[Election-Methods] How is the Nanson and/or Baldwinnon-monotonic?

[John Wong]

Thanks, I'll try to reproduce this. However, this seems rather complex. How 
nonmonotonic is Nanson/Baldwin Method?

>From: James J Faran <jjfaran at blaschke.math.buffalo.edu>
>To: John Wong <johnwong00 at hotmail.com>
>CC: election-methods at electorama.com
>Subject: Re: [Election-Methods] How is the Nanson and/or Baldwin 
>non-monotonic?
>Date: Thu, 20 Sep 2007 09:56:09 -0400
>
>OK, here's a description on how to generate a Nanson example.  A similar
>method should generate a Baldwin example.
>
>Start with a profile that gives the Borda ranking A>B>C:
>
>ABC: 2
>BAC: 1
>
>This gives Borda scores A:5, B:4, C:0, and A beats B pairwise, so A is
>the Nanson winner.  We want to have enough voters to move (increasing
>ranking of A) without changing the ranking of C so that, after the move,
>C then has a better Borda score than B.  This requires 5 voters of type
>either CBA or BAC.  Adding 5 voters of each type doesn't change the
>ranking, so take the profile
>
>ABC: 7
>ACB: 5
>CAB: 5
>CBA: 5
>BCA: 5
>BAC: 6
>
>Borda: A 35, B 34, C 30. A still wins Nanson, but if we switch,
>increasing A's rankings (5 CBA voters become 5 CAB voters),
>
>ABC: 7
>ACB: 5
>CAB: 10
>CBA: 0
>BCA: 5
>BAC: 6
>
>Borda: A 40, B 29, C 30. B is now eliminated, but A beats C pairwise, so
>A is still the Nanson winner. We need to make C beat A pairwise without
>messing up the Borda rankings, so we add Condorcet triplets of the
>correct type.  A is beating C by 3, so we need to add 4.
>
>Original Profile:
>ABC: 11
>ACB: 5
>CAB: 9
>CBA: 5
>BCA: 9
>BAC: 6
>
>Borda: A 47, B 46, C 42. C is eliminated and A beats B pairwise 25-20.
>
>New Profile (5 CBA voters become 5 CAB voters):
>ABC: 11
>ACB: 5
>CAB: 14
>CBA: 0
>BCA: 9
>BAC: 6
>
>Borda: A 52, B 41, C 42. B is eliminated and C beats A 23-22.
>
>We could also take 5 BAC voters and make them ABC voters and get another
>example.
>
>You should be able to find a Baldwin example by a similar technique.
>
>
>On Thu, 2007-09-20 at 00:55 -0700, 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.
> >
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>--
>James J Faran <jjfaran at blaschke.math.buffalo.edu>
>

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