[EM] Try this method on your favorite election scenario

[Kevin Venzke]

Hi Forest,


>________________________________
> De : Forest Simmons <fsimmons at pcc.edu>
>À : EM <election-methods at lists.electorama.com> 
>Envoyé le : Dimanche 6 octobre 2013 17h21
>Objet : [EM] Try this method on your favorite election scenario
>
>Ballots are ranked or rated.  If ranked, then equal ranking and truncation are allowed.
> 
>Let IA stand for Implicit Approval, which for any candidate X is the number of ballots on which X is ranked or rated above bottom, i.e. neither truncated nor rated at zero.
> 
>Let MPO stand for maximum pairwise opposition, which (for candidate X) is the maximum (as Y varies over the other candidates) of the number of ballots on which a strict preference of Y over X is indicated.
> 
>The winner of this method (IA/MPO) is the candidate with the highest ratio of IA to MPO.
> 
>Example
> 
>45 A>B
>35 B>C
>20 C
> 
>For A  IA is 45 and MPO is 55, so IA/MPO is 45/55 or 9/11.
>For B IA is 80 and MPO is 45, so IA/MPO is 80/45 or 16/9.
>For C IA is 55 and MPO is 80, so IA/MPO is 55/80 or 11/16.
> 
>The IA/MPO winner is B.
> 
>If, instead, the A faction votes 45 A, then the ratios become ...
> 
>For A  (the same) 9/11.
>For B  IA is 35 and MPO is still 45, so the ratio is 7/9.
>For C IA is still 55 and MPO is 45, so the ratio is 11/9.
> 
>This time C wins.

IA/MPO seems like a pretty good method. It seems to be guaranteed that at least one candidate will have a score >= 100%. That's elegant. With that assumption it seems easy to demonstrate that the method satisfies Plurality and SDSC/Minimal Defense.

My guess is that it must satisfy FBC since the component scores each do, and the only "processing" is taking the ratio.

I suspect that we have lost SFC compared to MMPO ("Strategy-Free": roughly, if A has a majority over B and there is no majority over A, B can't win), but it might be hard to contrive a failure scenario.

If it's right that IA/MPO satisfies FBC, MD, and Plurality, it's not in a crowded space... Though MAMPO satisfies those as well as SFC, it's probably less sensitive to the rankings. (MDDA has SFC but can fail Plurality.)

I should get my simulations running again. I seem to recall being disappointed with the performance of MDDA and MAMPO.


Kevin Venzke