[EM] Yes: FBC must speak of a set of same-preference, same-voting voters

[Markus Schulze]

Dear Mike,

you wrote (5 March 2005):
> Markus is right to point out that, as I've defined it, FBC has a
> problem when there's a tie. As Markus pointed out, a single voter
> can change the outcome only by changing a definite win to a tie,
> or changing a tie to a definite win.
>
> FBC, as defined so far,  has a problem with a tie. If the way that
> you could get your best outcome is by breaking a tie, and getting
> a certain outcome, then, if you don't do so, that same candidate
> might win the tie anyway, and so what you get when you break the
> tie isn't better than anything that you could get wihtout doing so.
> On the other hand, if, by voting someone over your favorite, you
> could make a tie, then you aren't electing with certainty someone
> who is better than anyone you could otherwise have gotten, since
> you aren't electing anyone with certainty.
>
> The obvious and easy way out of this is to replace "voter" with
> "set of voters who have the same peferences and vote in the same
> way".
>
> That fixes the problem. Thanks for pointing the problem out,
> Markus.

FBC says:

> By voting a less-liked candidate over his/her favorite,
> a voter should never gain an outcome that he/she likes
> better than every outcome that he/she could get without
> voting a less-liked candidate over his/her favorite.

Suppose there is more than one favorite candidate. Suppose A and B
are some of these favorite candidates. When this voter has to vote
B over A, then is this a violation of FBC? Accoding to the above
definition of FBC, this is not a violation of FBC since B is not
a "less-liked candidate". But is this also in spirit of FBC?

Markus Schulze