> In a presidential election, the probability that your vote is decisive is equal to the probability that your state is necessary for an electoral college win,

> In a presidential election, the probability that your vote is decisive is equal to the probability that your state is necessary for an electoral college win, times the probability the vote in your state is tied, conditional on your state being necessary. While perhaps correct on paper it isn't if you do not assume all else equals. If my probability of making a difference is 1 in sixty million, and I reason that voting isn't worth my time, and everyone else does the same, then it all breaks apart. Truth is, every vote makes a difference with a probability of 1, when considering the fact that a ballot's outcome can turn upside down due to voters not showing up, votes for odd candidates in protest or (when they're ignored) blank votes. See what happened in France when Chirac got re-elected facing extreme right wing contender Le Pen.