brnstnd@stealth.acf.nyu.edu (Dan Bernstein) (11/23/89)
The usual, rigorous, mathematical proofs of voting paradoxes do not apply to approval voting, as in Alien's MAUVE and WEIP systems discussed in news.groups. An example of the standard paradox: In this universe, 500 people vote for rec.aquaria, while 300 vote for sci.aquaria. In a parallel universe, 250 people vote for each of rec.aquaria and rec.aquarium, while 300 vote for sci.aquaria. So rec.aquaria wins in the first and loses in the second, even though the voters have the same opinions. This doesn't apply to approval voting because the vote for name A is independent of the vote for name B. In the example above, rec.aquaria will get its 500 votes whether or not rec.aquarium is present. Approval voting just adds up the votes for each name; and so rec.aquaria wins. This independence is crucial to the theoretical and practical success of approval voting. Herman Rubin considers this independence between names to be impossible, for reasons of psychological ``rationality.'' He argues, in the case of newsgroup creation, that someone who prefers sci.aquaria to rec.aquaria will vote against rec.aquaria, so as to improve sci.aquaria's chance of winning---even if rec.aquaria would be acceptable. But no sensible voter would adopt that strategy. After all, if everyone did, then both names would fail---and hence it's not the right strategy for someone who wants the group to pass. (Such reasoning---assuming that there is an optimal strategy, then assuming that everyone else will find it, and finally figuring out what it is---is called ``superrational'' by Hofstadter. I don't know if he originated the term.) ---Dan