[EM] Ordering defeats in Minimax

[Andrew Myers]

Hi all,

I recently added Minimax to the algorithms supported by CIVS, because it 
has some nice properties, especially regarding stability of the 
ordering. However, there's a bit of a challenge lurking. Minimax as 
classically defined assumes that all ballots are totally ordered. CIVS 
allows ties, however. So for any pair of alternatives there is a (W, L) 
pair where W is the number of people who prefer the first alternative 
and L is the number who prefer the second.

Recall that Minimax chooses the alternative whose strongest defeat is 
the weakest. What is the right way to define the ordering on defeats?

1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1)    
[currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)

I'm sure this has been discussed already at great length. Your advice is 
appreciated.

Best,

-- Andrew