Unless you have a really weird utility function that values voting in and of itself, what matters is the outcome of your vote. If the predicted outcome of changing your vote is really small, say 0.00000001% chance of being the tie breaking vote, otherwise nothing changes, then the utility of your vote should be near zero.
Unless you have a really weird utility function that values voting in and of itself, what matters is the outcome of your vote.
Not at all. My utility function might value my self-perception as a person who votes for X. It might value the ability to rant about how I did or did not vote for X and therefore all the bad policies are not my responsibility -- if only they have listened to me! It might value the warm glow of having done my civic duty of helping the forces of light triumph over the spawn of evil. Etc, etc. None of this is particularly weird.
If there's such a small chance of your vote making a difference in the election, you should be comfortable voting for trump.