1. The distinction about caring about only yourself versus every citizen equally is a false dilemma, so that means that neither equation will be the one that people use.
2. The value of f will be different in each equation.
3. If e is a variable of average value, then it’s not applicable in the self-interested calculation, because I’m looking at value to a particular person — me.
4. Though you mention it later in your essay, your equation doesn’t mention utility from voting apart from the electoral outcome (showing support, attracting attention to your values, exercising civic virtue, etc.)

I think this equation works regardless of the agent’s values:

U(V) = expected net utility of deciding to vote
P(e*) = expected probability of your vote being the deciding vote of the election
U(e*) = expected net utility of your candidate winning
U(e) = expected net utility from the action of voting, apart from the electoral outcome
C(o) = expected net utility of highest utility option you forgo by voting via opportunity vost

U(V) = P(e*)U(e*) + U(e)

If U(V) > C(o), then vote.