[EM] Fw: About non-monotonicity and non-responding to previous posts...

[Bob Richard]

Terry and all,

I, too,am interested in Stephane's explanation. Meanwhile, I thought he 
was referring to a different way of broadening the notion of 
monotonicity. I understood him to be saying that, because of strategic 
voting, the relationship between true preferences and outcome is 
non-monotonic even when the relationship between votes cast and outcome 
is monotonic. In any case, this is how I understand David Austen-Smith 
and Jeffrey Banks, "Monotonicity in Electoral Systems", American 
Political Science Review, Vol. 85, No. 2 (June 1991): 531-537. As I 
understand it, this important paper argues that, when monotonicity is 
defined relative to true preferences, and when the legislative process 
is considered in combination with the voting rule, monotonicity becomes 
a non-issue.

--Bob Richard

Terry Bouricius wrote:
> Stephane,
>
> In what way are you calling FPTP vote-splitting non-monotonic? It is
> normally considered monotonic in that a voter raising the rank of a
> candidate to number 1 can never hurt that candidate. Are you using the
> broader non-standard definition of monotonicity that some particular
> election method advocates have started using...where raising the rank of a
> candidate to number 1 may hurt that VOTER'S interests (rather than that
> first ranked CANDIDATE) by causing the election of that voter's least
> favorite candidate. I have feel that is an overly broad expansion of the
> concept of monotonicity, that some have seized on so they could claim
> there are examples of non-monotonicity where there really aren't.
>
> While I am one of those who thinks monotonicity is of relatively small
> practical importance compared to certain other criterion, I think our
> terminology definitions need to be standardized to allow us to understand
> each other...and I would say IRV is a non-monotonic system and FPTP is
> monotonic. Can you show that this is wrong?
>
> Terry Bouricius
>
> ----- Original Message ----- 
> From: "Stéphane Rouillon" <stephane.rouillon at sympatico.ca>
> To: "Abd ul-Rahman Lomax" <abd at lomaxdesign.com>
> Cc: <election-methods at lists.electorama.com>
> Sent: Wednesday, November 04, 2009 11:20 PM
> Subject: [EM] About non-monotonicity and non-responding to previous
> posts...
>
>
> Miss Dopp was promoting FPTP in the past, saying IRV is non-monotonic,
> until I showed that FPTP vote-splitting behaviour is non-monotonic too.
>
>   
>> - more voters prefer B to C
>> - a fraction of those voters will vote for A because they even prefer
>> A to other candidates
>> - thus C can get elected because of vote-splitting between A and B
>>
>> Even if more voters prefer B to C, the result is that C wins over B.
>> This is clearly non-monotonic.
>> This is a typical vote-splitting case using FPTP.
>>     
>
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>   

-- 
Bob Richard
Executive Vice President
Californians for Electoral Reform
P.O. Box 235
Kentfield, CA 94914-0235
415-256-9393
http://www.cfer.org

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