[EM] Proposal: Majority Enhanced Approval (MEA)

[fsimmons at pcc.edu]

----- Original Message -----
From: "C.Benham"
> 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


Chris,

Both of these problems go away if we count tied ranks as 1/2 point (the same way
that ties are counted in Copeland) and consider a candidate tied with itself so
that the diagonal entry for alternative X in the pairwise matrix has half the
number of ballots ono which X was ranked.

In your first example the points become

A: 51-24.5=26.5   B: 49-24=25  C:49-13.5=35.5

so B wins.

In the second example we get

A: 8-3.5=4.5
B: 8-5=3
C: 12-4=8

So B wins again.

The reason for including the self ties is that if we included a twin for each of
the candidates, the old winner and its twin should be tied as the new winners.

Forest.