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

[Stéphane Rouillon]

It depends how you define monotonicity (Mono-add-top; mono-add-plump; 
mono-later-no-harm; ...).

I consider that the spoiler effect is a special case of non-monotonicity.
With FPTP, you can easily let your third choice win by voting for your 
first choice
while you could have got your second choice elected by voting for him.
If you only want to consider monotonicity in regard to your first 
choice, you argue that FPTP is monotonic, which is right using that 
definition.

"with an IRV system a voter who votes for his first choice (instead of 
no voting) could harm the candidate’s chance of winning..."
This statement is false.
"with an IRV system a voter who votes for his first choice (instead of 
another of its preferred candidate) could harm the candidate’s chance of 
winning..."
This is the statement that is right.
Without the details in parenthesis, the statement is vague.

This is my understanding:

#1) If one considers voting for a preference instead of another => IRV 
can behave non-monotonically but most of the time is monotonic;
#2) If one considers voting for a preference instead of not voting => 
IRV can behave non-monotonically but most of the time is monotonic;
#3) If one considers voting for a first choice instead of not voting and 
the outcome without voting is not the elector first choice
=> IRV can behave non-monotonically but most of the time is monotonic;
#4) If one considers voting for a first choice instead of not voting and 
the outcome without voting is the elector first choice
=> IRV cannot behave non-monotonically.

Thus, using IRV, a voter can harm the result of an election by going to 
vote for his first choice, but if he does go vote for his first choice 
instead of
staying home it cannot hurt the election of his first choice, he can 
only hurt the election of another more preferred candidate that could
(rarely) lose to a least preferred candidate.

The terminology often used to summarized could be interpreted as 
describing the last case (#4) which is the only monotonic behaviour of IRV.

Stéphane Rouillon, ing., Ph.D.

Bob Richard a écrit :
> 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.
>>>     
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info
>>
>>   
>
> -- 
> Bob Richard
> Executive Vice President
> Californians for Electoral Reform
> P.O. Box 235
> Kentfield, CA 94914-0235
> 415-256-9393
> http://www.cfer.org
>   
> ------------------------------------------------------------------------
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>