[EM] Majority winner set

[Markus Schulze]

Dear Craig,
dear Bart,

Craig wrote (29 Nov 2000):
> I agree with this, however, is there a definition of sincere voting that
> will differentiate between sincere & strategic voting in Approval?  If you
> consider Approval voting a preferential voting system with two numbers - 1 &
> 2, it is basically a modified borda count.  Someone votes insincerely in any
> circumstances in which they like any of the 1's better than any of the other
> 1's, or any of the 2's better than any of the other 2's.  But, by the same
> token, in true rank ballot systems, if you give two candidates different
> numbers when you like them the same, then you're also voting insincerely.
> You would probably be voting insincerely if you truncated your vote as well.
> I'm not sure that there is a definition of sincere voting that fully
> differentiates between sincere & strategic voting.

To my opinion, "sincerity" must be defined in such a manner that at least
a given voter, who changes his voting behaviour because of strategical
considerations after he has got additional information about the voting
behaviour of the other voters, votes "insincerely."

******

Bart wrote (29 Nov 2000):
> How about this -- all voting is strategic, unless you are using a voting
> system in which you can guarantee that insincere voting is never
> useful.  It's just that sometimes strategy dictates that you vote
> sincerely, and other times it doesn't.  If you need to decide whether
> sincere or insincere voting is called for, you are using strategy (i.e.
> voting strategically).

Of course, it is possible that a given voter makes strategical considerations
and gets to the conclusion that voting _sincerely_ is the best _strategy_.
But nevertheless it makes sense to differ between sincere voters and
insincere voters. When a given voter makes strategical considerations and
gets to the conclusion that he cannot get any advantage by voting insincerely,
then this is a desirable situation. When a given voter makes strategical
considerations and gets to the conclusion that it is advantageous to vote
insincerely, then this is not a desirable situation.

In other words: It is not a problem that a given voter makes strategical
considerations after he has got additional information about the voting
behaviour of the other voters. But it is a problem when this given
voter changes his own voting behaviour because of these strategical
considerations.

******

I suggest the following definition of sincere voting in Approval Voting:

   A voter votes "sincerely" when he approves all those candidates
   he prefers to the incumbent and disapproves all those candidates
   to which he prefers the incumbent.

Markus Schulze