[EM] IA/MPO
Forest Simmons
fsimmons at pcc.edu
Wed Oct 9 17:51:46 PDT 2013
Kevin,
thanks for working on the property compliances.
I agree that this method does satisfy the FBC, is monotone, and is at least
marginally clone independent, like Score and ratings based Bucklin and MMPO.
I am not as expert as you in the various defense criteria.
My main focus so far is that the method seems to remedy some of the
problems of Approval and some of the problems of MMPO.
Approval has a problem with this (true preferences) scenario:
30 A
3 A>C
15 C>A
4 C
15 C>B
3 B>C
30 C
Of course, (under Approval voting) the two 15 member factions should, and
would bullet C, if they were sure of the numbers, but it is more likely
that due to disinformation from the A and B parties (and other sources of
uncertainty) they would not truncate their second preferences, so A and B
would be tied for most approval.
However, IA/MPO robustly elects C.
Our friend MMPO has a problem with
19 A>B>C
18 B>C>A
18 C>A>B
15 D>A>B
15 D>B>C
15 D>C>A
electing the Condorcet Loser D, (unless some preferences are strategically
collapsed). But IA/MPO elects the "right winner" A, with no need to
collapse preferences among members of the ABC clone set..
Can you think of any other examples where one or the other of IA or MMPO is
by itself inadequate? Does IA/MPO always improve the outcome in such cases?
My Best,
Forest
On Tue, Oct 8, 2013 at 9:06 PM, Kevin Venzke <stepjak at yahoo.fr> wrote:
> 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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