The preceding model applies when there is a direct election. If there is an indirect election, such as an American presidential election via the Electoral College, the calculations are different. Consider the Electoral College for a two-candidate election when the unit rule holds: all of a State's electoral votes go to the candidate who wins a majority of the popular vote in the State. For simplicity consider a person's vote to be decisive if two conditions hold: a change in the assignment of the electoral votes of the person's State would swing the outcome (create or break a tie) in the Electoral College; and the person's vote breaks a tie within the State.
Let S=51 denote the number of States (including D.C.) and let 
denote
the number of Electoral College votes for State k, 
, with
. Let 
denote the number of electoral
votes for candidate one from States other than k. State k's electoral
votes could swing the Electoral College outcome if 
. Let 
denote the number of subsets s of States, not
including k, such that 
. The
unconditional probability that State k's electoral votes could swing the
Electoral College outcome is
That probability is tedious to evaluate. To avoid the tedious calculation here, I observe that it is of the same order of magnitude as the probability that a single voter breaks a tie in an electorate of size 50:
That crude approximation loses one implication of the exact formula, which is the intuitively obvious point that larger States have a bigger probability of swinging the Electoral College outcome than smaller States do.
Because the population of a State is anywhere from one to two orders of magnitude smaller than the population of the United States as a whole, the probability that a person's vote is decisive for a State popular vote outcome is in a range from four to ten times larger than the direct election probability for the United States as a whole. Compare the no-poll probability in Table 1 for a population of 1,000,000, which is .0008, to the probability for a population of 100,000,000, which is .00008. To find the joint probability that one is decisive for the State outcome and one's State swings the Electoral College, we multiply the probabilities of the two events. This entails an assumption that the two events are independent. Multiplying the smaller probabilities for the State outcomes by the crudely approximated probability for the Electoral College outcome, we find that the probability of being decisive is roughly the same as it would be if the presidential election were decided by a direct popular vote.
At the crude level of calculation attempted here, having the Electoral College appears not to make much difference for the probability that an individual is decisive for the national election outcome. It might be interesting to extend such calculations, in at least two directions. (1) Rigorous calculation of the Electoral College outcome probabilities, combined with use of actual State population sizes, would show either a bias in favor of residents of small States or a bias in favor of residents of large States. (2) It would be interesting to apply similar kinds of calculations to determine the probability that a voter is decisive for party control of the House of Representatives.