Is It Individually Rational to Loosen Up Near the End of a Pandemic?

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With distribution of vaccines starting in the next month or so, should one rationally change one's behavior? If one assumes that one's choice in a period has no effect on other periods, then the answer is no. Holding risk of infection constant, the decision calculus is essentially the same in each time period of a pandemic, reflecting the trade-off between the costs of infection (including death) and the cost of social distancing in that month.

But the periods of a pandemic are not independent. Infection conveys at least some degree of immunity, and this explains the common sentiment that maybe it would be worth getting Covid over with. All else equal, it makes more sense to distance at the end of a pandemic (just before vaccines) than at the beginning. Getting sick at the beginning of the pandemic saves one from having to worry about it for the rest of the pandemic, while getting sick at the end of the pandemic doesn't buy one any freedom from worry.

A quick simulation analysis quantifies this: Suppose that social distancing destroys one-quarter of the utility of being alive each month, that the risk of infection if not distancing is one in twenty (and zero otherwise), that the risk of death given infection is one in one hundred, and that one will live fifty more years if one does not die in the pandemic. If the pandemic will last twelve months, a person looking only after his or her own interests should distance only for the last four months and only if not yet infected.

Similar logic can lead to another counterintuitive result, that past some level of infectivity in the general population, one should be less cautious. If viral spread is so pervasive that you are eventually likely to become infected even if you are cautious, you might as well get infected earlier rather than later. At relatively low risk levels, increased prevalence of Covid should lead a rational maximizer of self-interest to greater precaution, but at very high risk levels, increased prevalence could rationally lead to reduced precaution, at least if those previously infected have less reason to socially distance.

Near the end of the pandemic, however, this possibility is unlikely, because the first argument outweighs the second. With infection rates very high and a vaccine around the corner, one would thus expect rational people to act more carefully rather than less. And yet, we see reduced social distancing and ever-increasing rates of infection. Why? Part of the answer surely lies in changes in the weather, but that may be an incomplete explanation. There may be individual incentives to act with less caution, even if the social calculus still tilts in favor of heavy social distancing.

Some of these incentives are obvious: Maybe costs of compliance increase over time. It is not so hard to comply for a while, maybe even fun, but loneliness grows. And the risk of death from infection has fallen over time. Both these answers focus on the amount of time from the beginning of the pandemic to the present, rather than on the duration of the pandemic that remains. Might there also be arguments that it is individually rational to be less careful, the closer we are to the end of the pandemic? Yes.

Let's assume that individuals care to some extent not only about the prospect that they themselves will get sick, but also at least somewhat about the prospect that they may infect others. At first, it might seem that this should make no difference. It doesn't matter whether the costs one takes into account are costs to oneself or costs to others. It's still best to be more cautious near the end of the pandemic.

But multiplier effects may be greater earlier in the pandemic. One must worry not only about infecting others, but also about those whom they might infect, and so on. Much of the costs of one's own lack of care may be many degrees removed. But if the end of the pandemic is near, then multiplier effects might be stopped, as soon as everyone receives the vaccine. It may be too early for logic of this sort to matter. But the most vulnerable people might receive vaccines in December, reducing the indirect costs of infecting others today. Also, if we are nearing the top of the wave, individual incentives at self-preservation will soon kick in, reducing multiplier effects. Similarly, if one believes the story that people will be more careful shortly before being vaccinated, that itself is an event that will reduce the infection multiplier, and so there is less reason to be careful beforehand. I am skeptical that this line of thinking explains current behavior, though. It seems more likely that people are becoming more indifferent to others' welfare than that they are rationally taking into account that social distancing might not advantage others as much.

A separate argument is based on the iterated prisoner's dilemma. If many individuals' interest narrowly conceived is to not socially distance but society as a whole benefits from everyone social distancing, then the game is a many-player iterated prisoners' dilemma.

The two-player version is simple enough: It may be that for each of two roommates, it would be collectively rational to socially distance but not individually rational. In a one-period game, each roommate would not cooperate, regardless of the other roommate's choice, just as each prisoner in the prisoners' dilemma has an incentive to rat out the other regardless of what that person does. But when the game will be continued over multiple periods, each roommate may cooperate given the continued cooperation of the other roommate, applying a strategy like tit-for-tat.

The iterated prisoners' dilemma breaks down as the end of the game nears. There is no reason to cooperate in the final period of the game, just before administration of the vaccine, because there will be no benefit from doing so in generating further later cooperation. But if that's true, then there is no reason to cooperate in the penultimate period of the game, and so on. In the real world, cooperation is not black-and-white. Social distancing occurs on a continuum that is not easily measurable, and so each roommate's failures at social distancing may matter only if repeated over a sufficient number of periods to amount to a clear violation of the cooperation norm. Later in the game, the benefit from weakly signaling cooperation becomes attenuated. Each roommate rationally loosens up, while still claiming to be taking every reasonable precaution.

But what if there are many millions of players? One's own individual actions will likely have a negligible effect on infection rates in society as a whole, so why should one ever cooperate? If one cares about social welfare, even though not enough fully to internalize effects on others, the iterated prisoner's dilemma story becomes plausible. One infects others not only with the virus but also with non-cooperation, and one may worry about multiplier effects with non-cooperation too. Later in the game, this is less worth worrying about. For your behavior to have an indirect adverse effect on others, it must cause others to behave recklessly and for that in turn to lead to infection, but such effects are less likely in the end game.

But one doesn't need to think that people care about the effect of their behavior on the national average level of compliance to believe the iterated prisoners' dilemma story. Each of us belongs to small groups--families, workplaces, and so on--and in these groups it is more plausible to believe that one's own refusal to socially distance will lead to a breakdown of cooperation. These small groups can themselves be seen as atomistic actors in broader communities, concerned themselves about setting a good example.

The mechanism works less through conscious worries about indirect effects than through social norms. And we should not be surprised that social norms will break down as the pandemic proceeds. The anticipated end of a social norm may lead to the breakdown of the social norm even before the end, just as an anticipation that one's company will switch to business casual next month might lead people to go casual this month too. If I will be able to violate social distancing soon, it may be less of a breach of the social distancing norm now. At one level, this is illogical; the social norm should survive until it is no longer needed. But if one thinks that others may think that still others may think that it is logical to transition gradually into reduced social distancing, then one may be less scolding of someone who breaks social distancing prematurely. Anticipating a lower cost of breach, more will break the social norm, in a vicious circle.

I am not arguing that people should break social distancing norms. We need them more than ever with the end of the pandemic in sight! But it is good to be realistic in acknowledging that it may well be individually rational for many people not to socially distance, even when it is socially destructive, especially people whose own risk from Covid is low. That recognition can help us solidify the social norm. If we are past the point where social norms can serve as a useful form of social opprobrium and informal regulation, that may be justification for increasing the force of formal rules and laws. The greater the breakdown of norms in combatting a negative externality problem, the greater the case for government regulation. If the breakdown in social distancing reflects a rational individual calculus partly attributable to the upcoming end of the pandemic, individual incentives must be recalibrated, and there is no reason to expect private ordering to achieve optimal compliance levels.