[EM] Dominated deterrent strategies work

[MIKE OSSIPOFF]

I accidentally said "order-reversal", when I meant "falsification
of a preference", in the definition of conditional complete
expressiveness.

Blake once objected to wv's defensive truncation strategy, to deter
offensive order-reversal, on the grounds that, whether or not
the opponet order-reverses, the defensive truncation can only worsen
the outcome for the truncators.

So defensive truncation is a dominated strategy, one that can only
worsen the outcome, if it affects it at all, if it's used instead
of some other particular strategy.

But defensive truncation is part of a desirable equilibrium, an
equilibrium that the defensive truncator likes.

There's ample precedent for using a dominated strategy when it's
part of a desired equilibrium.

For instance, say there's a crime for which statistics indicate that
it's very unlikely that its perpetrator will again commit a crime.

If we incarcerate the perpetrator, we add the cost of incarceration
to the cost of the crime itself.

So if we have a policy of incarcerating people who commit that crime,
having that policy is a dominated strategy. It's dominated by the
strategy of not having that policy. Whether the person commits the
crime or not, our cost can be greater if we have that policy, but
can't be less.

But that dominated strategy is part of an equilibrium that society
likes: No crime, no incarceration. The person worsens his outcome
if he commits a crime and is incarcerated. Society doesn't improve
its outcome if it drops the policy when the person doesn't change
his strategy of not committing the crime.

With many people, for many crimes, that equilibrium usually obtains, even
if they'd considered the crime.

So, as I said, there's ample precedent for using a dominated strategy
that's part of a desired equilibrium. wv's deterrence of offensive
order-reversal is similar to the justice system example that I
described above. It works there, and it will work for wv too.

You might say, "Yes, but there's still crime." Sure, but not as
much, because, as I said, that equilibrium apparently obtains for
most people. And, as I said, offensive order-reversal would be
impossible to plan & organize without getting caught. And Margins
doesn't deter offensive order-reversal; it merely prevents it from
working, if enough people rank a compromise over their favorite.
If people don't have compunction about order-reversing, as Rob LG
contends, then they have nothing to lose by trying it, in many
situations, in Margins.

Specialists on game theory have said that if a strategy configuration
is an equilibrium, it will be found by the players.

But if there's no equilibrium in which order-reversal doesn't occur,
that isn't at all promising for such a method. If, as Rob LG
contends, people will use any strategy that would improve their outcome,
then that any non-equilibrium non-reversing strategy configuration
won't last.

Maybe one more method description is needed: methods that--even if voting of 
a false preference is ruled out as a strategy--have situations
that have no equilibria in which no one
votes a less-liked candidate equal to another candidate that he
votes for and the CW wins. Maybe methods like that, and conditionally
completely expressive ones, should be defined together in a separate
section starting with: "If falsification of a preference is ruled
out as a strategy:".

Condorcet(margins) is such a method. That's a long way from wv's
complete expressiveness under those same conditions.

Whether or not people will
offensively order-reverse, margins has nothing to
offer in the way of sincere equilibria.

Mike Ossipoff


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