[EM] Majority winner set

[LAYTON Craig]

Markus wrote (in part):

>Second:
>
>Your definition of "sincerity" is implausible. You wrote
>(24 Nov 2000):
>> A voter votes sincrely if he doesn't vote a preference
>> that isn't a sincere preference or leave unvoted a sincere
>> preference that the balloting system would have allowed him
>> to vote in addition to the preferences that he actually did
>> vote.
>
>Example:
>
>  Suppose that Approval Voting is used. Suppose that the
>  sincere opinion of a given voter is A > B > C > D > E and
>  that this voter decides to approve A, B, C and D.
>
>  The day before election day, this voter hears that candidate
>  E has no chances to win and that only candidate B and
>  candidate C have realistic chances to win. Therefore, this
>  given voter decides to approve only candidate A and
>  candidate B.
>
>  Due to your definition of "sincerity," this given voter votes
>  "sincerely." But (1) in so far as this voter changes his
>  voting behaviour after he has got additional information
>  about the voting behaviour of the other voters and (2) in so
>  far as this given voter changes his voting behaviour because
>  of strategical considerations, it is clear that this given
>  voter votes strategically. Therefore your definition of
>  "sincerity" isn't suitable to differ between sincere voters
>  and strategical voters.

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.