[EM] How Approval locks onto the CW in two or three moves

[Russ Paielli]

A couple of days ago, Forest Simmons posted an interesting message about 
how Approval can elect a third-party candidate within a few election 
cycles if that party is truly preferred by the electorate.

His argument seems reasonable enough to me, and it helped me to 
understand the different tendencies of Approval and IRV. Let me state 
what I think they are.

Like plurality, IRV tends to reach a stable equilibrium with two 
dominant parties. In that equilibrium state the effect of uncompetitive 
spoilers is eliminated, but minor parties are unlikely to win. If a 
minor party does somehow manage to defy the odds and become seriously 
competitive, IRV can end up electing a relatively unpopular candidate 
(just as plurality can with a strong third-party candidate).

Approval, on the other hand, will not necessarily reach a stable 
equilibrium with only two dominant parties. If I understand it 
correctly, it could allow any number of parties to reach a stable state 
of parity. That could be revolutionary, of course. Imagine the 
Libertarians and Greens actually competing on an equal footing with the 
Democrats and Republicans!

But I see a potential problem. If several parties reach parity, 
strategic voting becomes difficult, and the voter could end up with very 
difficult decisions. Do Greens approve the Democrat as a hedge against 
the Republican, or do they not? It's the same old problem, except now 
it's much more complicated. Now Greens may need to worry about letting 
the Libertarian get elected if they don't vote for the Democrat. As a 
matter of fact, they may need to think about approving the *Republican* 
to prevent the *Libertartian* from getting elected! Or vice versa.

The bottom line is that the election could be tipped in any of several 
different directions depending on where voters decide to "draw the line" 
between their approved and disapproved candidates. Maybe this is 
obvious, but I wonder how many have really thought about the potential 
consequences. I am not claiming that the disadvantages of Approval 
outweigh the advantages; I'm merely pointing out the potential problems.

The Approval strategy "formulas" that have been put forth are 
interesting, but in many cases they will be of no practical use to 
voters. Why? Because they are based on how other voters are expected to 
vote, which is obviously uncertain. The best strategic cutoff point 
could depend critically on that uncertain information, in which case the 
formulas will be useless as a practical guide for voters.

I understand that Approval is used by several professional societies, so 
it has been tested to some extent. As far as I know, however, it has 
never been tested in large-scale partisan public elections, so it is 
largely untested. Elections for professional societies tend to be very 
uncontroversial and participation is often poor, with only something 
10-20% of the members even bothering to vote in some cases (even though 
you can vote by mail).

--Russ