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This is a great example, but how do I knoew where to add four?<br><br>> Subject: Re: [Election-Methods] How is the Nanson and/or Baldwin non-monotonic?<br>> From: jjfaran@blaschke.math.buffalo.edu<br>> To: johnwong00@hotmail.com<br>> CC: election-methods@electorama.com<br>> Date: Thu, 20 Sep 2007 09:56:09 -0400<br>> <br>> OK, here's a description on how to generate a Nanson example. A similar<br>> method should generate a Baldwin example.<br>> <br>> Start with a profile that gives the Borda ranking A>B>C:<br>> <br>> ABC: 2<br>> BAC: 1<br>> <br>> This gives Borda scores A:5, B:4, C:0, and A beats B pairwise, so A is<br>> the Nanson winner. We want to have enough voters to move (increasing<br>> ranking of A) without changing the ranking of C so that, after the move,<br>> C then has a better Borda score than B. This requires 5 voters of type<br>> either CBA or BAC. Adding 5 voters of each type doesn't change the<br>> ranking, so take the profile<br>> <br>> ABC: 7<br>> ACB: 5<br>> CAB: 5<br>> CBA: 5<br>> BCA: 5<br>> BAC: 6<br>> <br>> Borda: A 35, B 34, C 30. A still wins Nanson, but if we switch,<br>> increasing A's rankings (5 CBA voters become 5 CAB voters),<br>> <br>> ABC: 7<br>> ACB: 5<br>> CAB: 10<br>> CBA: 0<br>> BCA: 5<br>> BAC: 6<br>> <br>> Borda: A 40, B 29, C 30. B is now eliminated, but A beats C pairwise, so<br>> A is still the Nanson winner. We need to make C beat A pairwise without<br>> messing up the Borda rankings, so we add Condorcet triplets of the<br>> correct type. A is beating C by 3, so we need to add 4.<br>> <br>> Original Profile:<br>> ABC: 11<br>> ACB: 5<br>> CAB: 9<br>> CBA: 5<br>> BCA: 9<br>> BAC: 6<br>> <br>> Borda: A 47, B 46, C 42. C is eliminated and A beats B pairwise 25-20.<br>> <br>> New Profile (5 CBA voters become 5 CAB voters):<br>> ABC: 11<br>> ACB: 5<br>> CAB: 14<br>> CBA: 0<br>> BCA: 9<br>> BAC: 6<br>> <br>> Borda: A 52, B 41, C 42. B is eliminated and C beats A 23-22.<br>> <br>> We could also take 5 BAC voters and make them ABC voters and get another<br>> example.<br>> <br>> You should be able to find a Baldwin example by a similar technique.<br>> <br>> <br>> On Thu, 2007-09-20 at 00:55 -0700, John Wong wrote:<br>> > How is the Nanson and/or Baldwin non-monotonic? I've been trying to develop <br>> > an example where they are non-monotonic, but I'm having trouble.<br>> > <br>> > _________________________________________________________________<br>> > Share your special parenting moments! <br>> > http://www.reallivemoms.com?ocid=TXT_TAGHM&loc=us<br>> > <br>> > ----<br>> > Election-Methods mailing list - see http://electorama.com/em for list info<br>> -- <br>> James J Faran <jjfaran@blaschke.math.buffalo.edu><br>> <br><br /><hr />Make your little one a shining star! <a href='http://www.reallivemoms.com?ocid=TXT_TAGHM&loc=us' target='_new'>Shine on!</a></body>
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