[EM] What do we mean by "your vote counts"?

[Jan Kok]

Mike Ossipoff wrote (many things, including):
>True, Approval doesn't let you vote all your preferences, but at least
it 
>reliably counts all those that you vote. That can't be said for IRV.

What do we mean by "counts"?

One meaning is used in arguments about why people should vote.  "Your
vote counts.  If the election was otherwise tied, your vote could be the
deciding vote."  So, one meaning seems to be, there is a nonzero
probability that the outcome of the election could be changed if you
cast a vote.

In fact, the probability that your vote will affect the outcome of an
election is pretty small, except in very small elections.  (Thus, I find
it amusing that a substantial fraction of the population bothers to
vote.  On an individual basis, there are probably better ways for each
person to spend his or her time than studying the candidates and voting.
But for societies as a whole, there is benefit IF a representative
sample of the population votes, and the voting method encourages voting
behavior that leads to choosing candidates with good utility for the
society.)

Is Mike using the word "counts" in a fundamentally different way?  Or is
he just indicating that _given some poll results or other predictions of
likely voting patterns_, in a typical election under a given election
method, the chance that your ballot will affect the outcome of the
election (in a way favorable to you - monotonicity!) is substantially
better with Approval than with IRV?

I'd like to see a mathematical definition of "counts" (as applied to
elections), if it is different from what I have guessed, above.

Cheers,
- Jan