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Or maybe it did, if you voted for the winning side. What if you ordered the winning votes and losing votes randomly, side by side, and eliminated pairs of oppos
by glastra 8y ago
Or maybe it did, if you voted for the winning side. What if you ordered the winning votes and losing votes randomly, side by side, and eliminated pairs of opposing votes. You would be left with a set of winning votes, cast by individual people. You could attribute the victory to exactly those people.
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 <= 1 as Y + 1 <= X, measured in "decisive votes per person", or something along those lines.
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".