Exaggerated opinions

[David Marsay]

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. :-(
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