[EM] Condorcet Criterion for plurality.

[LAYTON Craig]

Mike wrote:

>You want  applicability to all methods? The following
>definition of Condorcet's Criterion applies to all methods.
>No it doesn't assume that they all use the same balloting system.
>That's because they don't use the same balloting system. Hey,
>while you're at it, why not assume that they also use the same
>count rule? :-)
>
>Condorcet's  Criterion:
>
>If there's a sincere CW, and everyone votes sincerely, then that
>sincere CW should win.
>
>A voter votes sincerely if he doesn't vote a false preference or
>leave unvoted a sincere preference that the balloting system in
>use would have allowed him to vote in addition to the preferences
>that he actually voted.

Okay, I'm working on my own definitions, but this doesn't seem right.  Say I
have a Condorcet system in which you can't indicate ties (must use
sequential preferences: 1,2,3 etc), but you may truncate votes.  What is a
sincere vote?  There are situations in which you must either vote a false
preference OR leave unvoted a sincere preference that the balloting allows
you to vote.  Similarly, what of a plurality vote in which you like two
candiates the same (your two favourites).  If you vote for one of them, is
that an insincere vote?  If you don't vote at all, then you're leaving a
preference unvoted that the system allows you to express (one of the
favoured candidates over some other candidates).  There is a contradiction
in the sincerity definiton.

>Of course voting a false preference means voting X over Y when
>the voter doesn't really prefer X to Y.
>
>By "preference", I mean pairwise preference.
>
>[end of definition]