[EM] Corrected "strategy in Condorcet" section
Michael Ossipoff has convinced me that winning votes Condorcet does not suffer from the mess that margins Condorcet does. I've therefore corrected my paper (http://www.cs.brown.edu/~ws/approval.pdf) to indicate this. ws This message was sent using IMP, the Internet Messaging Program. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Correction of false statements by Ossipoff & Schudy about range voting.
Steve Eppley wrote in part: >>Warren Smith's example, in which a voter has total knowledge of all other votes before casting her own vote, is implausible in the elections we're interested in reforming.<< I might be mistaken, but when I was introduced to this group it was more about studying methods than "reforming elections." Folks who get all on board with election reform when their candidate loses tend to not discuss things in terms of "methods" but of "practices" and we're spending an inordinate amount of time on matters that mix voter behaviour with the mathematics underlying an election method. I've proposed before that there should be a way to axiomitize the distinctions (I'm not smart enough to propose one, but I joined the list to learn about how all the different methods work, not to try to impose one that I like...) For what it's worth from all I've learned about methods on this list if I were going to "reform" anything about the mess that is US national elections I'd pick approval for party primaries and some Condorcet-compliant method for the general elections. But from my parochial perspective the most badly broken aspects of US elections aren't related to the choice of election method - I have first-hand experience with supposedly illegal dis-enfranchisement. The surest way to win re-election is not to allow your opponents' supporters the opportunity to vote, and if you can get away with that then it doesn't matter which method is used to count the votes. election-methods mailing list - see http://electorama.com/em for list info
[EM] Range Voting Strategy
Clarifications on my claim that range voting strategies use extremes: 1) This claim is only valid in large elections, not small ones. See Myerson and Weber's paper, which is cited in mine, for details on the reasonable assumptions made for this claim. 2) It is true that if a voter is indifferent to voting for a candidate or not, 0.5 is also a rational vote. But whenever 0.5 is a rational vote in Myerson and Weber's model, all other votes are rational too. Warren Schudy This message was sent using IMP, the Internet Messaging Program. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Intermediate Ratings Never Optimal?
One of the basic theorems of Linear Programming is that when there is an optimal value of a linear objective function it will occur at least one corner of the feasible region. In the rare cases that it occurs at two corners of the feasible region, it will also occur at every point on the line segment connecting the two corners. In infinite precision Range voting the set of feasible votes (i.e. ways of marking a ballot) form an hypercube of dimension N if there are N candidates. The corners of this hypercube are the points where all ratings are at extreme values. It is possible (but unlikely) that a linear objective function could be maximized along a entire line segment on the boundary of this feasible region. FWS election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Correction of false statements by Ossipff & Schudy about range voting.
At 12:34 PM 7/22/2007, Chris Benham wrote: >I don't have a "password", so I can't access the given puzzle solution. Yeah, irritating. I think you can get a password by asking for it, there is a procedure > Warren Schudy's "never" I suppose meant "never in a remotely >plausible public political election scenario". Where is the proof? This is backpedalling. It's common for writers to make the claim, raw, without proof beyond an example which shows that a voter could regret voting sincerely. The problem with such a proof is that it can ignore all the situations where the voter could regret *not* voting sincerely. And, frankly, the pain of the latter is worse, other things being equal. That is, if you lost value because you were sincere, you can -- and most will -- say to themselves, well, at least I was honest. What do you say to yourself if you lose value because you exaggerated? In any case, *now* Benham revises the claim to make it one which is far more difficult to test. Indeed, the only way to test it thoroughly is with simulations. But, wait a minute, these people don't trust simulations. Now, why are we supposed to trust *them*? The simulations are reproducible. And, indeed, I'm going to present one; I've taken a very simple tack with the three-candidate election described, looking at the voter's utilities and payoffs for the two strategies proposed: "Approval style" and "Sincere satisfaction rating." Or if you want to call it an "acceptance rating," fine. > I knew there was the odd exception in elections with very few > voters and/or the voter has >much more precise information than s/he could ever plausibly have in >a public election. Or the reverse! It turns out that in the zero-information case, where it is equally likely for all candidates to win, as far as the voter knows, it is in the voter's interest, clearly, to vote sincerely. Now, when I look at Warren's pages, I find that there is nothing new I have discovered. It's all there, but the problem is that ranked method supporters have read it skeptically, too skeptically. It's one thing to question Smith's *conclusions*, I question them all the time, he passes too far beyond what his evidence actually proves, sometimes. But his reports of what he has found, his expert testimony, if you will, should be taken at face value. Naturally, subject to verification. But it is a long-standing legal principle that testimony is presumed true unless controverted. In any case, I found a way to do an election simulation that takes a drastic shortcut; it turns out that if your vote counts at all, in Range, the election is equivalent to an election with only one other voter! I have not nailed down all the details, there are some aspects of the probabilities that are not crystal clear to me, though I intuit that I've got it right, but I'm sure there are people here capable of detecting any mistakes I've made. It is categorically false that the optimum strategy is Approval style. The voter loses expected satisfaction by voting in this way. In another post, I outlined the procedure. I'll repeat the outline here: There is a voter with preference A>B>C, and the sincere ratings or utilities or expected satisfaction are such that the A>B preference is equally strong with the B>C preference. We will use a Range 2 election, so the possible ratings are 2, 1, and 0, and these are the sincere ratings of our subject voter for the candidates A, B, and C. With zero knowledge of the rest of the vote, what is the expected satisfaction for the voter for the two recommended strategies? Kids are calling, gotta go. But I now have the answers. It's quite interesting. >Regarding "social utility", I'm of the school that says that to the >extent that it is a real and wonderful thing it will look after itself if we do >our best to ensure that the election method is as fair and >strategy-resistant as possible. > >Chris Benham > > > > > > > >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] Juho--Schudy's statement is correct.
I think Warren Schudy could have written a stronger negative comment about Range Voting. Comparing it to Approval in his paper, he said it offers "little or no gain" (see below). That suggests outcomes with Range Voting would tend to be at least as good as with Approval. Outcomes with Range Voting could be much worse. What happens if many altruistic voters tend to try to vote sincerely and selfish voters tend to use the optimal strategy of extremizing to the limits of the range? Ugh. --Steve Eppley - Michael Ossipoff wrote: -snip- > On Jul 21, 2007, at 8:05 , Abd ul-Rahman Lomax wrote: > >> At 11:00 PM 7/20/2007, Chris Benham wrote: >> >>> I think Warren Schudy put it well in a July 2007 draft paper: >>> >>> "Range voting is a generalisation of approval voting where you can >>> give each candidate any score >>> between 0 and 1. Optimal strategies never vote anything other than 0 >>> or 1, so range voting >>> complicates ballots and confuses voters for little or no gain." >>> -snip- election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Correction of false statements by Ossipoff & Schudy about range voting.
I partially agree with Chris Benham (see below). Warren Smith's example, in which a voter has total knowledge of all other votes before casting her own vote, is implausible in the elections we're interested in reforming. I don't know which methods Chris had in mind when he wrote "as fair and strategy-resistant as possible" but I'll take a moment here to defend the social utility of the best majoritarian preference order methods (such as MAM). Recall the example someone posted here several weeks ago intending to undermine the value of the majority rule criterion. Three friends, say X, Y and Z, are ordering a pizza. (It doesn't matter if they're friends; in the worst case they're not and they expect to never hear from each other again.) Z is terribly allergic to mushrooms so he strongly prefers pepperoni, but a mushroom pizza is slightly preferred by X and Y. There was no time to deliberate--which of course is implausible in the elections we're interested in reforming--so majority rule picks the mushroom pizza. Or does it? When X or Y proposes mushroom pizza, what if Z responds by proposing "pepperoni pizza plus the transfer of $1 from Z to X." When Y hears this proposal, he thinks to himself that he'd prefer "pepperoni plus 50 cents" over mushroom, so Y proposes "pepperoni pizza plus a transfer of 50 cents from Z to Y." Suppose X is even more indifferent between pepperoni and mushroom than Y is, and would prefer mushroom over pepperoni for just a dime. X is clever, though, and bids 49 cents instead of a dime. There was no deliberation; Z never admitted the allergy. X and Z, a majority, both prefer X's final proposal over mushroom pizza. More precisely, X's order of preference is: "pepperoni plus $1 to X" "pepperoni plus 49c to X" mushroom "pepperoni plus 50c to Y" = pepperoni Y's order of preference is: "pepperoni plus 50c to Y" mushroom "pepperoni plus $1 to X" = "pepperoni plus 49c to X" = pepperoni Z's order of preference is: pepperoni "pepperoni plus 49c to X" "pepperoni plus 50c to Y" "pepperoni plus $1 to X" mushroom pizza The only alternative for which no majority prefers some other alternative is "pepperoni plus 49c to X." In the language some people use, it's the only alternative that's "unbeaten" pairwise. Economists and political scientists call the transfer of 49 cents from Z to X a "side payment." Side payments are a specific case of the more general solution: proposals that bundle alternatives. That can also be called vote trading. in the case where the bundling is accomplished by trading votes on otherwise unlinked issues. A preference order on bundles is one way an individual can express her utilities, and is much more meaningful about her utilities--potentially allowing interpersonal comparisons of utilities--than the unitless votes expressed in Range Voting. For example, the three friends learned that the utility difference for Y between mushroom pizza and pepperoni pizza is approximately 50 cents, since Y chose not to bid below the 49 cents that X bid. Candidates wanting to win try to figure out a winning platform. Given a good preference order method, the winning platform will be some "centrist" compromises, and competition will not be deterred. Candidates are creative; they can bundle together a platform of policies on unrelated issues, including side payments from some voters to others, and they'd have an incentive to try to figure out a platform (like X's proposal of Z's pizza plus 49 cents from Z to X) that minimizes the possibility that another candidate will find some platform preferred by a majority. That competition should tend to drive them toward platforms that score well for social utility. If the good preference order method of the previous paragraph also permits candidates to withdraw after the votes are cast, there will be little incentive for voters to strategically misrepresent their sincere orders of preference. Warren Schudy neglected to consider such Condorcetian methods in his paper about Approval. (He also neglected to consider that the voting method--and candidates' beliefs about voter behavior, given the voting method--affects candidates' decisions on whether to run, and on what platforms, and hence will affect the voters' preferences. Many people in this maillist make the same mistake--treating the set of alternatives and the voters' preferences as constant when comparing wildly different voting methods--and it's a huge mistake.) If the good preference order method also permits each voter on election day to begin by selecting a ranking published before election day and modifying it if desired--perhaps by drag & drop; see the feature in the new NetFlix user interface for an example--before submitting it as her vote, then we won't have to worry, when there are many candidates, about the possibility that vote
Re: [EM] Intermediate RV rating is never optimal
Abd ul-Rahman Lomax wrote: bits and pieces At 05:33 AM 7/21/2007, Michael Ossipoff wrote: That's incorrect. It's exactly the same in RV as in Approval. In your example, with B at your Approval cutoff, it doesn't matter how you rate B. In what I wrote, B was not at the voters "approval cutoff." I didn't give an approval cutoff. Approval cutoff is an artificial insertion; it's a device for converting range ratings to approval votes. This is the situation described: The voter prefers A>B>C, with the preference strength between A and B being the same as the strength between B and C. There is nothing here about Approval cutoff, there is nothing that says that the voter does or does not "approve" of *any* candidate. I think we safely say that max-rating a candidate is equivalent to "approving" that candidate. Ossipoff confused the fact that the candidate was intermediate between A and C in sincere rating, i.e., being midrange, with being "at your Approval cutoff." If the preference strength between A and B is weaker than that between B and C then with the winning probabilities being equal (or unknown) then the voter's best strategy is to max-rate A and B. If instead the preference strength between B and C is weaker, the voter does best to min-rate B and C (and of course max-rate A). Since the situation you describe is at the border of these two (max-rate B or min-rate B), we can say that "B is at your approval cutoff". And, quite clearly, it *does* matter how you rate B in some scenarios; for example, if the real pairwise election is between A and B, then the optimum vote is to rate B at minimum. And if it is between B and C, then the optimum vote is to rate B at maximum. Of course it can "matter" after the fact, but with both possible "real pairwise elections" being equally likely at the time of voting, in Abd's scenario it probabilistically makes no difference what rating the voter gives B. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Correction of false statements by Ossipff & Schudy about range voting.
Warren Smith wrote: Warren Schudy in a July 2007 draft paper: "Range voting is a generalisation of approval voting where you can give each candidate any score between 0 and 1. Optimal strategies never vote anything other than 0 or 1, so range voting complicates ballots and confuses voters for little or no gain." Ossipoff: Warren Schude's statement was correct --CORRECTION: optimal strategies can vote other than 0 and 1, and voting 0 or 1 can be suboptimal. Examples include http://rangevoting.org/RVstrat1.html http://rangevoting.org/PuzzlePage.html#prob19 Also, just in the following incredibly trivial total knowledge example TOTAL FROM OTHER VOTERS: A=85.4 B=85.5 YOUR VOTE:A=? B=? the vote A=1 B=0 is equally as optimal as A=0.9 B=0.1. This also falsifies the statement "Optimal strategies never vote anything other than 0 or 1". I don't have a "password", so I can't access the given puzzle solution. Warren Schudy's "never" I suppose meant "never in a remotely plausible public political election scenario". I knew there was the odd exception in elections with very few voters and/or the voter has much more precise information than s/he could ever plausibly have in a public election. Regarding "social utility", I'm of the school that says that to the extent that it is a real and wonderful thing it will look after itself if we do our best to ensure that the election method is as fair and strategy-resistant as possible. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] Social Utility (aka Bayesian regret, aka Voter Satisfaction) methodology
My writeup explaining this is http://rangevoting.org/BayRegDum.html just so that we no longer (hopefully) heaar any more howlers about how SU "assumes sincere voters." My public-source voting simulation program IEVS is available to all, but with the restriction that is you make any improvements to it, I have to get them, and I have to be credited... http://rangevoting.org/IEVS/IEVS.c This program allows you to measure Bayesian Regret for any voting method under any voter behavior. However, the voting method you like best, or the voter behavior you like best, may not yet be available inside IEVS. In that case I suggest you add them. IEVS is designed to make it maximally easy to add new voting methods, new probability models, and new voter behaviors. Warren D Smith http://rangevoting.org <-- add your endorsement by clicking "endorse" & filling out form... election-methods mailing list - see http://electorama.com/em for list info
