Does a single vote count?

Over at Pure Pedantry, Jake posits the following:

I always get in arguments with mathematically-inclined people about whether to vote or not. The mathematically-inclined point out very reasonably that the chances of your vote being decisive are perishingly slim.

(These mathematics are explained clearly in this PBS video by economist Gordon Tullock explaining why he does not vote. Hat-tip: Marginal Revolution)

I've always felt that the mathematical argument is the wrong one to take. The election is not a lottery, where there is a single winner (or a set of winners). In that case, there is a definite chance of being "the one" who is chosen. An election, in contrast, is not at all like a lottery. The "deciding" vote could be any and all of the votes that push the election toward the winning candidate. No one person is a "winner" in an election. Rather, the winning party is the "winner". Since it was a group effort, then all the ballots cast toward the winner are "winning votes."

Of course, we like to say, "so-and-so cast the winning vote", like this is something in a movie. However, unless a person has knowledge that his/her vote would be the vote to decide the election, then that vote is as consequential as any other one cast. After all, if the first person who voted didn't cast a vote for candidate A, then the total number of votes cast for candidate A would be one less, regardless of what the last person does. If the last voter KNOWS what his or her vote will do, then that person is - imho - a "winner", but - then again - that vote would be rigged.

So maybe, then, the winning candidate is the one who casts the winning vote, since that person would be the only one who directly benefits from the outcome of the vote, while also (presumably) having voted for him/her-self. Therefore, in all possible iterations of voters-casting-a-winning-ballot, the only constant would be the candidate (except in the case of a 100% win). I've not done the calculations on this, but (to go back to my original point), I've always thought this was a bit of a nonsensical question (at least from the mathematical POV).

Finally, this whole thing seems to me analogous to making a mathematical argument about the non-existence of North Korea. I mean, mathematically speaking, its estimated population is only 0.36% of the total world population (23 million/6.5 billion), but you cannot say they don't exist. In fact, the North Koreans - even though they have such an insignificant impact on world population that they statistically won't exist in a random sample - have been a significant player in East Asian politics. The impact of something, therefore, cannot be based solely on numbers.