Reconciling collective risks and individual decisions

This article was co-authored with Laurence Barry, and initially written in French during the 2020 Summer.

The early days of the SARS-CoV-2 (or COVID-19) pandemic have seen a proliferation of calls for “individual responsibility”, starting with strong calls (and even an obligation in some countries, including France) to stay home as much as possible in the early spring of 2020, before it became mandatory to wear a mask in public (often closed) places during the summer. To paraphrase Coluche « dire qu’il suffirait que les gens restent chez eux pour qu’on puisse sortir… ». This call for each person’s responsibility is made in the name of all and for the good of all, symbolizing this very particular solidarity that the pandemic reminds us of: the risk that I choose to run does not only concern my person but also constitutes a risk for those around me. To formulate it in probabilistic terms, McKendrick (1926) stated that “the probability of occurrence increases with the number of existing cases“. This conception of individual responsibility, which is quite intuitive a priori, actually runs counter to the classical conception of economics: the rational (and responsible) individual makes choices that concern him, and that concern only him. The collective good is deduced by summing up individual utilities, independent of each other. But here is the problem: with the epidemic, an interdependence of utilities is created, so that the well-being of so-and-so, who chooses not to wear a mask, can harm the health and therefore the utility of many other people. How then can we think in economic terms of this “individual responsibility” in the context of the epidemic?

From individual preferences to collective well-being

The central assumption of the economic theory of behavior is that everyone is capable of ranking, in order of preference, all sorts of alternatives that are proposed to him. And if I have to choose one of two, I will systematically choose the one I prefer. As Mas-Colell et al (1995) show, a simple assumption of continuity of preferences then translates into the existence of an individual utility function reflecting these preferences. This approach could suffice in Jean-Jacques Rousseau’s state of nature, when man is imagined living alone. But in society it is necessary to be more realistic, and to take into account the interactions between individuals. Organizing life in society, by promoting cooperation and seeking to ensure collective well-being, cannot be done by simply understanding individual well-being. To use an example from Jean-Jacques Rousseau, it is in the interest of several hunters to work together to hunt down a deer, because no hunter can do it alone[i] (Rousseau, 1755). The first difficulty is therefore to ensure collaboration for the hunt, but also and above all, if a deer is killed, the problem of the distribution of the meat arises.

Throughout the 18th century Francis Hutcheson and Adam Smith in England, Jean-Charles de Borda and Nicolas de Condorcet tried to formalize this notion of “collective well-being”, showing that there were unfortunately many paradoxes, especially when it came to the well-being of a nation. At the same time, Kant formalized the categorical imperative: “Act only according to the maxim that makes you want it to become a universal law“. In other words, before making a decision to act, one should ask oneself what would happen if everyone acted in this way. The rationality of the individual must be collective, and take into account humanity as a whole. In her reading of Kant, Arendt (1991) puts forward the sensus communis, this sense common to all men and which links the judgment of each one “to the whole human reason”. Thinking for oneself then becomes “thinking by putting oneself in the place of all others, in what she calls an “enlarged mentality”.

Tocqueville reverses the terms of the equation. In democratic countries, according to him, one can no longer put forward the value of self-sacrifice: one must be able to demonstrate that « l’homme en servant ses semblables se sert lui-même (…) Aux Etats-Unis on ne dit presque point que la vertu est belle. On dit qu’elle est utile » (man, in serving his fellow men, serves himself (…) In the United States, it is hardly said that virtue is beautiful. We say that it is useful). This implies, however, “small sacrifices”, made because they are beneficial to the person who makes them. Tocqueville (1981) then exhorts his readers to act in their own interest “of course”, i.e. taking into account the interest of all. This collective rationality is in fact a common practice within small groups, such as the family. It is not uncommon, in fact, to put aside one’s personal interest for the good of the family. But it is more complex to implement within a larger, more heterogeneous, even more abstract group.

The stowaway versus common interests

A resolutely optimistic vision would consist in believing that if all the members of a group have common interests, then everyone will act to achieve them. A well-known example is that of global warming: collectively, the interest of all is the reduction of greenhouse gases at the global level; but individually, each country has the temptation to delay the implementation of measures that could penalize its economy, hoping however to benefit from early actions of neighboring countries. This is the free rider principle: there is a collective benefit to be gained from cooperation, but individuals have more incentive to seek to benefit from the “cooperation” of others. In economic terms, they seek to have a benefit without bearing the costs.

This problem, extensively studied in Olson (1965), is classic for the majority of “public goods”[ii] which satisfy two characteristics: being non-rival and non-excludable, i.e. whose consumption by some does not reduce the quantity available to others and whose access cannot otherwise be restricted. Axelrod & Hamilton (1981) explained that the cooperation necessary for the promotion of common goods does not necessarily depend on a form of altruism, but more simply on reciprocity between agents, based on conditional cooperation: they cooperate if they think that others will do the same. Several studies have shown that most people function in this way, but their behavior is very sensitive to their beliefs, hence the importance of maintaining their beliefs in equality (or egalitarianism): everyone should cooperate, no one should get preferential treatment. Fehr & Fischbacher (2004) have shown that a small proportion of free riders is enough to cause a breakdown[iii] in cooperation. This probably explains the various injunctive norms around “social distancing”, ensuring that a free-rider is punished in an exemplary manner. Indeed, as Brito et al (1991) point out in relation to vaccines, even if compulsory vaccination is suboptimal, it may be necessary if the proportion of people willing to volunteer is below the threshold necessary for the immunity of the population as a whole.

The case of vaccination

Vaccination is in fact an almost perfect example of this free rider problem, via the notion of herd immunity. The more the rate of immunized people in a group increases, the more the risk for a non-immunized person to meet an infectious person decreases, and beyond a certain threshold (around 80% for most diseases, such as whooping cough, smallpox, polio, etc.), it becomes impossible for the disease to remain in the population and it eventually disappears. For vaccinated contagious diseases, at the collective level, it is desirable that 80% of the population be vaccinated; but if vaccination has significant side effects, it may be rational at the individual level not to wish to be vaccinated.

Two important aspects then come into play: the perception of risk, and the belief in the risk behavior of other members of the community. Having a minority of free riders (say less than 20%), because they think the risks are too great, is not problematic. But if the perception of risk changes, the equilibrium can be disrupted, and group immunity no longer exists. Also, trust in authority is essential, as Charpentier (2020) reminds us.

Herd immunity works through an implicit social contract: those who are medically able to be vaccinated must be vaccinated. The counterpart is that those who do not wish to respect this contract should undertake to ensure that their actions do not entail any additional cost for those who do respect it, in particular by imposing a strong social distancing, by avoiding public places, so as not to contaminate people with weak immune defenses, who are themselves obliged to rely on herd immunity.

Pandemics and their individual responses

As Daniel Kahneman said in Konnikova (2020), « people, certainly including myself, don’t seem to be able to think straight about exponential growth. What we see today are infections that occurred 2 or 3 weeks ago and the deaths today are people who got infected 4 or 5 weeks ago. All of this is I think beyond intuitive human comprehension ». Perhaps the free rider attitude and disregard for social distancing constraints is simply that one does not understand what exponential growth is: one does not really measure the impact of one’s own contagion on the group as a whole. This point was shown in Lammers et al. (2020) using the interpretation of the baseline reproduction number R0 of epidemiological models. The R0 corresponds to the average number of people that a contagious person can infect: it is thus a visualization of the contagiousness of an individual on his surroundings. With an R0 of 1, the pandemic is under control, and the growth is linear. But if it exceeds 1, the growth is exponential. With an R0 of 1.5, 4 people will infect 6 others, who in turn will infect 9 others, etc. In about 15 iterations, 1750 people will be contaminated. With an R0 of 2, these 4 individuals will have contaminated more than 130,000 people (i.e. 75 times more), in about 15 iterations! In other words, while at the level of the specific individual the increase is barely perceptible (he contaminates 2 people instead of 1.5 on average), the collective effect is, on the other hand, extremely important and hardly conceivable.

Figure 1: number of people contaminated after 1, 3, 5, 7, 9 iterations, for different values of R0 (between 1.8 top left and 2.4 bottom right).

Numerous studies in behavioral science have shown that we are more sensitive to a single identifiable person than to an avalanche of numbers. It would then be by example that we could convince each other to cooperate for the common good. The wearing of face masks is interesting because while surveys have shown that a majority of people wear masks to protect themselves, the masks have the primary effect of protecting others from asymptomatic transmission of SARS-CoV-2. It also has the advantage of making the new social norm visible and actively involving all members of the community. By becoming a symbol of solidarity, wearing the mask engages everyone’s cooperation. Conversely, photos of people at the beach or in public parks who do not respect social distancing have probably had a detrimental impact in terms of behavior change.

The debates around tracking apps are another striking example of the difficulty of gaining acceptance for cooperation. As with the mask, they are most often presented as a way of being alerted if one has been in contact with a contaminated person, and therefore as a means of protecting oneself; much more rarely is the possibility of alerting others of one’s own contamination, sometimes a stranger whom one will never be able to alert without the application. Moreover, while they were recommended by many epidemiologists (di Domenico et al. 2020; Ferguson et al. 2020; Ferretti et al. 2020), they were denounced either because they would infringe on personal freedom or because they would present dangers of detour. In an important contribution, experts in cryptography have tried to alert public opinion to the possible malicious uses of these applications; through fifteen or so examples that seek to capture the imagination, it is no longer the stowaway who is put forward as a means of undermining cooperation, but the frankly malicious individual who would seek to harm his or her neighbors (Vuillot et al. 2020).

The place of individual freedom

In the context of vaccination, and more recently on the wearing of masks, the argument of freedom of choice is often put forward by opponents, suggesting that the exercise of freedom was unconstrained. As Frankfurt (2003) notes, most religions limit a person’s behavior to the extent that they act in accordance with the precepts of their God or church. In a more secular context, Jean-Jacques Rousseau asserted that “obedience to the law one has prescribed for oneself is freedom. For the concept of freedom is always accompanied by the notion of responsibility: I am free when two conditions are met. First, I have the capacity to act (or not to act) in a particular way, and second, I accept responsibility for my actions. When I refuse to wear a mask during a pandemic, I accept the first condition but reject the second. In other words, I assert my right to act, or not to act, but I do so in a way that refuses to accept any responsibility for the consequences my actions (or inactions) may bring. As Friedrich Hayek stated, “freedom means not only that a person has the right to choose and bears the burden of his choices, but also that he must bear the consequences of his actions, for which he will be praised or blamed. Freedom and responsibility are inseparable.

Insurance as a collective response?

In the context of health, Wikler (2002) stated that “if people know they are taking risks but accept them as the price of pursuing goals to which they assign higher priority, then it is not the business of public health to insist that health be valued above all”. While this precept may apply to traditional health insurance, it is more difficult to apply to epidemics; as explained above, in contagious diseases, the individual choice to take a risk has repercussions for the rest of the community. Moreover, the insurance logic of covering the risk through mutualization does not work well in the context of an epidemic; we are in the classic case of a systemic risk where individuals and their risks are not independent. In reality, contagion brings to the fore a solidarity of a different kind from that promoted by insurance, as Barry (2020) notes. It is an interdependence where the behavior of one impacts the risk of the other and which requires the cooperation of all to be controlled. To think collectively is therefore ultimately to adopt values of solidarity and cooperation.

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[i] As Skyrms (2004) reminds us, this deer-hunting dilemma is also called the insurance game in game and social choice theory.

[ii] One could also think of the “commons”, which are goods with limited capacity. SARS-CoV-2 has shown that the health system can be saturated, which makes it a rival good.

[iii] Mathematically, this break is interesting because we can then see vaccination as a non-linear set of public goods, as Lim & Zhang (2020) do.


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