Abd ul-Rahman Lomax writes: > At 08:01 AM 11/2/2006, Michael Poole wrote: >>The Majority Criterion is an objective criterion. > > It looks that way. When you look closer, there are some ragged > edges. What does "prefer" mean? Is there a threshold in preference > strength below which it is effectively the same "rating." I.e., the > voter might make a choice, if forced to by the method, but really has > no *significant* preference.
Wikipedia: By the majority criterion, a candidate X should win if a majority of voters answers affirmatively to the question 'Do you prefer X to every other candidate?'. A voter who cannot honestly or easily answer "yes" to some candidate is not a problem for this formulation of the majority criterion. The existence of such a voter is an argument in favor of some other criterion, but does not make the MC subjective. If you want to change the "prefer" to "strongly prefer", pick a new name for your modified criterion. > Further, it is alleged that Approval does not satisfy the Majority > Criterion. It seems to me that this requires a few assumptions that > have not been made explicit. It does not require any additional assumptions. Approval can only capture preferences between members of the approved set and the not-approved set. Clones are a good general example. With small numbers of voters -- for example, one -- Approval can result in ties if the voters mark who they approve (or strongly approve) of rather than who their favorite. >> When you ask about >>preference strength, it becomes extremely subjective -- and attempts >>to normalize the subjective effects (for example, rescaling each >>voter's expressed preferences to a common minimum and maximum) obscure >>honestly expressed preferences. While one can reasonably complain >>that objectively defined measures to not maximize subjective goals, >>the superiority of the subjective measure should be established[1] >>first. > > Doublespeak, I'd say. It is quite clear that there is some basis for > variation in preference strength. It's real. It is no more subjective > than preference itself; simple preference has taken the complex space > of voter expectation and has reduced it to a binary relation. A lot of > data is lost. > > Is that data of value? I've shown situations where it clearly is of > value, where the Majority Criterion will clearly choose a winner who > will be a disaster for the society. And historical examples can be > shown. That data is not of value because my question was not "Is there some reason for the variation in preference strength?". The argument advanced in favor of Range Voting is that it maximizes a certain social utility function. Exactly *which* function depends on whether a ballot scores are normalized. My question is why that particular function is an appropriate optimization goal. I suspect that the expected time to choose a disastrous winner is lower for Range Voting than for methods that satisfy the Majority Criterion. True or not, comparing actual past performance to hypothetical future performance is not a reasonable way to judge. >>Ultimately, social utility is not a static function[2]; election >>results alter the function both directly and indirectly. > > Yes, of course. But the very idea of elections is to derive some kind > of conclusion from the state of the voters at the time of the > election. This very idea is defective, that is, not optimal, but once > we accept it, that further expectations will change after the election > is irrelevant. The election is attempting to determine "the choice of > the electorate." And we are attempting to define what that means. > > Essentially, how is the choice made, and for what purposes and to what > ends. If we don't consider the ends, but merely consider a very > limited metric, on the argument that this metric is "objective," even > though it is entirely based on subjective comparisons by all the > voters, we end up with an artificially constrained result that will be > distorted, under some conditions -- I would argue that it is commonly > so -- away from optimum. The impact of an optimization goal on future system behavior should not be dismissed so lightly. You can balance on a unicycle, but you seldom have to worry about balance in a sedan. When there are only two viable parties, Range Voting's use of strength of preference apparently encourages the factions to be strongly (even bitterly) divided: that will maximize the difference in scores between the two candidates among supporters of each party. I am not sure that more parties will necessarily resolve that; as Kevin Venzke showed, a voter is most likely to affect a Range Voting election by giving only extreme ratings. The only non-personal justification I could find in the rest of your email for a Range or Approval style vote is the pizza example. I am less interested in contrived examples -- I could contrive some involving an irrational fear of pepperoni -- than in a formal definition of Range Voting's social utility function. Michael Poole ---- election-methods mailing list - see http://electorama.com/em for list info
