[EM] Proposal: Majority Enhanced Approval (MEA)

[C.Benham]

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