[EM] This might be the method we've been looking for:

[C.Benham]

Forest,

I don't understand the algorithm's definition. It seems to be saying 
that it's MinMax(Margins), only computing X's gross pairwise score 
against Y by giving X 2 points for every ballot on which X is both 
top-rated and voted strictly above Y, and otherwise giving X 1 point for 
every ballot on which X is top-rated *or* voted strictly above Y.

But from trying that on the first example it's obvious that isn't it. 
Can someone please explain it to me?

Chris Benham


Forest Simmons wrote (2 Dec 2011):

Here’s a method that seems to have the important properties that we have 
been worrying about lately:

(1) For each ballot beta, construct two matrices M1 and M2:
In row X and column Y of matrix M1, enter a one if ballot beta rates X 
above Y or if beta gives a top
rating to X. Otherwise enter a zero.
IN row X and column y of matrix M2, enter a 1 if y is rated strictly 
above x on beta. Otherwise enter a
zero.

(2) Sum the matrices M1 and M2 over all ballots beta.

(3) Let M be the difference of these respective sums
.
(4) Elect the candidate who has the (algebraically) greatest minimum row 
value in matrix M.

Consider the scenario
49 C
27 A>B
24 B>A
Since there are no equal top ratings, the method elects the same 
candidate A as minmax margins
would.

In the case
49 C
27 A>B
24 B
There are no equal top ratings, so the method gives the same result as 
minmax margins, namely C wins
(by the tie breaking rule based on second lowest row value between B and C).

Now for
49 C
27 A=B
24 B
In this case B wins, so the A supporters have a way of stopping C from 
being elected when they know
that the B voters really are indifferent between A and C.

The equal top rule for matrix M1 essentially transforms minmax into a 
method satisfying the FBC.

Thoughts?


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