If everyone in your clan is what we’ll call “narrowly rational”, and so abstains from voting, the predictable outcome will be bad. But it is not rational, for individuals within a group that will foreseeably face a Prisoners’ Dilemma, to shrug and say “that sucks” and wait for everything to go to hell. Instead, people work to find means of reshaping their confederates’ behavior to prevent narrowly rational but collectively destructive choices.
A smarty-pants might come along and point out the weak foundations of the pro-voting ideology, declaring that he is only being rational and his compatriots are clearly mistaken. But it is our smarty-pants who is being irrational. Suppose he makes the “decisive argument” (which one is much more likely to make than to cast the decisive vote, since the influence of well crafted words need not be proportionate to 1/n). By telling “the truth” to his kinsmen, he is very directly reducing his own utility, not to mention the cost he bears if his preferences include within-group altruism. In order to be rational, we must profess to others and behave as though we ourselves believe things which are from a very reductive perspective false, even when those behaviors are costly. That is to say, in order to behave rationally, our relationship to claims like “your vote counts!” must be empirically indistinguishable from belief, whether or not we understand the sense in which the claim is false.
Of course, it would be perfectly rational for a smarty-pants to make his wrongheaded but compelling argument about the irrationality of voting to members of the other clan. But it would be irrational for members of either group to take such arguments seriously, by whomever they are made and despite the sense in which they are true.
So, when elections have strong intergroup distributional consequences, not only is voting rational, misleading others about the importance of each vote is also rational, as is allowing oneself to be misled (unless you are sure you are an ubermensch apart, and the conditions of your immunity don’t imply that others will also be immune).