[EM] MAMPO is probably better than MDDA

[Chris Benham]

Kevin Venzke wrote (Feb 22,2007):

>Hi.
>
>This is the definition of MAMPO:
>
>1. A candidate's opposition score is equal to the greatest number of
>votes against him in any pairwise contest.
>2. The voter ranks; those ranked are also "approved."
>3. If more than one candidate is approved by a majority, elect the one
>of these with the lowest opposition score.
>4. Otherwise elect the most approved candidate.
>
>MAMPO satisfies FBC, SDSC, and SFC like MDDA does. But MAMPO also satisfies
>Woodall's Plurality criterion.
>

Kevin,
I'm interested in your opinion of my stab at something similar that 
meets Irrelevant Ballots:

"1 and 2 as for MAMPO.
3. Give each candidate a score that is equal to its approval score minus 
its opposition score.
4. Elect the candidate with the highest score".

With sensible approval strategy, this seems to 'perform well' (in terms 
of strategic criteria) with 3 or 4
candidates. The approval component seems to easily rescue MMPO from its 
greatest embarrassments.

One hope is that the truncation incentive of Approval and the 
random-fill incentive of  MMPO will mostly
cancel each other out.

There may be some smarter way to combine approval and pairwise 
opposition scores, perhaps weighting
them unequally. And if anyone likes it I'm open to a suggestion for a name.

Chris Benham



>Hi.
>
>This is the definition of MAMPO:
>
>1. A candidate's opposition score is equal to the greatest number of
>votes against him in any pairwise contest.
>2. The voter ranks; those ranked are also "approved."
>3. If more than one candidate is approved by a majority, elect the one
>of these with the lowest opposition score.
>4. Otherwise elect the most approved candidate.
>
>MAMPO satisfies FBC, SDSC, and SFC like MDDA does. But MAMPO also satisfies
>Woodall's Plurality criterion.
>
>Woodall's scenario showing that MDDA fails the latter:
>
>20 ab
> 5 ba
>24 bc
>24 ca
> 9 dab
> 9 dbc
> 9 dca
>
>"a,b,c are preferred to d by 49,49,48 voters respectively, which are not
>majorities, but a>b by 62, b>c by 67 and c>a by 66, so that a, b and c
>are all disqualified.  Thus MDDA elects d.  But d has 27 votes in total,
>and so is debarred by b who has 29 first-preference votes."
>
>MAMPO manages to elect B since D lacks majority approval, and 62 is
>the lowest maximum such score.
>
>For what it's worth. I think MAMPO does a fairly reasonable thing in only
>deviating from approval when multiple candidates have a majority, and
>then only in favor of one of the candidates that has a majority!
>
>Kevin Venzke
>
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