Peter Salib & Guha Krishnamurthi have posted this draft on SSRN (forthcoming, U Chicago L Rev. Online). Here is the abstract:

Economists will tell you that your vote does not matter. Or at least it does not matter if what you care about is who wins a large election. Because the margin of victory is irrelevant to determining the winner, all of the votes beyond the single vote that puts one candidate ahead of the other have absolutely zero effect on the outcome. Thus, the only election in which your individual vote matters at all is the election that, without you, would end in a tie. Given the sheer unlikelihood of a tie, if voting has even minimal cost, or is even mildly inconvenient, you are almost certainly better off abstaining.

That, at least, is the traditional story. But recent elections, including the most recent American presidential election between Joe Biden and Donald Trump, tell a different one. They show us that, at least in close, high-stakes American elections, votes do not decide the winner. Litigation does. And critically, vote margins do matter in litigation. The larger the margin of victory, the less likely litigation will overturn a result: as the pre-litigation margin of victory grows, the available arguments become fewer and less credible, and thus less likely to change the outcome. Thus, it is beneficial for a candidate to accrue votes beyond the tipping point of the election, at least until the “margin of litigation”—the number of votes that post-election litigation could plausibly overturn.

In light of these observations, this Essay proffers two novel claims about the paradox of voting: First, we contend that, based on the mechanics of post-election litigation, it is possible that at least some votes should rationally be cast in expectation of having an electoral effect. Second, for closely related reasons, we argue that the margin of litigation can impact the perceived legitimacy of an election. It is therefore possible that at least some votes should be rationally cast to ward off the dangerous results that may arise from perceptions of illegitimacy, including decreased governmental efficacy, but also civil unrest and violent conflict.