[EM] Condorcet-Monroe concept

[Kristofer Munsterhjelm]

Here's an idea for making a Condorcet version of Monroe:

Let the "voting game" for two possible winner sets (a selection of s
candidates out of the c possible) be like this:

Call the winner sets W1 and W2.

First I choose an assignment of voters to candidates in W1, respecting
the thresholds given by Monroe (that each candidate must have an equal
number of voters assigned).

Then you choose another assignment of voters to candidates in W2, also
respecting these thresholds.

Then my score, d[W1,W2] is the number of voters who prefer the candidate
assigned to them in the first assignment; and your score, d[W2,W1] is
the number of voters who prefer the candidate assigned to them in the
second assignment.

My objective is to maximize d[W1,W2] and yours is to maximize d[W2,W1].
Since this is a zero sum game, there's a minimax equilibrium. This
minimax equilibrium provides the values for d[W1,W2] and d[W2,W1] in the
Condorcet matrix.

Now use your Condorcet method of choice to elect the winning set based
on that matrix.

In the single-winner case, this simply is the Condorcet method because
the only way to assign all the voters to one candidate is to, well,
assign them to that candidate, and then d[{a},{b}] is the number of
voters who ranked a ahead of b.

I don't know if the equilibrium is computable in polytime, though.

I would imagine that the method would be better behaved than STV,
although it might also be more factionalized since it uses a larger
quota. I don't know how to introduce a tunable quota (like Droop vs
Hare) in it.

-km