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
cik@l.cc.purdue.edu (Herman Rubin) (11/23/89)
In article <4037@sbcs.sunysb.edu>, brnstnd@stealth.acf.nyu.edu (Dan Bernstein) writes: > 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. ....................... > 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. Suppose that those in favor of sci.aquaria think that rec.aquaria is only marginally better than the previously existing alt.aquaria. This may very well be the case (I do not know, and I did not participate in the vote). It may even be that sci.aquaria would defeat rec.aquaria almost unanimously among those who want an aquaria group in the regular groups, and still lose in approval voting. It only takes one person who wants rec.aquaria and not sci.aquaria to get this result. | 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.) There are times that a superrational strategy can be justified, but I see no evidence of it in this case. My previous paragraph shows that this can be false. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)
brnstnd@stealth.acf.nyu.edu (Dan Bernstein) (11/26/89)
In article <1738@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: > Suppose that those in favor of sci.aquaria think that rec.aquaria is only > marginally better than the previously existing alt.aquaria. > It may even be that sci.aquaria would defeat rec.aquaria almost > unanimously among those who want an aquaria group in the regular groups, > and still lose in approval voting. In other words, if the voters are confused and vote on different issues, the results of the vote will be messed up. So? > There are times that a superrational strategy can be justified, but I see no > evidence of it in this case. Maybe you recognize superrationality as the Kantian imperative? There's an excellent reason that voters will use it in this case: the superrational solution is stable. In certain cases, superrationality is unstable; Hofstadter calls this ``reverberant doubt.'' (And those cases are the examples used by non-Kantian thinkers.) But here it's stable. Write out the equations if you don't believe me. (Shall we move this to sci.math?) Even better, run an approval vote on, say, the new newsgroup for pagan dicussions, and observe that it works. ---Dan