The probability that your vote matters can easily be modeled with a binomial distribution. In any of the large-scale elections you seem to be referencing, that probability will be vanishingly small.
But the expectation value may be much larger; http://works.bepress.com/cgi/viewcontent.cgi?article=1046&context=aaron_edlin has the argument (crucially dependent on the fact that your probability of breaking an exact tie is of order 1/n). I don’t buy their argument that people actually think that way, but the expectation calculations seem sound.
The probability that your vote matters can easily be modeled with a binomial distribution. In any of the large-scale elections you seem to be referencing, that probability will be vanishingly small.
But the expectation value may be much larger; http://works.bepress.com/cgi/viewcontent.cgi?article=1046&context=aaron_edlin has the argument (crucially dependent on the fact that your probability of breaking an exact tie is of order 1/n). I don’t buy their argument that people actually think that way, but the expectation calculations seem sound.