At 10:32 AM 7/26/2007, Steve Eppley wrote: >I have time only for a few quick comments about Mr. Lomax' message (below). > >First, he appears to have misunderstood what I meant about altruistic >voters. I asked what would happen if they voted sincerely (and selfish >voters extremize). Somehow he misinterpreted that as if I'd asked what >would happen if they misrepresented their preferences.
Sorry. The problem is in assuming a definite correlation between selfish and extremizing. Extremizing is misrepresenting to the system one's true preferences. It seems intuitively likely to me that the *ideal* system would respond to such a voter by giving them what they want, which has been distorted by their vote, so it can easily be less than their true preferences would indicate. However, we are dealing with Range Voting, and a particular kind of Range Voting which we already know is less than ideal. Better than most of what is on the table, but less than ideal. Many consider that Range may, in many scenarios, reward extreme votes to be a serious argument against it. I'd say that the arguments which have been so made are incomplete, but that is really a side issue here. The issue here is what the optimal strategies are in Range Voting. There may be no general answer. I believe that I have found a case where the voter optimizes personal utility by voting sincerely. I am not *yet* claiming general application for this, but, contrary to some assertions, this is not a small election. It can be as large as desired. My conclusion comes from a more accurate determination of utilities than has been happening with the simulations, it asks a different question (there is a *specific* utility pattern involved, rather than random distributions of patterns), and the simulations have been, it turns out, Range 999999. It has been assumed by many that Range with greater N is better. The proofs aren't in, as far as I know, very little work has been done with *low* resolution Range. And my case is maximally low resolution, almost Approval. >Second, about optimal Range Voting strategy. It looks to me from my >own analysis and that of others that, from the individual voter's point >of view, the vote most effective at maximizing that voter's expected >utility is one that extremizes (except in some unimportant rare cases >where another vote can be as good.) The case I propose is actually a quite general one, not truly rare, the only thing rare about it is zero knowledge. We understand that if the voter knows the election environment, and in particular, if the voter faces, in spite of the number of candidates, a pairwise election with high certainty, the optimal strategy extremizes *those* votes. But what about the others? A sincere vote for a candidate who can't win *cannot possibly lower utility,* and there are other considerations besides winning. Votes have effects. If a candidate is lousy, but has some support, Approval may give that candidate very low votes. If the candidate gets twice as good, there really may be no more votes. The real status of the candidate is not revealed, as long as the candidate is not rising to first place for a significant number of voters. As to second place, we really need to know who is in true *third* place! So the claim that intermediate votes are without value is clearly false. The assumption is that all value is in determining the winner, and that is false. People also value being honest and sincere, by the way. What I am finding is that optimal strategy depends on the preference pattern for the voter. We already knew that, didn't we? The claim is being made that approval strategy is best (for the voter) *regardless of preference pattern*. Is it? I have a counterexample. And it is a bit > I haven't had time to hunt for Mr. >Lomax' definition of optimality to check whether he defines it from the >perspective of the (social utilitarian) voting system designer, rather >than from the perspective of the voter who seeks to maximize his/her own >utility. The latter! We already knew that the optimal voting pattern from the point of view of maximizing overall social utility is the sincere vote. (Indeed, the optimal pattern is non-normalized sincere voting, there is a way to define that). However, the claim is that the voter has different utilities. I must also point out that classic game theory falls flat, often, at predicting human behavior, and often analysts assume that this means that people aren't rational. However, many of the failures disappear if we consider that people might be, within certain limits, optimizing social utility. And we are not suckers, or altruistic, for doing so, except with a very narrow definition of altruism. We are acting to preserve our genes! And we are defining "our" as social animals, who act for the welfare of the social group. So even if it is true that optimal individual behavior is to vote the extremes, many may choose not to do so. They will do so, I suggest, when the loss in individual expected utility is small. We will rarely lie when the reward for lying is small, for there is a cost to lying entirely aside from game theory considerations. In my view, extreme votes are not lying; they are, rather, truer expressions of preference. If I want so much for a candidate to win, A over B, that I will downrate B, *I may have a higher preference than I was thinking.* To my mind, a full vote preference does not have to be any particular preference strength, in absolute terms. It's up to the voter to decide! So I don't like to call extreme votes "insincere." For convenience, I call simple expression of utility, generally normalized, which is a distortion in itself, "sincere," with everyone else. But it really means something more precise, such as normalized accurate perception of utilities, or absolute perception of utilities. In short, what I've called "fully sincere." For short. By using the word "sincere," unfortunately, we call up all kinds of moral judgements. We believe it is better for people to be sincere than to lie or not disclose. But what is ironic to me is that, to prevent some sort of reward for distortion, some of us want to prohibit telling the full truth! Since some won't. >Are we all agreed that extremizing is the (game-theoretically) optimal >Range Vote in the case where there are only two candidates? Yes. Not necessarily the "best" vote, but best for maximizing the voter's personal utilities. Whether or not the voter wants to vote that way is another story. Consider the pizza election. With two flavors only, pepperoni and mushroom. There are three voters (there can be *many* voters, but let's say its proportional, my two voters are standins for twice as many as the opposing faction.) Two prefer pepperoni, but only slightly. The other, quite simply, cannot eat pepperoni, so we can say that the preference strength is maximal. The lone voter obviously should vote Approval style. But what about the voters whose utilities are, say, 100 and 99? They really do love mushroom, but pepperoni has only a slight edge? What's the best pizza to choose? And does our voting method and recommended strategy choose it? If not, we really should be considering why not and what we might do about it. That doesn't mean we can solve the problem. The problem is artificially constricted if we limit ourselves to "election methods." That's not how real groups would resolve this question. Note that Range, with enough voters, won't always pick what I consider the ideal pizza, it depends on how many voters and the preference spreads. But Range+2 will. Range+2 is top-two range, and it is known to outperform standard Range in utility. And I think the simulations actually understate its performance. Hold a Range+2 election with the two candidates (and perhaps some others, doesn't matter; I originally stated the pizza election as three to avoid the normalization problem, to allow normalization without harm. In the two candidate case, normalization can *drastically* distort the utilities.) What will happen? Pepperoni and Mushroom will have a runoff. But the pepperoni voters now know that there are many voters who have a strong preference. They may elect to change their vote, to give up a tiny bit of utility in order to make a huge difference for a few. We do this all the time! We do it when we pay taxes that are used to support people in dire need. But if they judge that the strong preference is fake or not serious or whimsical, on the part of the minority, they may stick to their guns. And they will, quite properly, prevail, as they should have the right to do. They are the majority. All this, though, is dicta. The best personal utility optimizing strategy for the 2-candidate case is extreme voting. However, when the benefit is small, voters may well elect to simply vote sincerely, understanding that this means that they may be giving up a small benefit in favor of a larger benefit to a minority. You could call that altruistic, but it is really social behavior. These trades ultimately benefit everyone, for many interactions take place, many choices, and if every one of them maximizes overall benefit, and positions shift, as they do (it is not always the same set of voters who are losing and who are benefiting), over time, if net social utility is being maximized, so is personal. So the optimal strategy *in one election* may be extreme voting -- it certainly is for some cases, maybe even most -- but that is not necessarily the best strategy for Life. Including elections. And, properly, the decision is the voter's. Nobody should be telling the voter what to do, the advice, unless it is purely informative, is insulting. Telling someone what their optimal strategy is insulting, unless carefully specified. *If you want to accomplish A, then your optimal strategy is ..." but, in that case, to avoid introducing bias, one should also state the reasonable alternative goal, and maximizing overall SU is the clear other option, leading to a different and, indeed, possibly more pleasing strategy: vote sincerely and accurately. ---- Election-Methods mailing list - see http://electorama.com/em for list info
