John Wong wrote: > How is the Nanson and/or Baldwin non-monotonic? I've been trying to > develop an example where they are non-monotonic, but I'm having trouble. >
I think this is an example of Borda Elimination (Baldwin?) failing mono-raise. 31: A>B 32: B>C 03: A>C 31: C>A 03: C>B Borda scores: C103, A99, B98. Eliminate B, and C wins. Now change the 3 A>C ballots to C>A (i.e. do nothing but raise C on some ballots without changing any rankings among other candidates). 31: A>B 32: B>C 03: C>A 31: C>A 03: C>B Borda scores: C106, B98, A96. Eliminate A, and B wins. Note that this doesn't work for (original?) Nanson, because that elects C both times (because both times A and B have below average Borda scores and so are eliminated). Here is a demonstration from Douglas Woodall that that method fails mono-raise: > dabc 40 Borda scores: a 154 average Borda score 150 > bcad 26 b 152 > cabd 24 c 154 > cdba 10 d 140 > > With the profile as given, only d is excluded, which results in > abc 40 Borda scores: a 104 average Borda score 100 > bca 26 b 102 > cab 24 c 94 > cba 10 > Now c is excluded and a wins. But if the ten cdba ballots in the > original profile are replaced by cdab, then the Borda scores become > a 164, b 142, c 154, d 140, so that b and d are both excluded and c wins. > John Wong wrote: > How nonmonotonic is Nanson/Baldwin Method? John, The normal meaning of "monotonic" is that it meets the mono-raise criterion, a binary yes-no test. Woodall has other "monotonicity" criteria/properties. Your question can be interpreted in more than one way. http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf http://wiki.electorama.com/wiki/Monotonicity_criterion Chris Benham ---- Election-Methods mailing list - see http://electorama.com/em for list info
