The error is a result of assuming the coin is exactly 50%, in fact polling uncertainties mean your probability distribution over its ‘weighting’ is smeared over at least several percentage points. E.g. if your credence from polls/538/prediction markets is smeared uniformly from 49% to 54%, then the chance of the election being decided by a single vote is one divided by 5% of the # of voters.
You can see your assumption is wrong because it predicts that tied elections should be many orders of magnitude more common than they are. There is a symmetric error where people assume that the coin has a weighting away from 50%, so the chances of your vote mattering approach zero. Once you have a reasonable empirical distribution over voting propensities fit to reproduce actual election margins both these errors go away.
The error is a result of assuming the coin is exactly 50%, in fact polling uncertainties mean your probability distribution over its ‘weighting’ is smeared over at least several percentage points. E.g. if your credence from polls/538/prediction markets is smeared uniformly from 49% to 54%, then the chance of the election being decided by a single vote is one divided by 5% of the # of voters.
You can see your assumption is wrong because it predicts that tied elections should be many orders of magnitude more common than they are. There is a symmetric error where people assume that the coin has a weighting away from 50%, so the chances of your vote mattering approach zero. Once you have a reasonable empirical distribution over voting propensities fit to reproduce actual election margins both these errors go away.
See Andrew Gelman’s papers on this.