[EM] IA/MPO
Kevin Venzke
stepjak at yahoo.fr
Tue Oct 8 21:06:22 PDT 2013
Hi Forest,
>________________________________
> De : Forest Simmons <fsimmons at pcc.edu>
>À : EM <election-methods at lists.electorama.com>
>Envoyé le : Mardi 8 octobre 2013 16h59
>Objet : [EM] IA/MPO
>
>Kevin,
>
>I'm afraid that IA/MPO does fail Plurality:
>
>33 A
>17:A=C
>17:B=C
>33 B
>
>The IA/MPO ratio for both A and B is 50/50 = 1, while the ratio for C is 34/33, which is greater than 1.
>
>But this is about the worst violation posssible, and it doesn't seem too bad to me.
>
>If equal top ranking were not allowed, then Plurality would not be violated. Or (in other words) the method satisfies a weaker version of Plurality that says if C is ranked on fewer ballots than X is ranked top but not equal to) C, then C cannot win.
>
>
>I don't know if that is helpful.
Actually, we are OK here because Plurality only counts strict first preferences. This aspect is useful when trying to make proofs about it. In this particular case, I say that if Plurality disqualifies some candidate X to due another candidate Y, I know that pairwise opposition to X exceeds X's approval, so X's score is below 100%. (And the same sentence is true if you swap in SDSC/MD for Plurality.) Since we know somebody will have >=100% as a score, X won't win.
I think the question for methods like this is how far away you can get from the ideal strategy resembling approval strategy. I feel optimistic because the role given to MPO is large. In MDDA and MAMPO majority threshold rules are hard-coded and key to seeing any ranking sensitivity. They satisfy SFC (basically a weak LNHarm) but I think IA/MPO is awfully close to satisfying that as well.
Basically:
Let a be the approval of candidate X
Let b be the approval of candidate Y and also Y's opposition to X
Let c be the maximum opposition to Y
Then IA/MPO violates SFC when a/b > b/c and a > b > 0.5 > c. Possible to do, but it would hardly ever happen, I think.
Kevin Venzke
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