Earlier quoted context omitted.
From a mathematical perspective it's pretty silly to claim your vote doesn't matter just because it's not the tie breaking vote. You should give this a read: https://www.skishore.me/voting.html . Frankly this viewpoint has always puzzled me. Your specific claim that a vote almost certainly doesn't matter because elections don't come down to a single vote seems...unsupported, to put it politely. It might be more intui…
Bit logically where was he wrong? It seems like a bit of a paradox to me. You keep say it’s wrong but can you point out exactly where his reasoning is wrong? My vote yesterday simply didn’t change any of the outcomes. That is a fact. None of the races were won by a single vote.
Now, to extrapolate this to all of the winning voters, simply "sample" reorderings, or average it, and you have a spread responsibility amongst all those people who voted for the winning candidate/party.
In other words, votes cast for the winning side did decide the result, because of their collective behaviour. The effect of a single vote can be defined in statistical terms as being interdependent with the rest of the votes in the same direction. This means any winning vote cannot be said to lack all effect, meaning or power. If the vote is not without effect, then it must have some effect, albeit not absolute.
Another way to look at this is that if the voting is won by a difference of exactly one vote, whose vote was it anyway? You would spread the responsibility of turning the election equally amongst all voters for that side.
If we wanted to somehow quantify the "contribution" to winning that each vote has, we have to take into account how many votes were actually required to win. Let X be the number of votes in the winning side and Y in the losing side. Of all the X votes in the winning side, only Y+1 were actually necessary to win. So the contribution of each voter could be (Y + 1)/X, which is always So if the voting is won by exactly one vote, all votes in the winning side are decisive: without any one of them, the voting would not be won.
If, however, everyone voted for the same side, it would be 1/X, where you could remove all but one vote and still be short of removing a whole "decisive vote".