The real "paradox of voting" seems to me to be an integral part of the public choice argument itself. If voting is irrational, then no one should vote. But if no one votes, then it certainly becomes rational to vote because chances of effecting outcomes is then very high. In other words, the more people pay attention to the public choice theory of irrational voting, the more rational voting would become.
Finally, not everyone gets much of a thrill from voting, including those who don't like the choices on offer, those who feel they have better things to do with their time than wait in line to vote, and those who are convinced that their vote cannot make a difference. Those individuals comprise the majority of Americans who do not, in fact, vote. For them, it is certainly rational not to vote based on their subjective valuations of the costs and benefits of voting.