Looking closer, I tripped on this one: >> Note that YYYY will now attract the same 5 voters who had gone for >> NNNN, and the new NNNN will get 0 votes.
Saying it more carefully: >> Note that previous YYYY, now labelled NNNN, will attract the same 5 voters who had gone for NNNN, and the new YYYY will get 0 votes. I did change some details, and kept some the same: Candidate labels are inverted, Y vs N. Voters look for the SAME Y vs N candidate names. Thus the 5 winning votes go to the formerly YYYY candidate who is now labeled NNNN. But this is a side issue. Plurality is FULLY capable and neutral in an example such as here where voters approve ONE of a collection of candidates. We want to move to more capability when we realize that it matters that Plurality cannot satisfy desires such as to "approve all who are Y to both issues 1 and 2". DWK On Sat, 29 Mar 2008 15:18:14 -0400 Warren Smith wrote: >> Building on those thoughts, let's try something with Plurality: >> Start with that collection of voters and issues. >> Invert all the issues so that a Y will attract the same voters as an >> N did, and an N will attract those who had gone for Y. >> Note that YYYY will now attract the same 5 voters who had gone for >> NNNN, and the new NNNN will get 0 votes. >> The collection of voters, while owning no claims to randomness, >> remain as legitimate as they had been. > > > --true. However, you seem to think this > means now plurality-voting looks better. That is not so. > > In your new scenario, each issue is won by "N" by majority vote. > But plurality gives the election to the worst winner YYYY > and gives zero votes to the best candidate NNNN. > > Plurality still looks maximally bad in your new scenario. > These inversions really never change the picture. > > ---- > > I managed to prove some more theorems In the YN model with > random voters and canonized issues. > Plurality and approval voting both will elect a candidate with more than 50% > Ns > in his name (i.e. a quite poor one) at least a constant fraction of > the time; Condorcet > cycles will exist asymptotically 100% of the time. > I do not know how Borda, Condorcet, and IRV will behave > in the random-voter YN model. Computer simulations seem called for > since my unaided mind is not solving that. -- [EMAIL PROTECTED] people.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. ---- Election-Methods mailing list - see http://electorama.com/em for list info