[EM] To Condorcetists:

[Juho Laatu]

[I rewrote the message whose draft version I sent out earlier by mistake.]

Now I have a reasonable definition of Mike Ossipoff's strategy that is supposed to be valid for all Condorcet methods (and even for all FBC failing methods). The strategy is "if there are winnable unacceptable candidates and winnable acceptable candidates, find that winnable acceptable candidate that is most likely to win all the unacceptable candidates, and rank him alone at top". Here use of terms acceptable and unacceptable means that the voter has some higher than marginal interest to make one of the acceptable candidates win instead of the unacceptable ones.

Let's study it in the US framework. I'll use the Republican candidate, the Democrat candidate and Nader to describe what could happen.

The key idea of the strategy is that the voter can bury his non-winning favourites (Nader) without concern since they will not win anyway. The strategy says that the voter may bury also winnable favourites if another acceptable candidate is more likely to win all the unacceptable ones (not covered in this example). The reason why this burial might benefit the voter is that there might be an intentional strategic loop caused by other strategists (Republicans), and that strategic loop could make R win instead of D. Alternatively there might sometimes be also a loop caused by sincere votes.

I'll address some reasons why the strategy might not be on optimal strategy for real life elections to be applied always in all Condorcet elections.

[The rewritten part follows.]

In this example we can assume that the candidates are roughly positioned on a one-dimensional left-right axis where the order of the candidats is N, D, R.

1. What will Nader supporters lose if they bury their favourite:
There are benefits to voting for your favourites also when those candidates can not win. The Nader voters see obviously already today some reasons to vote for Nader in Plurality elections although Nader has no chances to win. The voters maybe want to lift the political weight of Nader and his opinions, or make him or his followers win in some future election, or they may just want to carry a message that they do not like either one of the current major parties. They do so although their vote is likely to help the Republican candidates (the worst winnable candidate). If the election method would not punish them as much as Plurality does (e.g. Condorcet), Nader voters would probably be even more interested to show support to their favourite. It thus doesn't sound like the Nader voters would be happy to bury their favourite if the election method was changed from Plurality to Condorcet. In real life elections optimality of a stratgey is thus not measured only in terms of who is the winner of this election but in some much wider sense.

2. What will Nader supporters win if they bury their favourite:
If the Republicans decide to strategically bury the Democrat under Nader, when Republicans have 48% support, Democrats 42% and Nader 10%, more than 42/48 of the Republican voters should follow the planned strategy and vote R > N > D. This is not probable. So the Nader voters have no reason to worry that ranking Nader first would help R to win D. Nader supporters could cancel the Republican strategy (and thereby make their compromise candidate D win instead of R) by burying their favourite, but in practice the Republican strategy is not likely to happen nor be successful if it would be attempted. With high probability there will be no benefits.

The proposed strategy seems to be based on the theoretical vulnerability of Condorcet methods to the burial strategy. One should however clearly separate theoretical vulnerabilities from what is likely to happen in practical elections. Also in this example it seems that in practice the benefits of the strategy reman at theoretical level while the benefits of sincere voting and ranking Nader first would be lost right away if voters would follow the strategy. It is not likely that Nader supporters would consider it beneficial to "betray" their favourite.

Are these arguments sufficient to "prove" that the proposed strategy would not be optimal for the Nader supporters of this example. (Also the "Condorcetists" are welcome to pont out possible holes in the arguments.)

Juho