Now I'll try to tackle the second question: On Thu, 7 Nov 2002, Adam Tarr wrote in part:
> - I will admit this is the first election method I've dealt with where I > have trouble manipulating small examples. Here's a very small example that > was giving me trouble: say we are electing two candidates out of four. > My > ballot is: A(>B=C=D). The pairwise matrix will be 6x6 (with 6 empty > slots). With respect to my ballot, every comparison is equivalent to one > of the following: > > AB vs. CD > (k1 + j2 = 1 + 1 = 2? k2 + j1 = 0 + .5 = .5?) > > or > > AB vs. BD > (k1 + j2 = .5 + 1 = 1.5? k2 + j1 = 0 + 1 = 1?) On this one I get M=A and m=D, so k1=.5, k2=0, and j2=.5+.5=1, as you have noted, but I get j1=.5, since B=D=m, instead of the j1=1 that you got. > > or > > AB vs. AC > > (k1 + j2 = k2 + j1 = 1.5 + .5 = 2) > > Do the summations I wrote make sense? The results (except the trivial last > one) seem a bit odd. I was toying with this example to try and measure how > equivalent your Condorcet-PR method is to PAV in situations where the > voters vote in an approval-like fashion. It does seem odd that AB should beat CD by a larger margin than AB's win over BD when B and D are ranked equally. Perhaps we should interpret the difference AB-CD as just A when B is equal in rank to a member of CD. In other words, if we have two sets H and K, then we should interpret H-K as consisting of those members of H that are not equivalent to any member of K. [Two candidates are "equivalent" on a ballot if they have equal rank.] If we do this, then AB beats CD by the same margin as in the AB vs. BD contest, which makes more sense. Thanks for pointing that out. Forest ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em