[EM] Condorcet Criterion for plurality.

[LAYTON Craig]

Martin Harper wrote (in part):

>At the very least, it can change what a 'sincere' vote is - suppose you
have a
>particularly twisted plurality-like method, which is counted in exactly the
>same way - most crosses wins - but where the instructions on the ballot
read:
>"mark a cross next to the person you'd least like to be elected"
>
>If you vote sincerely, then you vote for the person you'd least like to be
>elected. Which is pretty much the worst possible thing to do from a
strategic
>point of view, of course.

I don't think you should define a sincere vote on the instructions on the
ballot paper.  You're talking about a case in which the electoral
authorities deliberately mislead people about how their votes will be
counted.  A sincere vote in a plurality count method is one in which you put
your first preference first.  I don't think it is a problem to define all
systems in terms of preferences for the purposes of determining a sincere
vote.  Approval can be defined as a two tiered preference system (1's and
2's).  Even a system like Cumulative could be translated into strict
preferential terms, say with four candidates and four votes;

A2
B2
C0
D0

translates into standardised preferences as

no first or second preference
A&B =3rd
no further preferences

The second is not necessarily a more incorrect way of thinking about the
system than the first.