They don’t know the difference in the value between the candidates and they don’t know they probably of being decisive. If it’s not rational to buy a lottery ticket in such situations, why would it be rational to vote?
But I think his framing is misleading. It’s true that a robust, precise, and dialectically persuasive estimate would take a lot of work. But it would also take a lot of work (much more than Brennan does here!) to show that most people have no good reason to think that one candidate would be better than the other, or that they epistemically must be indifferent. Yet that is what Brennan really needs to show, if he is to undermine the rationality of voting.
(It’s actually a bit unclear what Brennan’s target is in that post: he moves back and forth between talking about whether voters know whether it’s rational to vote and whether it is rational, given voters’ knowledge, to vote. These are not the same thing! To be clear: I’m concerned with the latter.)
To justify acting, we do not need to know the precise “difference in value between the candidates” or the precise “probability of being decisive”. Given how many people are affected by the results of a major election (like the U.S. Presidency), it suffices to have justified credence that (i) one candidate is overall better than the other, and (ii) the contest is likely to be close. (For the latter: Zach Barnett shows that granting the underdog so much as a 10% chance of an upset win typically generates a sufficient chance of “difference-making” for these purposes.)
And I think it’s perfectly commonplace for these two conditions to be met! It’s generally public knowledge which elections are expected to be close. As for the value claim, in contrast to Brennan’s “unknown lottery” analogy, I would think any number of simple heuristics could lead one to a (tentatively) justified expectation here. Here’s but one: “Oppose an openly authoritarian candidate who undermines democratic norms and institutions, stokes social divisions, and undermines the social trust that’s essential to a harmonious and flourishing society.” I’m sure you can think of others.
Of course, for any such factor in isolation, one can imagine cases in which other factors would outweigh it. But so what? Maximizing expected value does not generally require high probability that the option in question will actually turn out to be best. (It’s even compatible with knowing that the option in question is not objectively best.) As Jimmy Lenman has argued, we’re completely clueless about the actual long-term value (whether positive or negative) of any action whatsoever — including mass murder. But (contra Lenman!), the sensible consequentialist response is that so long as you’ve no special reason to think that the long-term unknowns systematically favour going one way rather than the other, their influence on the expected values of your choices simply washes out. And the same is true of short-term unknowns.
So Brennan’s argument is off-track. Putting aside worries about systemic epistemic bias (which are real enough, but not our focus here): Even if he’s right that most voters should give significant credence to the possibility that their candidate would unexpectedly do more harm than good, they should (if unbiased) assign a comparable degree of belief to the possibility that their candidate would unexpectedly overperform by a similar amount, e.g. in areas that aren’t covered by the limited heuristics used in coming to favour that candidate.
In short: Yes, there are a lot of unknowns, in voting as in everything else in life. But no, that doesn’t show that voting is irrational, or that paralysis/abstaining is somehow superior. For that, you’d need to show that the expected value of abstaining was greater than the expected value of voting for a candidate that seems better. That’d be a hard thing to demonstrate, and Brennan hasn’t even come close.
In slogan form: Use your best judgment, don’t suspend it!