[EM] Details of the Enhanced MinMax(AWP) procedure:

[fsimmons at pcc.edu]

Details of the Enhanced MinMax(AWP) procedure:

First form the matrix M whose entry M(x,y) in row x and column y is one if
alternative x pairwise beats y, is zero if  y beats x, and is 1/2 if x and y are
tied and the tie cannot be broken by approval scores.  In particular each
diagonal entry of M is 1/2, because each x is in a tie with itself that cannot
be broken by approval scores.

[Note that M is essentially the Copeland matrix with 1/2's down the diagonal and
other ties broken by truncation numbers.]

Next form the matrix A whose (i,j) entry is zero if M(j,i) is zero, but
otherwise is the number of ballots on which alternative j is ranked while
alternative i is not ranked.

For each alternative C let m(C) be the maximum element in row C of matrix A, i.e.

      m(C)=max{A(C,j)| j is an alternative}.

Let L be a list of the alternatives x1, x2, ... in increasing order of m(x).

Definition:  one alternative x1 covers another alternative x2 iff no component
of row x2 in M is numerically greater than the corresponding component of row
x1, and at least one component of row x1 is greater than the corresponding
component of row x2.

[Note that the Copeland winner is always an uncovered candidate.]

If the first member c1 of L is uncovered, then elect c1, else ...

If the first member  c2 of L that covers c1 is uncovered, then elect c2.  Else ...

If the first member  c3 of L that covers c2 is uncovered, then elect c3.  Else ...

Etc.