are making it impossible for Dole to win. That's our goal in single-winner reform. *** To be continued in an immediately subsequent message *** Mike Ossipoff _ Dont just search. Find. Check out the new MSN Search! http://search.msn.click-url.com/go/onm00200636ave/direct/01/ Election-methods mailing list - see http://electorama.com/em for list info
[EM] Continuation of that 1996 March 24 posting to EM, advocating wv
Let me demonstrate this with an example. A much more reasonable un-contrived example than the ones in the anti-Condorcet paper: Voters' sincere preferences: 40%: Dole, Clinton, Nader 25%: Clinton 35%: Nader, Clinton, Dole [The Clinton voters have no 2nd choice listed for simplicity, because it wouldn't matter under realistic conditions anyway, because in this 3-candidate race they have no reason to vote a 2nd choice, because it will matter later when I discuss an _implausible_ eventuality] If voters vote complete sincere rankings, Clinton wins by Condorcet by Copeland. The difference between those 2 methods isn't tested here, since there's no circular tie to solve. Clinton beats Dole 60-40, Clinton beats Nader 65-35. Now say the Dole voters truncate, or bullet-vote, and don't rank Clinton. This could be done strategically, but will be quite commonly done without any strategic intentions. Here are the resulting rankings: 40%: Dole 25%: Clinton 35%: Nader, Clinton Now we have a circular tie, in which the Dole voters have allowed Nader to beat Clinton 35-25. The other pairwise results are as above. Nader beats Clinton beats Dole beats Nader. A circular tie. Alright then who's least beaten by Condorcet's rule? Well the Dole voters can't do anything about the fact that Dole has a majority against him, a 60-40 majority. Nore can the Dole voters' truncation change the fact that there is no majority against Clinton. Clinton only has the smaller of the 2 extremes against him, 35%. Dole has 60% against him, and Nader has 40% against him. Clinton wins. The Condorcet winner who'd beat each one of the others in separate 1-on-1 elections wins. *** Now, you may at some point hear someone express concerns about order-reversal, so let's try it in this example. Let's say the Dole voters attempt order-reversal strategy, in order to make Clinton very beaten, hoping that will help Dole: 40%: Dole, Nader 25%: Clinton 35%: Nader, Clinton This time the Dole voters have caused Clinton to be beaten 75-25. As before, the Dole voters can't do anything about the fact that Dole has a majority against him, a 60% majority. But another thing the Dole voters can't do anything about is the fact that Nader _doesn't_ have a majority against him. The Dole voters, since they don't constitute a majority (Dole couldn't lose if they did) don't have the power, on their own, to make someone be beaten by a majority. They only did it to Clinton with the help of the Nader voters. But no one's helping them do it to Nader. Therefore, there's not a thing the Dole voters can do to keep Nader from winning. Well there's 1 thing they can do: They can avoid the fruitless risky order-reversal attempt. Notice that all it took to punish the order-reversal, to make it impossible for it to succeed, was for the Clinton voters to not vote a 2nd choice, or at least to not vote for Dole. But it wasn't even necessary for the Clinton voters to know which side would be the big side with the capability of trying order-reversal-- merely not voting a 2nd choice completely thwarts any order-reversal attempt. So then, that's the defensive strategy against order-reversal: Don't vote for the candidate of the likely order-reverser. In general, don't vote for anyone you like less than the likely Condorcet winner. In a 3-candidate race, there's no reason for the Clinton voters to vote a 2nd choice anyway. In a larger election, more candidates, it could be uncertain who's Condorcet winner, but all voters have access to the same strategic information, and the Dole voters know that. So the mere fact that other voters even _might_ expect the possibility of order-reversal, and vote accordingly, is enough to deter the order- reversal. I re-emphasize that this won't happen anyway. Bruce I have agreed that the devious strategy of order-reversal won't be tried in a public election on a scale sufficient to change the election result. *** Sorry about going into such detail about something that won't happen. *** Now, what would Copeland do in the 2 above cases, where the Dole voters truncated, and where they order-reversed? Well, first of all, Copeland is always completely indecisive in a 3-candidate race, and relies completely on a tie-breaker. Bruce proposes, in his Regular-Champion method, that Condorcet use Plurality as its tie-breaker. So what would happen? In both circular tie examples, Regular Champion's Plurality tie-breaker would pick Dole. If we want something better than Plurality, the above example would suggest that we need somethng better than Copeland or Regular-Champion, to paraphrase something that was recently said to you. *** Our goal in single-winner reform can be summarized by saying that we want to get rid of the need for defensive strategy to the greatest extent possible. A group of voters consisting of a full majority of all the voters has the power to make happen whatever they want to. Easy enough if they all vote the same candidate in 1st place, but not so
