Can non-expected utility theories explain the paradox of not voting?

Many people vote in large elections with costs to vote although the expected benefits would seem to be infinitesimal to a rational mind. We exhibit two necessary conditions that a theory of rational decision must satisfy in order to solve the paradox. We then show that prospect and regret theories cannot solve it because each theory meets either one or the other necessary condition, but not both. However, the paradox of not voting is consistent with an amended version of third-generation prospect theory in which the reference is merely to vote or abstain.