Hi Abd, --- En date de : Dim 11.4.10, Abd ul-Rahman Lomax <a...@lomaxdesign.com> a écrit : > > In a given election yes, it is easy to miss the mark. > But in general, > > aiming for the median voter is the most reliable. > (That is assuming you > > don't know utilities, which I'm really not sure you > showed how to find.) > > To see this, you assume utility is based on issue > space distance, and > > that the voters aren't distributed unevenly. > > I didn't show how to find utilities, I only showed various > possibilities consistent with the votes.
Yes, and my response is what can I possibly do with that? You used one method that was rather Borda-like in character. One can't evaluate methods using a Borda-like criterion or you'll end up advocating something Borda-like. > To study voting system performance, I'm saying, one must > *start* from utilities, not from preference order without > preference strength information. Voter behavior is not > predictable without preference strength information. > Strategy, in general, doesn't make sense without an > understanding of preference strength. We sort of have been doing this when Juho questions the story behind my scenarios. > > Thus when you have a situation where every voter > chimed in on some > > question, and they didn't do that for any other > question, you should > > expect (on average) a utility problem when the outcome > goes against the > > majority opinion. > > I'll agree that this is the "norm." However, it can go > drastically wrong. > > How can we detect the exceptions? Right, that's the question. > Sure, the majority criterion and the condorcet criterion > are usually a sign of good performance, but it is obvious > that exceptions exist, and we should not denigrate a voting > system if it, under an exception condition, it violates the > criteria! I wouldn't, no. But I would presumably have some model that explains why violation of the criterion worked. > I was just pointing out that the outcome you claimed was > obviously bad wasn't. It might be that, on average, this > outcome would be poorer than the other, Yes, I'm afraid that's what I call "bad." If I didn't call this "bad" I would also have to be pretty undecided about the resolution of most two-candidate FPP elections. > but it was not a truly bad outcome, > under reasonable assumptions of likely > utility, the first utility scenario I gave, which used Range > 2 utilities, i.e., normalized and rounded off so as to make > all the votes sincere and sensible. The bullet voters then > had equal bottom utilities for the other candidates, and > those who ranked had stepped utilities. Simple. And showing > that A was, indeed (with these assumptions, which seem > middle-of-the-road to me), the utility maximizer, by a > fairly good margin! This was the Borda-like thing I mentioned above. > You can make a contrary assumption, that the A voters were > "strategic." That they "really" would be happy with B. I'm > assuming, instead, that their votes would be sincere. And > likewise the votes of the other voters. > > Look, A *almost* has a majority in first preference. I'm > very suspicious of claims that an election outcome is > "terrible" if it depends on some close-shave majority that > failed. You are really missing my complaint then. According to your stepped utility analysis C voters don't like B that much at all. If they know that the method interprets such votes that way, then it is really bad to vote sincerely for C. I initially read your last paragraph with disbelief. In my interpretation, C and his votes are just noise. The task of the election method is to pick the right candidate between A and B, just as it would be in FPP (where C would probably have died off pre-election). To be unable to do this is quite useless in my view. --- En date de : Dim 11.4.10, Abd ul-Rahman Lomax <a...@lomaxdesign.com> a écrit : > > This should rather say, if I proposed utilities behind > the scenario, I > > could make those utilities say anything I wanted. > > I pointed out some extremes, which reveal as the ideal > winner A, B, or C. In other words, you are apparently > agreeing with me. Yes. > However, I believe that I showed that a > middle-of-the road assumption about underlying utilities, > with stated assumptions that were not designed to make it > turn out some particular way, A could indeed be the best > winner. Yes you did. > (I did not set out to "prove" that A was the best winner, > but rather just to attempt to infer utilities from the > voting patterns, which didn't allow me to assume equal > ranking except at the bottom). > > The matter hinges on the A voters, who are, after all, > almost a majority. Why did none of them rank B or C? The > only reasonable assumption is that they have strong > preference, and that's what ices it. I'm happy to say that A voters have a strong preference, but why should only the A voters get to benefit from this? Are you saying the other voters don't have a strong preference against A? > This is the classic > reason to violate the Condorcet or Majority criteria: a > strong preference of a minority, particularly when the > margin is thin. > > If, in fact, B and C were true clones, with only minor > preference between them, the assumption of a significant > reduction of utility between them (which is the other factor > that lowers the rating for B and C) would fail. > > If the method allowed equal ranking, we'd see that in the > votes, and B might win. The A votes would be the same, the B > bullet voters would be the same, but the other B and C > voters would equal rank B and C. Because of the B bullet > voters, B would win by a small majority. > > So my result for A could be an artifact of the voting > system not allowing equal ranking. I used Range 2, which > doesn't give a lot of room for "creative interpretation." > That was much easier with Range 10, as I showed. With Range > 2, there wasn't any other reasonable way to interpret the > votes. It's possible that with equal ranking it would be different, but if we are not going to ask a method to behave unless voters use equal ranking, I guess we could just use Approval. Kevin Venzke ---- Election-Methods mailing list - see http://electorama.com/em for list info