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

[John Wong]

This is a great example, but how do I knoew where to add four?

> Subject: Re: [Election-Methods] How is the Nanson and/or Baldwin	non-monotonic?
> From: jjfaran at blaschke.math.buffalo.edu
> To: johnwong00 at hotmail.com
> CC: election-methods at electorama.com
> 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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