I’m a great fan of Kindred Winecoff, especially when I disagree with him, which is often. Today Winecoff joins forces with Phil Arena expressing disdain for the notion that there might be any virtue or utility to voting other than whatever consumption value voters enjoy for pre-rational, subjective reasons. There are lots of interesting arguments in the two pieces, but the core case is simple:

1. The probability that any voter will cast the “decisive vote” is negligible, effectively zero;
2. Even if a voter does cast the “decisive vote”, the net social gain associated with that act is roughly zero because different people have stakes in opposing outcomes. Once you subtract the costs to people on the losing side from the gains to winners, you find that there is little net benefit to either side prevailing over the other.

The first point is a commonplace among economists, who frequently puzzle over why people bother to vote, given that it is a significant hassle with no apparent upside. The second point is a bit more conjectural — there is no universally defensible way of netting gains and losses across people, so economists try to pretend that they don’t have to, resorting whenever possible to fictions like “Pareto improvement”. But the point is nevertheless well-taken. In terms of subjective well-being, whoever wins, at the resolution of a close election a lot of people will be heartbroken and bitter while another lot of people will be moderately elated, and the world will continue to turn on its axis. Over a longer horizon, elections may have big consequences for net welfare: perhaps one guy would trigger nuclear armageddon, while the other guy would not. But in evaluating the consequences of casting a vote, the conjectural net benefit of voting for the right guy has to be discounted for the uncertainty at the time of the election surrounding who is the right guy. After all, if armageddon is at stake, what if you actually do cast the “decisive vote”, but you choose poorly? It must be very unclear, who one should vote for, if victory by one of the candidates would yield widely shared net benefit (rather than partisan spoils), yet the contest is close enough for your vote to matter.

All of these arguments are right but wrongheaded. We don’t vote for the same reason we buy toothpaste, satisfying some personal want when the benefit outweighs the cost of doing so. Nor, as Winecoff and Arena effectively argue, can we claim that our choice to vote for one side and against another is altruistic, unless we have a very paternalistic certitude in our own evaluation of which side is best for everyone. Nevertheless, voting is rational behavior and it can, under some circumstances, be a moral virtue.

Let’s tackle rationality first. Suppose you have been born into a certain clan, which constitutes roughly half of the population of the hinterland. Everyone else belongs to the other clan, which competes with your clan for status and wealth. Every four years, the hinterland elects an Esteemed Megalomaniac, who necessarily belongs to one of the two clans. If the E.M. is from your clan, you can look forward to a quadrennium in which all of your material and erotic desires will be fulfilled by members of the other clan under the iron fist of Dear Leader. Of course, if a member of the other clan becomes Dear Leader, you may find yourself licking furiously in rather unappetizing places. It is fair to say that even the most narrow-minded Homo economicus has a stake in the outcome of this election.

Still, isn’t it irrational for any individual, of either clan, to vote? Let’s stipulate that the population of the hinterland is many millions and that polling stations are at the top of large mountains. The cost of voting is fatigue and often injury, while the likelihood of your casting “the decisive vote” is pretty much zero. So you should just stay home, right? It would be irrational for you to vote.

The situation described is simply a Prisoners’ Dilemma. 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. Unless one can plausibly take oneself as some kind of ubermensch apart, reshaping your confederates’ behavior probably implies allowing your own behavior to be reshaped as well, even though it would be narrowly in your interest to remain immune. In our example, this implies that rational individuals would craft inducements for others in their clan to vote, and would subject themselves to those same inducements. These inducements might range from intellectual exhortations to norms enforced by social sanctions to threats of physical violence for failing to vote. If we suppose that in the hinterland, as in our own society, physical violence is ruled out, rational individuals would work to establish pro-voting norms and intellectual scaffolding that helps reinforce those norms, which might include claims that are almost-surely false in a statistical sense, like “Your vote counts!”

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).

But is voting virtuous? I think we need to subdivide that question into at least two different perspectives on virtue, a within-group perspective and a detached, universal perspective. Within the clans of our hinterland, voting would almost certainly be understood as a virtue, a sacred obligation even, and to not vote would be to violate a taboo and be shunned or shamed, if physical violence is ruled out. Perhaps by definition, the social norms that most profoundly affect behavior are those endowed with moral significance, and a clan that did not define voting as a moral obligation would be at a severe competitive disadvantage. Further, at a gut level, people seem to have an easy time perceiving actions that are helpful to people within their own social tribe as virtuous, especially when it counters harmful (to us) actions of other tribes. From the perspective of almost everyone in our hypothetical hinterland, voting would be a virtue, for themselves and members of their own clan.

However, observing from outside the hinterland and from a less partisan point-of-view, voting does not seem especially virtuous. Whoever wins, half the population will be treated abhorrently. Since getting to voting booths involves climbing steep rock faces, as external observers we’d probably say that the whole process is harmful, and that it’d be better if the Hinterlonians found some less miserable means of basically flipping a coin to decide who rules, or better yet if they’d reform their society so that half its members weren’t quadrennially enslaved by a coin-flip. Even from outside, we’d probably recognize not voting as a sort of sin in its anthropological context, just as we’d condemn shirking by a baseball player even when we don’t care which team wins. But we’d consider the whole exercise distasteful. It’d be like the moral obligation of a slave to claim responsibility for an action by her child, so that the whipping comes to her. We’d simultaneously recognize the virtue and wish for its disappearance.

But lets leave the hinterland, and consider a polity in which there is a general interest as well as distributional interests. After an election, the losing clan might be disadvantaged relative to the winning clan, sure, but the skew of outcomes is much smaller than in the hinterland, and “good leadership” — whatever that means — can improve everyone’s circumstances so much (or bad leadership can harm everyone so dramatically) that often members of a clan would be better off accepting relative disadvantage and helping a leader from the other clan win. Now there are two potential virtues of voting, the uncomfortable within-clan virtue of the hinterland, but also, potentially, a general virtue.

Let’s consider some circumstances that would make voting a general virtue. Suppose that citizens can in fact perceive the relative quality of candidates, but imperfectly. In economist-speak, each citizen receives an independent estimate, or “signal”, of candidate quality. Any individual estimate may be badly distorted, as idiosyncratic experiences lead people to over- or underestimates of candidate quality, but those sorts of distortions affect all candidates similarly. Individuals cannot reliably perceive how accurate or distorted their own signals are. Some individuals mistakenly believe that candidate A is better than candidate B, and would vote for A. But since candidate B is in fact superior, distortions that create a preference for A would be rarer than those leave B’s lead in place. In this kind of world, voting is an unconflicted general virtue. There is a candidate whose victory would make the polity as a whole better off, despite whatever distributional skew she might impose. If only a few people vote, however, there is a significant possibility that voters with a mistaken ranking of quality will be overrepresented, and the low quality candidate will be chosen. The probability of error shrinks to zero only as the number of voters becomes very large. The expected quality of the election victor is monotonically increasing in the number of voters. Every vote improves the expected welfare of the polity, however marginally, and so every vote does count.

Even in worlds where voter participation is a clear public good, the Prisoners’ Dilemma described above still obtains. In very narrow terms, it’s unlikely that the personal benefit associated with a tiny improvement in expected general welfare exceeds the hassle of schlepping to the polls to cast a vote. Yet the cost of low voter participation, in aggregate and to each individual, can be very high, if it allows a terrible candidate to get elected. So, what do rational, forward-looking agents do? They don’t fatalistically intone about free-rider problems and not vote. As in the hinterland, they establish institutions intended to reshape individual behavior towards the collective rationality from which they will individually benefit. A polity might make voting compulsory, and some do. Short of that, it might establish strong social norms in favor of voting, try to enshrine a moral obligation to vote, and promote ideologies that attach higher values to voting than would be implied by individual effects on outcomes. As before, in this kind of world, it is those who make smarty-pants arguments about how voting is irrational who are behaving irrationally. Rationality is not a suicide pact.

In both of the sort of worlds I’ve described, we’d expect voting to be considered a virtue within competing clans or parties, as we pretty clearly observe in reality. We’d only expect voting to be considered a general virtue, one in which you exhorted others to vote regardless of their affiliations, in a world where people believed in a general interest to which citizens of every group have imperfect access. I think it’s interesting, and depressing, to observe growing cynicism about universal voting in the United States. Political operatives have always sought advantage from differential participation, but it was once the unconsidered opinion of patriotic Americans that everyone who could should vote. Maybe I’m just a grumpy old man, but now it seems that even “civically active” do-gooders focus on getting-out-the-vote on one side and openly hope for low participation on the other. To me, this suggests a polity that increasingly perceives distributional advantage as overwhelming any potential for widely-shared improvement. That can become a self-fulfilling prophesy.

Winecoff dislikes Pascal’s Wager, so lets use an idea from finance, optionality, instead. Suppose that there is no general welfare correlated to election outcomes, and apparent signals thereof are just noise. Then, if people falsely believe in “national leadership” and vote based on a combination of that and more partisan interests, we’d have, on average, the same distributional contest we’d have if people didn’t falsely believe. At worst we’d have a differently skewed distributional contest as one side manipulates perceptions of general interest more adroitly than the other. But suppose that there is a general interest meaningfully correlated to election outcomes, in addition to distributional concerns. Then “idealism” about the national interest, manifest as citizens working to perceive the relationship between electoral outcomes and the general welfare, voting according to those perceptions, and encouraging others to do the same, could lead to significant improvements for all. There’s little downside and a lot of upside to the elementary-school-civics take on elections. With this kind of gamma and so low a price (polling stations are not stuck atop mountains!), even hedge fund managers and political scientists ought to be long electoral idealism.

Note: I’m overseas and I don’t live in a swing state. I won’t be voting on Tuesday, by absentee ballot or otherwise. I deserve your disapproval, although not so very much of it. Social norms are contingent and supple. (Pace Winecoff and Arena, whether one lives in swing state should condition norms about voting. Why is left as an exercise to the reader. Hint: Consider the phrase “marginal change in expected welfare” — whether applied to members of an in-group or the polity as a whole — and the fact that cumulative distribution functions are typically S-shaped.)