Aeon writer Julia Maskivker asks
Source: Given how little effect you can have, is it rational to vote? But her answer, though in accord with my own, is unconvincingly supported.
Rather than argue from some set of vague moral principles involving duty to community (which could in my opinion have been made much more clear and well supported), I would argue instead from the personal self-interest that Dr Maskivker considers inadequate.
In the modern world many elections are close enough that there is a non negligible probability of a tie. And in the case of a tie every vote has the potential of changing the result.
Furthermore, even when one’s preferred policy option is certain to lose (or to win), the demonstration of a higher level of support can deter those who defeat it (or encourage its elected supporters) in a way that benefits the individuals who wanted it.