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

[Forest Simmons]

> From: Russ Paielli <6049awj02 at sneakemail.com>
> Subject: [EM] How Approval locks onto the CW in two or three moves
>
> 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).
>

The more equal the different parties are in their strengths, the more 
likely voters will use zero info strategy.  And (in my opinion) that's 
when Approval outshines other methods the most, because the winner under 
zero info strategy is the candidate that is considered above average by 
the most voters.

What other method can reliably find this candidate?

No Condorcet method can:

51 A>B>>C
29 B>>A>C
20 C>B>>A

Here B is approved by 100 percent of the voters, and A disapproved by 49 
percent, but A wins under Condorcet, IRV, Borda, etc.

Approval itself cannot even find this candidate B, given too much 
information:

The Condorcet Winner A would win under Approval, too, given 
even fairly crude (but honest) polling data.

The zero-info result is better than the non-zero info result.

The zero-info case is not the problem.  The dis-information case is the 
problem.  But as I showed before, this problem clears up quickly when 
there is a CW.

When there is no CW, there may still be a stable Approval equilibrium. 
If not, the winners cycle within the Smith set, yielding a kind of 
temporal fairness for their supporters.

Forest