[EM] 2 understatements

[MIKE OSSIPOFF]

It's occurred to me that, in the example that I've used to show'
that Condorcet(margins) is doubly falsifying, not only does
that method only have equilibria with order-reversal, but it's also
true that all of its equilibria involve favorite-burial, the most
extreme and regrettable form of order-reversal.

That's true of the other doubly falsifiable methods too.

So, next time I write those definitions, favorite-burial will become
part of the definition, because the idea of defining the classifications
is to have a way of saying what voting systems are capable of.

At the opposite extreme, it's an understatement to say that
Condorcet(wv), in every situation, has an equilibrium in which everyone
sincerely ranks all of the candidates, and the sincere CW wins.

That's because it isn't just that there's an equilibrium like that--
it's that there's just plain no strategy, if order-reversal is
ruled out, under the conditions in the definitions' premise. No one
has any strategic reason to do other than sincerely rank all the
candidates. No one need concern himself with any strategy, such as
defensive truncation, etc.

And it isn't unreasonable to rule out order-reversal in wv.

(By the way, the other day I corrected my wording by saying that,
in the definition of conditional complete expressiveness, I should
say "preference falsification" instead of "order-reversal". But,
since, by assumption, there's no indifference about the CW, then any
preference falsification involving him will necessarily be an order-revesal. 
And so I prefer to leave the wording "order-reversal").

Since, with wv, offensive order-reversal only works against people who
are trying to help you, and since in public elections it would be
impossible to organize an order-revesal without getting found-out,
it's very plausible to rule out order-reversal in wv.

But because the 1st statement in the previous paragraph isn't true
of margins, and because in a wide range of faction-size configurations
attempted offensive order-reversal carries no penalty, I certainly
won't guarantee that there won't be rampant order-reversal in margins.

In fact, in my 100,49,75 example, and in a wide range of faction-size
congigurations, the A voters should employ offensive order-reversal.
They have nothing to lose by it, and much to gain.

There's every reason to expect that, in margins elections, margins
will often or usually reside at its order-reversal equilibria.

Mike Ossipoff


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