It doesn't seem that Nanson or Baldwin has quite the same degree of problem with monotonicity as IRV does. Is Baldwin/Nanson less non-monotonic?
>From: Chris Benham <[EMAIL PROTECTED]> >Reply-To: [EMAIL PROTECTED] >To: John Wong <[EMAIL PROTECTED]> >Subject: Re: [Election-Methods] How is the Nanson and/or Baldwin >non-monotonic? >Date: Fri, 21 Sep 2007 05:27:07 +0930 > > > >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 > _________________________________________________________________ A place for moms to take a break! http://www.reallivemoms.com?ocid=TXT_TAGHM&loc=us ---- Election-Methods mailing list - see http://electorama.com/em for list info
