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Not to mention that the Utilitarian principles behind this position lead to completely muddled thinking.

On the one hand, Father says that one cannot vote for a candidate if they hold morally-objectionable principles, and yet on the other he states that it's an obligation to vote for the candidate who is "more likely to promote the common good".  So do you vote based on the principles to which the candidate adheres or on the likelihood that he would act upon them.  It's a murky blur of principle and pragmatism.  It's no wonder why Catholics are so confused about this matter.

You'll need to cite the full context of this.  I bet that what he's saying is that one must decide on the option that is less likely or less probably evil ... when the conscience is not certain.  It's Catholic Theology 101 that one cannot do any positive evil ... even to prevent a greater one.

Well if we're going to talk about the inherent value of choosing a "lesser evil" (divorced from the context of Fr. Tauok) it does have some place in moral theology.  St. Alphonsus (per McHugh and Callan) taught that a preplexed conscience which cannot delay a decision must select the lesser of two evils.  That goes for individual, private morality.  In the public realm, the state is certainly allowed to tolerate lesser evils in the pursuit of staving off a greater one (this of course is a different situation, only bringing it up under the heading of lesser evils in general and their place in Catholic moral theology).  So it isn't right to say that it has no place at all, even if it has no place in the current context of there being a moral obligation to vote.

612. St. Alphonsus gives the following directions to assist one who is perplexed in conscience:

(a) If without serious inconvenience decision can be delayed, reliable advice should be obtained (e.g., from the confessor).

(b) If decision cannot be delayed, the alternative that seems the lesser evil should be chosen. Example: The natural law requires that Titus should not expose his life to danger unnecessarily. The positive law of the Church requires that he go to Mass on Sunday. It is a less evil to omit what is required by the law of the Church than to omit what is required by the law of God. Hence, Titus should decide that he is not obliged in his circuмstances to go to church.

(c) If decision cannot be delayed and the party cannot decide where the lesser evil lies, he is free to choose either; for he is not bound to the impossible.

1502. Is it lawful to advise another to commit a less evil in preference to a greater evil?

(a) If the other has not made up his mind to commit either evil, it is not lawful to advise that he do either. Thus, to counsel another to steal, and to make his victims the rich rather than the poor, is a species of seduction.

(b) If the person has made up his mind to commit the greater evil and the lesser evil is virtually contained in the greater, it is lawful to advise that he omit the former for the latter. For in thus acting one prevents the greater evil and does not cause the lesser evil, since it is virtually contained in the greater evil which the other person had already decided on. Thus, if Titus is bent on stealing $100, Balbus is not guilty of seduction, if he persuades Titus to take only $10. We are supposing, of course, that Titus is so determined to steal that it is out of the question to deter him from taking at least a small amount.

(c) If the person in question has decided on the greater sin and the lesser is not virtually contained in the greater, it is not lawful to recommend that he commit the smaller instead of the greater sin. For,if one does this, one does not save the other from the internal guilt of the greater sin intended, while one does add the malice of the lesser sin which was not intended. Thus, if Titus plans to kill Caius,it is not lawful to advise that he rob him instead, or that he kill Claudius instead, for robbery is a specifically distinct sin from murder, and Claudius is a different person from Caius. But, if Titus planned to kill Caius in order to rob him, it would not be unlawful to point out that the robbery could be carried out without murder and to advise accordingly.

1503. Not all theologians accept the last solution just given.

(a) Some reject it, and hold that, even when the lesser evil is not virtually contained in the greater, it is lawful to advise the lesser. They argue that what one does thereby is not to commit the lesser evil, to induce it or approve it, but only to permit it in order to lessen the harm that will be done, and they confirm their argument from scripture(Gen., xix. 8 ). According to this opinion, then, which has some good authorities in its favor, it would be lawful to advise robbery in order to dissuade another from the greater evil of murder.

(b) Others modify the solution given in the previous paragraph, and hold that it is lawful to propose the lesser evil or mention it, provided one does not attempt to induce the other person to carry it into effect.

Chapter 1: What is Conscience, how manifold is it, and what must be followed?

10.—Let us proceed to argue the other species of conscience. A perplexed conscience is one in which someone that has been placed in the middle of two precepts believes he sins no matter which side he chooses, e.g. if someone could save the life of the defendant in a trial by perjury, and on the one hand he is distressed by the precept of religion to not commit perjury, while on the other (deduced from an error) by the precept of charity towards his neighbor, and he cannot resolve himself to do one or the other. Thus it is a question of what he ought to do in this case. We respond: If he can suspend an action, he is bound to postpone it until he consults a learned man: but if he cannot suspend it, he is held to choose a lesser evil by avoiding a greater transgression of natural law than of human or divine positive law. Moreover, if he cannot discern what is the lesser evil, and he were to choose either part, he would not sin because in a case of this sort he would lack the freedom necessary for formal sin.

77.—4. It is a mortal sin to cause another man to be drunk, or to challenge him to a drinking contest with the intention of getting drunk, or with the knowledge that drunkenness is going to follow in him or in the other man. Lessius, loc. cit.

5. If for a just cause, e.g. a great evil could be otherwise impeded if the author of it is drunk, it is lawful to induce him to drunkenness, which at least is not voluntary, viz. apart from intention, and therefore he is inculpably drunk; e.g. a very strong wine, or toasting with a medicated drink, when the other man is deceived, not knowing its strength. Wherefore, one can so make others drunk, who otherwise would betray the city or abduct him. (Lessius, loc. cit., and Sanchez, l. 2, de matr. d. 11). But in this case, would it be permitted to induce someone to drunkenness if it were a voluntary act? There is a doubt. Lessius (l. 4, c. 3, d. 4, n. 32), affirms; because, he says, one may persuade and induce to a lesser evil that prevents a greater one. Laymann, (lib. 3, sect. 4, n. 6) more rightly denies it, because in no case may one induce someone to sin.

Quaeritur: Whether it is licit to induce someone to get drunk, to impede him from a more serious evil, say from committing a sacrilege or a homicide?

There are three opinions.

The first upholds it, and Lessius (l. 4, c. 3, d. 4, n. 53) holds it as probable, and Medina, Gob., Diana and others cited by Croix (l. 2, n. 224) think it is probable. The reason is because one may be prapred to commit a greater evil to induce someone to carry out a lesser one.

The second opinion, which Laymann (l. 3, sect. 4, n. 6), Bonacina (tom. 2, d. ult. de praec. eccl., q. 1, p. 1, n. 3), Palaus (t. 7, tr. 50, d. 3, p. 5) and the Salamancans (tr. 25, c. 2, p. 4, n. 51) hold it, saying it is licit to induce another to material drunkenness, i.e. when he would otherwise make himself drunk without sin, say by placing a very strong wine in front of him, or one that is medicated; because then on his side he would not sin, and on the other the damage of drunkenness is permitted to avoid even graver damage to others. But it is not licit to say one can induce formal drunkenness, namely when it is by his own sin, since this is intrinsically evil and therefore never permitted. Nor is it opposed (as they say) the reason of Lessius, for they respond that this avails when a lesser evil is included in a greater evil, precisely when you lead one that wishes to kill his enemy to only strike him; but not when the evil is disparate.

The third opinion, at length, which the Continuator of Tournely upholds (loc. cit., Unde 9), and Holzman (tom. 1 p. 155, 735), along with Arsdek., says it is not permitted to induce anyone to drunkenness whether formal or material, on account of fleeing both evils, because (and in this they speak rightly), an evil, even if it is material, against the natural law is truly an evil, which is why one may never cooperate with it. Still, these not withstanding, the first opinion seems sufficiently probable to me, and other learned men that I have consulted, whether the drunkenness were material or formal, on account of the reasoning that has been provided, because it is licit to induce another to a lesser evil so that he would be impeded from a greater one, according to what we will say in book 3, number 57. Nor is what the Salamancans say (loc. cit., against Lessius) opposed, for, although the evil of drunkenness does not seem included in that greater evil of sacrilege or murder, since they are per se disparate evils; nevertheless, really, virtually it is already included in that greater spiritual evil, since every spiritual evil includes, nay more exceeds, every temporal evil, so much that anyone is held more to suffer every temporal evil to avoid even the lest spiritual evil. Nor does it impede us to say that it is not lawful to persuade a lesser evil to be imposed on a third, because then the one persuading would be the direct cause of damage of the third, because it would not happen to him unless he would persuade, for this occurs when an evil is imposed on a third innocent man, who is not held to suffer the damage, to avoid the spiritual evil of another; but not in our case, where he who is induced to drunkenness, is indeed held to tolerate (as we said above) every temporal evil to put to flight a greater spiritual evil.

57.—Whether it is lawful to persuade or permit a lesser evil to avoid a greater one?

The first opinion rejects this, according to what Laymann (de char. c. 12, n. 7) holds, with Azor and others. The reason is, because the comparative does not abolish the positive; for this reason, one who persuades a lesser evil, truly persuades an evil. Laymann and Azor place the limitation, unless the evil would be virtually included in the other greater act. So, if you could persuade a man prepared to kill someone that he should only cut off his hand, nevertheless it is the same thing, but not planned by the other. So also for one wishing to commit adultery if you could persuade him to commit fornication with someone that was free in general, but not in particular. The Salamancans admit this (loc. cit. § 1, n. 58 ) provided he would decide to carry out both evils. (with Navarre, etc.) But Laymann instinctively says (as well as Sanchez with the second opinion, as will soon be said), that he expressly rejects this limitation because (as he says) then a lesser evil is proposed, not that he would perpetrate another, but that he would withdraw from the greater.

The Second opinion is more probable and holds it is licit to persuade a lesser evil if the other is determined to carry out a greater evil. The reason is because the one persuading does not seek an evil, but a good, namely the choice of a lesser evil. (Sanchez, de matrim. lib. 7, d. 11, n. 15, with de Soto, Molina, Navarre, Medina, Sylvest. and many others, and the Salamancans loc. cit. with Cajetan, Soto, Palaus, Bonacina, etc; Croix thinks it is probable, lib. 2, n. 223, moreover, Sanchez teaches the same thing in n. 19, with Cajetan, de Soto, Vocar, Valent.). It is licit to persuade a man prepared to kill someone that he should steal from someone instead, or that he should fornicate. And the defenders of this opinion argue it from St. Augustine (in c. Si quod verius, caus. 33, q. 2) where he says: “If he is going to do something that is not lawful, now he might commit adultery and not murder, and while his wife is living he marries another, and does not shed human blood.” From such words, “now he might commit adultery,” Sanchez proves (dict. n. 15), with de Soto, Molina, Navarre, Abb., etc., that the Holy Doctor spoke not only about permitting, but even persuading. And Sanchez adds this (n. 23) with Salon, it is not only lawful for individuals, but even for confessors, parents, and others, to whom the duty is incuмbent to impede the sins of subordinates.