Approval equilibrium. Pushover strategy.

[Mike Ositoff]

In reply to Mike Allen's letter:

The Smith Criterion says:

If every member of a particular set of alternatives beats
everything outside that set, then the winner should come from
that set.

The Smith set is the smallest set of alternatives that beat
everything outside that set.

Choosing from the Smith set meets the Smith Criterion.

Obviously the Smith Criterion is only for comparing various
rank-counting methods.

***

Quite right about the pushover strategy in IRO. I haven't 
talked about that offensive strategy, because I've been
emphasizing IRO's big problem of defeating Condorcet winners
& forcing abandonment of favorites even if no one uses
offensive strategy.

Pushover strategy can, of course also be used in Runoff. Again,
they don't call IRO "Instant Runoff" for nothing.

***

Also quite right about that Approval example not being a wrong
outcome.

And the things that critics of Approval point to are things
that don't happen at equilibrium. An equilibrium, as defined
by the 1st proponent of Approval, is an outcome that doesn't
contradict the voter beliefs that led to that outcome.

At equilibrium, Approval gives as good results as you could ask
for.

Someone named Myerson showed that, at equilibrium, Approval is
all that would be needed to drive dishonest politicians, or
politicians of questionble desirability, out of office.

Mike Ossipoff