Thursday, November 05, 2020

Political Beliefs, Uncertainty, and the Expected Value of Paralysis

Jason Brennan argues that most people can't have the faintest clue about the expected value of voting for either candidate in an election:

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!


  1. Hi Richard,

    A few of quibbles:

    (1) Both you and Brennan seem to be conflating the question of whether it is rational for someone to vote with the question of whether that someone has good reason to think that the expected utility of her voting for one candidate is greater than that of her voting for the other candidate. These two are not the same. There could be symbolic, deontological, or self-interested reasons for voting that have nothing to do with the relative expected utility of voting for one or the other candidate. And this could make it rational to vote, right?

    (2) When you talk about whether someone has good reason to think that "one candidate would be better than the other" are you just talking about whether they would be a better President while in office or are you talking about what the overall effect of their being elected is for the world over all time? I think that it would be pretty easy to argue that we're clueless whether electing, say, Obama was better than electing McCain. After all, did this make a difference to whether Trump was to be elected? What difference did electing Trump make? How will electing Trump make a difference to who will be elected to the presidency hundreds or thousands of years from now? What difference will these effects make to the world hundreds, thousands, or millions of years from now? It seems that we're clueless.

    (3) You seem to think that we could have a justified credence "that one candidate is overall better than the other." Again, better for the world or a better President? And do you think that we can have a justified credence that the overall effects from now until the end of time of having one candidate elected is better than having the other candidate elected? Or do you think that we could have a justified credence "that one candidate is overall better than the other" without having a justified credence about this?

    1. Hi Doug!

      re: (1): Yes, sure, this discussion is implicitly restricted to assessing the rationality of voting *for the purposes of changing the outcome of the election*.

      (2) I mean the overall effect. I wouldn't want to cause a great four years followed by subsequent apocalypse, for example.

      (3) Yeah, I was thinking that general cluelessness wasn't a barrier to our having a justified (tentative) credence that one outcome would be overall better than the other. But you raise an interesting challenge below, which I'll reply to separately!

  2. Let me say why I don't think that your response to the cluelessness objection works in this case. Suppose, for the sake of argument, that the expected value of the next four years given a Biden presidency is greater than the expected value of the next four years given a Trump presidency. Assume also, as you concede, that we're clueless about what the long-term effects of either presidency would be. Even so you can't just assume that the expected values of these unknown effects simply wash out. We simply don't know whether they'll wash out. Indeed, we have reason to think that it won't just wash out, for American politics tends to be reactionary. A shift to the left now tends to result in a shift back to the right later and vice versa. But you seem to just assume that this is not the case. For you seem to suggest that it's just obvious there is no reason to think that the long-term unknowns systematically favor going one way rather than the other. In fact, we have every reason to think that an Obama or a Biden presidency is likely to result in something like a Trump presidency. And, so, I think that we're pretty clueless about not only the very long-term consequences but also the not-so-long-term consequences of a given presidency. For all we know, it makes no difference given the reactionary nature of American politics. Or for all we know the expected value of a presidency has more to do with how far the candidate is from the middle rather than how good a president that he or she will be. For perhaps future polarization of American politics looms larger than how good a job the person does while in office in terms of how good the future will be.

    1. This is a really interesting objection! I'd (following Brennan) been implicitly focusing just on our possible cluelessness regarding the effects of the various (e.g. economic) policies implemented by the president during their term. I didn't find that too problematic. But I think the case you make here is much more troubling for me than Brennan's was, since you identify special reasons for expecting asymmetrically harmful unknowns, via a kind of historical homeostasis.

      I've a couple of thoughts. One is that, if you're right, I'm inclined to follow the expected value where it leads. If I really came to believe that the next presidency would make no expected difference to the long-run history of the world -- that any progress (for good or ill) would subsequently be met with an equal and opposite reaction (for ill or good) -- then I would no longer care about the election. I'd still be appalled by the bad things that are done, but I'd view them more fatalistically: if better things had happened now, that just would've made it worse later, so what does it really matter?

      But I guess I'm skeptical of endorsing such a strongly fatalistic view -- though a sufficiently weakened version may plausibly moderate our view of the stakes of these elections at least to some degree.

      One reason for my skepticism is that there's a hell of a lot of path dependence in public policy. Once you get broad-based social services implemented, for example, they tend to (grow in popularity and) remain. As do crazy kludges like employer-based health insurance. Various kinds of non-partisan institutional reforms also seem likely to have lasting effects, while it isn't so clear what the opposing 'backlash' would be. "Scary" (to some) changes like gay marriage are, once tried, swiftly accepted and normalized.

      Which policy and ideological disputes are salient also seems to change over time, so a political party I currently find appalling might not be nearly so bad the next time the pendulum swings back to them (though, yes, they might just be bad in different ways), especially if they prove unsuccessful in their current alignment.

      But most of all, the "equal and opposite reaction" suggestion just seems really strong, and I don't see much reason to believe it. Some changes prompt backlashes, but not all, and I don't see much reason to expect their magnitudes to be equal (on average), or for their valenced effects to be exactly opposed. I'm pretty optimistic about long-term social progress, for example. While our current society is far from perfect, I don't expect racism or homophobia will ever be as bad as they used to be, for example. So, despite the risk of some backlash, I tend to think that the sooner we make progress (in good directions), the better.

      So, I remain hopeful. But I could be wrong!

  3. Thanks, Richard. Just to be clear, I'm not suggesting that "the next presidency would make no expected difference to the long-run history of the world -- that any progress (for good or ill) would subsequently be met with an equal and opposite reaction (for ill or good)." Rather, I'm suggesting that we just don't have a clue. That is, I'm suggesting that Brennan is correct about our not knowing the difference in the value between the candidates. The problem is that there are at least three possibilities: (1) the best candidate to vote for is the one with the best policies (because these policies will do most good in the short-term and the long-term expected utilities are a wash); (2) the best candidate to vote for is the one with the most moderate -- good or bad -- policies (because more extreme policies lead to greater polarization of the electorate and a backlash from the other side, both of which have worse consequences than bad policies do); and (3) the best candidate to vote for is the one with the most extreme -- good or bad -- policies (because this will put those policies to the test once and for all, eliminating them from the political discussion if they fail and causing them to be entrenched in the way social security has become if they succeed, and these good consequences outweigh the risk of implementing bad policies in the short-term).

    What's more, consider the case where my vote makes a difference. Suppose that the election comes down to one state and in that state my vote gives the candidate that I voted for a one-vote lead, whereas had I not voted there would have been a tie. Suppose that I know which candidate is best. Do I know what would happen if there is a tie? Do I know whether that would be better or worse than the outcome in which the best or worst candidate wins by one vote? I have no idea. And, so, all this leads me to believe that it can't be rational for me to vote on the grounds that I'm justified in believing that the expected utility of my voting is greater than the expected utility of my not voting. For I'm clueless as to what the relevant expected utilities are. What's more, it's not even clear whether I should be seeking to maximize expected utility or instead to be risk adverse in the way that the Allais paradox suggests that I should be. Lastly, I'm uncertain as to whether the values by which I judge whether a policy is good or bad are correct. So, again, I seem to be clueless.

    1. *shrug*, I guess it strikes me as reasonable to give most credence to (1), and to think that (2) and (3) come pretty close to cancelling each other out. (I doubt most people have even considered the possibility of (2) or (3). But having now done so, it doesn't seem to me that they should swamp our base expectations from (1).)

      Why would you need to "know what would happen if there is a tie?" So long as you have reason to think it'd be better for your candidate to win than for the other to do so, it'd seem equally reasonable to prefer their straight win to a tie (unless there's some special reason to think a tie would be better, but I don't know why that would be).

      Note that my question isn't whether many voters are "justified in believing" that the EV of their voting is positive, but rather just whether the EV of their voting is in fact positive, for many of them, given their evidence. The latter is much less demanding, and I think compatible with a large amount of cluelessness.

  4. One more question: Suppose that I work as a cook. It's just before 6 PM on election day and my shift is about to end. Polls close at 7 PM. My boss wants me to work overtime (which pays overtime) until 7 PM. My options include: (O1) work overtime and donate the extra wages to the most effective charity that I can find, (O2) work overtime and use the extra wages for an additional night on the town, (O3) refuse to work overtime and go vote, and (O4) refuse to work overtime and go home and watch TV. Do you think that it's rational for me to vote in this situation? That is, do you think that it's reasonable for me to think that the expected utility of O3 exceeds that of every available alternative? It seems obvious to me that it isn't. And your reasoning in your post seems to assume that we're supposed to just ignore the opportunity costs associated with voting. Is that not the case?

    1. It'll depend on the details. It's certainly not always the case that voting is worth your time. But it's also not always the case that it isn't (especially since the relevant alternative, for most people, does not involve donating extra to effective charities). I ignored the opportunity costs in my post because I think they're often pretty trivial. But sure, not always.


Visitors: check my comments policy first.
Non-Blogger users: If the comment form isn't working for you, email me your comment and I can post it on your behalf. (If your comment is too long, first try breaking it into two parts.)

Note: only a member of this blog may post a comment.