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

[Chris Benham]

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