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

[John Wong]

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 <chrisjbenham at optusnet.com.au>
>Reply-To: chrisjbenham at optusnet.com.au
>To: John Wong <johnwong00 at hotmail.com>
>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
>

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