[EM] Proposal: Majority Enhanced Approval (MEA)
C.Benham
cbenhamau at yahoo.com.au
Sun May 16 11:07:32 PDT 2010
Forest Simmons wrote (12 May 2010):
>Here's another proposal. Let M be the matrix whose (i,j) element is the number of ballots on which
>candidate i is ranked ahead of candidate j. I think that this is what you mean by the "normal gross
>pairwise matrix" that you mention below.
>
>For each candidate i, let d(i) be the difference of the maximum number in column i and the minimum
>number in row i. In other words d(i) is the difference is the maximum number of points scored against
>candidate i in a pairwise contest and the minimum number of points that candidate i scored in a pairwise
>contest.
>
>Generally speaking, the smaller d(i), the stronger candidate i.
>
>So list the candidates in increasing order of d(i) instead of the order of decreasing approval, and apply
>the enhancement as before:
>
>Let D1 be the candidate i with the smallest difference d(i). Elect D1 if uncovered, else let D2 be the
>smallest d(i) candidate among those that cover D1, etc.
>
>This method wastes the diagonal slots of matrix M just like all of the other standard Condorcet
>methods. But I would be interested if you would run it by your standard test cases.
>
>
>
Forest,
Your suggested method fails both the Minimal Defense and Plurality criteria.
49: A
24: B
27: C>B
"Forest scores"
A: 51-49 = 2, C: 49-27 = 22, B: 49-24 = 25.
A has the lowest score and is uncovered and so wins, violating Minimal
Defense (which says that A can't win because on more than
half the ballots A is ranked below B and not above equal bottom).
7: A>B
5: B
8: C
"Forest scores"
A: 8-7 = 1, B: 8-5 = 3, C: 12-8 = 4.
A has the lowest score and is uncovered and so wins, violating the
Plurality criterion (which says that A can't win because C has more
top-preference votes than A has above-bottom votes).
Chris Benham
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