This question treated in the abstract as a general question and not a question about the upcoming presidential election is difficult to address. My response was addressed to a situation where there are two serious intrinsic evils to choose. Using LilyM’s example of Maximilian Kolbe, I can imagine a saint sacrificing himself for another, but I can’t imagine a saint participating in a choice between the death of two other people. Should he choose the lesser of two evils judging the value of the persons? Should he refrain from making a decision, even though the persecutors offer him the right to vote? If a man holds a group hostage but gives you the choice of who, not you, should be executed, how would a Catholic respond? If in a lifeboat and resources are running out, and the majority are going to choose someone to throw overboard, and you have the option to vote, how do you make your decision? Do you have a duty to vote?
But ‘choosing the lesser of two evils judging the value of the persons’ is in a very real sense exactly what St Kolbe did when it boils down to it. He judged the value of his own life to be lesser than that of his fellow prisoner, being that he was unattached whereas the fellow was a family man, and accordingly volunteered himself.
And he didn’t throw up his hands, back away and say ‘this is evil, it is too difficult, I will have no part in it and I will simply let the Nazis kill whomever they decide to kill’.
But I digress. Voting is not a situation where the results are immediate, easily foreseeable and totally unavoidable. In that sense it is unlike your or my scenarios.
It’s not a matter of ‘doesn’t matter whether you vote for x or y, umpteen number of people are beyond a doubt certain to be killed, and killed quickly’.
So it is a situation where you also have to bear in mind the future enactment of the policies the candidate campaigns on, and the likelihood of influencing them once in office.
So that if you assist the least-worst candidate to get in (say the one who is against abortion except in cases of rape and incest as opposed the one who believes in having it on demand and also wants partial birth abortions to be legal as well), you know that you will also have a greater chance, through continuous campaigning, of prevailing upon that person to change their minds in a favourable direction even after their election - to the point where perhaps that candidate ends up outlawing abortion altogether.
Whereas if through your inaction the more hard-line candidate gets in, the exact same campaigning is more likely if anything to harden them in their pro-abort stance.