Dear Markus
In response to your posting of 25 April.
As far as I can see, your criteria are necessary, but not sufficient
to give your:
> The reason: It is very difficult and risky to manipulate
> with irrelevant candidates or with order-reversal, because
>
> a) there must be a suitable candidate, who can change the
> result of the elections without being elected,
>
> b) you have to know very exactly how the other voters will vote,
>
> c) it can happen, that a less prefered candidate wins the
> elections if you vote tactically without knowing exactly
> enough how the other voters vote.
It seems to me that Borda meets your criteria and yet encourages
exaggeration. Condorcet/Dodgson also meets your criteria and has
something like your (c). I suggest that we need another criterion.
Consider a voter to be 'tempted' if, knowing how all other voters
voted, they could get a better result than by voting according to
their preferences.
Conjecture: Markus' criteria imply voters are sometimes tempted.
Observation: the tempted voters are players in a game in which they
can either be honest or vote tactically. Their 'minimax' strategy has
the least risk, or 'down side'.
Extra criterion:
The tempted voters are faced with a game in which their minimax
strategy is to vote according to their true preferences.
Conjecture A: Condorcet/Dodgson meets this.
Conjecture B: Only Condorcet/Dodgson meets this. (Not so sure about
this one!)
I have a proof of A for slightly different criteria. I'm not sure
about B, but the alternatives I've looked at fail.
Cheers.
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Sorry folks, but apparently I have to do this. :-(
The views expressed above are entirely those of the writer
and do not represent the views, policy or understanding of
any other person or official body.
