We show that approval voting strategic equilibria are closely related to
Condorcet Winners. There exists an approval equilibrium with a clear
font-runner F and runner-up R if and only if the F is the clear Condorcet
Winner and R the Condorcet runner-up. In contrast, we show that Condorcet
methods can elect a Condorcet Loser with non-zero probability when voters
tactically. With strategic agents, approval voting is better at electing
Condorcet Winners than Condorcet methods!
As I've been saying here, in a series of elections in which voters base
their strategy on previous results, Approval quickly homes in on the voter
median candidate, the CW, and stays there.
I certainly don't disagree about the great merit of Approval.
But ws is being unfair to Condorcet. Yes, when Condorcet measures
defeat-strength by any measure other than winning-votes, then Condorcet
becomes a strategic mess. In fact, nearly all rank methods are a strategic
mess. That includes Instant Runoff.
But winning-votes Condorcet and a few other good rank methods dont have a
problem with tactical voting.
With those methods, the only strategy problem occurs when offensive
order-reversal strategy is attempted. Weve discussed this at great length
on this mailing list. Offensive order-reversal can be thwarted and penalized
by mere truncation. Truncation is an easy and natural way of voting, in
comparison to order-reversal. The defense is easier and more likely than the
offensive strategy. Some will refuse to rank candidates that they
sufficiently dislike. Some, in a devious voting environment, will try to
avoid ranking anyone worse than the CW, or wont rank candidates of voters
likely to order-reverse.
For deterrence against offensive order-reversal, it isnt even necessary
that the defenders know exactly where to truncate. The fact that voters
might be making the effort will deter the order-reversal. And, without
order-reversal, voters will have the benefit of those methods SFC
compliance. You need only vote sincerely to ensure that no one worse than
the CW will win, if a majority are voting with you. For that, you neednt
even know who the CW is.
The wv Condorcet method that I recommend for public elections is Schwartz
Sequential Dropping (SSD). But MDDA and MAMPO share wvs most important
In conclusion, Approval is as good as wv says it is, but Condorcet, in its
best versions, along with a few similar methods, is a lot better than wv
Though Approval will arrive at the voter median after a few elections, the
best rank methods will typically get there in their first election. Also,
with Approval, even when your favorite has outpolled your greater evil, it
may take a little courage to stop voting for your lesser-evil. Theres some
question about whether progressives will be able to. Never underestimate the
bad judgment of a voter. For the reasons mentioned in this paragraph, Id
rather give to the voters SSD, MDDA or MAMPO than Approval. They make less
demand on voters judgment.