[EM] New Condorcet Lottery

[Forest Simmons]

I would like to propose this Rivest-like two-player, zero-sum game related
to the de-cloned versions of Kemeny-Young, Borda, and Copeland that I
recently posted.

For each candidate k, let F(k) be the random ballot Favorite probability of
candidate k, and let R(k) be the random ballot favorite of candidate k on
the Reversed ballots.

Let P be the payoff matrix for the row player defined as follows:

P(i, j) is F(j) if candidate i pairwise defeats j.
P(i, j) is -R(i) if candidate i is pairwise defeated by j.
P(i,  j) is F(j)-R(i) if candidates i and j are pairwise tied, including
the case of i=j.

Remember the game is zero sum, so the column player's payoff is the
opposite of the row player's payoff.

In general optimal strategies for the players are stochastic mixtures of
the respective pure deterministic strategies, i.e. they are Lotteries.

Let L and L* be the respective optimal lotteries for the respective row and
column players.

L(k) and L*(k) are the probabilities with which the respective players
should bet on row or column k.

For the un-reversed ballots, the method winner is chosen by L.

For the reversed ballots the winner is chosen by L*.

That's the method ... more commentary next time....

Forest
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20220117/67ce3835/attachment.html>