[EM] Re: wiki

[Jobst Heitzig]

Dear Abd ulRahman!

You wrote:
> I'll disagree that "only randomized methods can do so," since there are
> other alternatives that are neither deterministic or randomized,
> beginning with the simple one of holding some kind of runoff.

Assume there is no sincere CW. Then each candidate is defeated by some
other. You suggest runoffs which count as deterministic in the sense
that the *whole* procedure will produce a single winner which depends
only on the ballots cast. I claimed there cannot be a group strategy
equilibrium in that case, that is, a way of voting such that after the
election there is no group of voters who can say 'If only we had voted
like so-and-so, we had the result so-and-so which we all prefer to the
result at hand'. It's quite easy to see that such an equilibrium does
not exist: Assume the whole election process elected X, and that X is
defeated by Y. Then the majority which prefers Y to X can say 'If only
we had voted Y>rest, we had the result Y which we all prefer to the
result at hand'. QED.

> Perhaps someone could take Mr. Heitzig's mail, with its concise
> definition, and use it to clean up the wiki page. I'd do it if I had time.

Please not "clean up" the page "imagine democratic fair choice" but add
a new page "democratic fair choice". That was the whole point of my
naming of the page. The idea is to have different descriptions for
different tastes.

Yours, Jobst