[EM] Condorcet Criterion for plurality.

[Martin Harper]

Markus Schulze wrote:

> Plurality can be defined (and usually is defined in the academic
> literature) on preferential ballots. You claim that as plurality
> depends on LESS than the complete preferences of the voters
> plurality cannot be defined on preferential ballots. But when
> you re-think your argument then you will observe that only when
> plurality depended on MORE than the complete preferences of the
> voters plurality couldn't be defined on preferential ballots.

Hmm - this feels wrong, but it's hard to put into words why... It just
seems to me that an integral part of a voting method is the type of
ballot - 'plurality-on-preferential' is different to plurality.
Similarly, changing the wording on the ballot significantly would also
indicate a slightly different voting method: there's a difference between
asking the voters to 'put in order until you don't care or don't know',
and asking them to 'put in order all those who you support'.

So 'plurality-on-preferential' fails condorcet - but how do you determine
if 'plurality' fails condorcet? Do you first prove that
'plurality-on-preferential' and 'plurality' are the 'same' method? And,
more importantly, how do you determine if Approval Voting passes the
criterion?