Herd Immunity, Vaccination, and the Law

The Holy Grail in the vaccine world is to achieve what is known as “herd immunity.” This describes the point at which the majority of a population is immune to a particular illness. Once herd immunity is achieved, the risk of further spread of the disease is minimized, because there are fewer transmission points (i.e., nonimmune individuals) by which the virus can spread.^{Footnote 2} Achieving herd immunity helps to protect vulnerable members of the population who cannot be vaccinated, such as infants and individuals with certain health issues.

The percentage of the population that needs to be vaccinated for herd immunity to obtain varies, depending on the illness. In most cases, herd immunity obtains when at least 90% of the population is vaccinated against an illness. In order to achieve herd immunity from the measles, which is highly contagious, 96%–99%^{Footnote 3} of the population needs to be vaccinated. The World Health Organization (WHO) estimates that the United States national average for vaccination against the measles is 91%.^{Footnote 4} In 2013–2014, 92.3% of kindergarten children in California were vaccinated with the vaccine against measles—the MMR (measles-mumps-rubella) vaccine.^{Footnote 5} A recent analysis of the data from the Disneyland-linked measles outbreak revealed an estimated vaccination rate of 50% to 86% among those exposed to the illness.^{Footnote 6} It is thus clear that vaccination levels are lower than would be desirable to guarantee herd immunity against the measles. What is not clear is what should be done about this.

The debate over mandatory vaccination is a heated one, often characterized as one between science and its opponents. Antivaccinators are often characterized as selfish, ill-informed, and irrational. And, although many of the claims on which the antivaccine movement rests are arguably without scientific credibility,^{Footnote 7} it is not true that vaccines carry with them no risk, and there remains a legitimate question about the extent to which the state can interfere with people’s choices to vaccinate. On the one hand, if fewer people are vaccinated, herd immunity drops, and this puts everyone at risk. On the other hand, it is desirable for coercive measures to be kept to a minimum whenever possible. Thus, it would be best if compliance with vaccination requirements could be secured voluntarily.

Securing Voluntary Compliance

To see if and how voluntary vaccine compliance might be achieved, consider the following. Parent A is deciding whether to have her children vaccinated against the measles. Factors relevant to her decision may include the following: (1) the risk associated with the vaccine, (2) the effectiveness of the vaccine in protecting against the measles, (3) the risk of contracting the measles without the vaccine, and (4) the risk of complications arising from the measles.

The antivaccine movement tends to latch on to the first factor concerning vaccine safety and has been fueled largely by the (discredited^{Footnote 8}) link drawn between the MMR vaccine and autism. Research concerning parental attitudes toward vaccination reveals that parents may also deem vaccination unnecessary, either because they assign a low probability to the possibility of their children contracting the disease or because they believe they can control whether their children are exposed to the disease.^{Footnote 9} The legacy of successful vaccination programs is that the dangers of illnesses like the measles are unfamiliar to parents and risks of exposure and complications may be perceived as low.

Insofar as these factors impede achieving herd immunity, one strategy to boost voluntary vaccination compliance would be through public health efforts designed to educate parents about the risks and benefits of vaccination and the dangers of contracting the measles. However, it is not clear that such education programs will be sufficient, for two reasons. First, there is little empirical evidence that parental attitudes can be changed through public education efforts. Although there is a growing literature concerning reasons for parental refusal of vaccination, there remains surprisingly little data on which interventions are most effective in reversing vaccination refusal.^{Footnote 10} Furthermore, the data that do exist suggest that parental attitudes concerning vaccination are not readily changeable. A recent American study of vaccine promotion revealed that education about vaccination tends not to influence parents to choose to vaccinate and, in fact, often has the opposite effect.^{Footnote 11}

Second, educational efforts may not address all relevant factors involved in parents’ decisions to vaccinate their children. Indeed, it is the third factor named previously—the risk of an unvaccinated individual contracting the measles—that is especially problematic. More specifically, the facts that (1) the risk of contracting the measles is dependent on herd immunity and that (2) herd immunity is dependent, largely, on whether other parents choose to vaccinate their children pose a serious challenge to securing voluntary vaccination compliance.

Game Theory and Vaccination

The interdependence of parental choices to vaccinate (that is, the fact that one parent’s choice to vaccinate will be influenced by the choice of another, and vice versa) sets the stage for a game-theoretic analysis of those choices.^{Footnote 12} Game theory is the study of strategic interaction among rational individuals. The players in the game are taken to be ideally rational, where this is usually understood to mean they are expected utility maximizers. In a strategic choice situation involving two or more rational players, an individual will choose on the basis of what she expects her opponent(s) to do: her action will constitute a best reply to the action she anticipates the other player(s) will choose.

Consider Parent A’s decision whether to vaccinate her children against the measles with the MMR vaccine. Assume, for the sake of the argument, that the MMR vaccine is 100% effective^{Footnote 13} at guarding against the measles; that when more than 96% of the population vaccinates their children, herd immunity is achieved; that wherever there is herd immunity there is a 0% chance of contracting the measles; that when less than 96% of the population vaccinates their children, there is no herd immunity; and that where there is no herd immunity the chance of contracting the measles is 100%.

The matrix in Table 1 represents Parent A’s choice situation, where “benefit” stands for the benefit of immunity from the measles, “cost” for the myriad costs associated with vaccination, and “measles” represents harms associated with contracting the measles.

Table 1.

Parent A’s Choice Situation

Parent A can choose between two strategies: “vaccinate” or “don’t vaccinate.” The first column of the matrix represents Parent A’s choice situation when there is herd immunity. In such a case, the option to vaccinate carries with it both the benefit of immunity from vaccination and the costs of vaccination. This cost can range from the inconvenience of going to the doctor to obtain the vaccine or more serious side effects associated with the vaccine. Importantly, however, when there is herd immunity, the individual benefit of immunity obtains regardless of whether Parent A vaccinates, because protection against the measles is already achieved by the efforts of the 96% of the population who vaccinate their children. Because, in this scenario, “don’t vaccinate” imposes no cost to Parent A but permits enjoyment of the benefit of herd immunity, Parent A should choose “don’t vaccinate.” In so doing, Parent A will be free riding off of the efforts of the 96%—enjoying the benefits of herd immunity from vaccination without bearing any of the costs associated with vaccinating.

The second column in the matrix represents Parent A’s choice where there is no herd immunity. Here “vaccinate” carries with it the same costs as before but confers the benefit of immunization that would otherwise be unavailable. If a parent chooses the option “don’t vaccinate,” she and her children avoid the costs associated with vaccinating, but the children face the potential harms associated with contracting the measles. Her choice to vaccinate in this situation then depends on whether the potential harms associated with the measles are greater than the costs associated with vaccination.

In this matrix, when 96% of the population vaccinates, Parent A, insofar as she is rational, will reason to the conclusion that it is to her advantage to refrain from vaccinating. That way she could enjoy the benefits of herd immunity without bearing any of the costs associated with receiving the vaccine. This is a free rider temptation. Thus, the basic logic in the case of vaccines is this. If a sufficient number of others get vaccinated, then everyone will be better off. But it would be best for any particular individual if all others got vaccinated and he or she did not. The trouble is that if everyone thought that way, no one would become vaccinated. There would be no herd immunity, and everyone would be at risk of falling ill.

In this picture of vaccination as a collective action problem, it emerges that public education about the safety and efficacy of vaccination is of limited value in encouraging parents to vaccinate their children. Until the threshold for herd immunity is met, all unvaccinated individuals are at risk of contracting the measles, and education can show parents that on a simple cost-benefit analysis they should vaccinate their children. However, once herd immunity is achieved, it is rational for parents to refrain from vaccinating their children, and no amount of education about the risks and benefits of vaccination can show otherwise.

Policy and Free Riders

Ensuring that populations are adequately protected against vaccine-preventable illnesses like the measles requires a means to both achieve and maintain herd immunity. One policy option is to continue with efforts at education about the risks and potential benefits of vaccination, but allow the exemption of conscience (i.e., for philosophical and religious reasons) and otherwise take no measures that go beyond the voluntary. That would preserve individual freedom (keeping antivaccinators happy) and may help to achieve herd immunity but would do nothing to maintain it once it is achieved. The likely result would be occasional measles outbreaks like the one that started in California. But this still leaves open the possibility of free riding, and there are good reasons to close that opportunity. First, eliminating free riding ensures that no one takes unfair advantage of the collective efforts of others, and everyone shares in the burden. Second, permitting free riding increases the risk of infection in the community and thus puts vulnerable members of the population—those who, for medical reasons, cannot be immunized—at risk of contracting the illness. Finally, the risks of measles for anyone should not be minimized. Although there have been no measles-related deaths reported to date in 2015 in the United States, from a global perspective there has been significant mortality over the years. For example, in 2013, there were 145,700 measles-related deaths worldwide.^{Footnote 14} Meanwhile, the WHO has estimated that vaccination prevented 15.6 million measles-related deaths between 2000 and 2013.^{Footnote 15} There are also (often serious) complications that accompany the measles, such as hearing loss, respiratory infections such as pneumonia, and encephalitis.^{Footnote 16}

An alternative, or possible supplement, to educational efforts would be to appeal to the common good in order to encourage vaccination. The free rider problem emerges because of a tension between individual self-interest and the good of the collective. If that tension could be resolved, then the problem would disappear. So if people can be encouraged to care about the welfare of the collective rather than just their own (or that of their children), then vaccination may be achievable without the use of force. But to the extent that parents are concerned with their own children’s welfare and not necessarily the common good (or the welfare of other people’s children), and to the extent that such concerns are not always readily changeable, appealing to those elements will prove ineffective. Add to this equation a risk of serious side effects from vaccinating one’s own children, and appeals to the collective good will quickly lose force.

This suggests that heavier-handed interventions may be needed to ensure vaccination compliance. Such measures are common in other policy fields. Take, for example, littering. Although it is best for everyone if people refrain from littering in the streets, an individual person’s small contribution of litter makes minimal difference to the cleanliness of her city’s streets. There is a temptation to free ride. But if everyone reasons this way, no one will use a trashcan, and the city’s streets will become full of litter. Because self-interest will not guarantee clean streets, and because appeals to the common good of keeping the city’s streets clean sometime prove ineffective, fines are implemented for littering.

Following this logic, we might say that similarly heavy-handed interventions may be needed in the case of vaccines. At the extreme end of the spectrum of such measures would be forced vaccination—administering vaccination against the will of parents or children. But to the extent that public policy should aim at the mildest measure possible to produce the desired result, such an intervention should be a last resort, and milder measures should be tried first.

California’s proposed legislation is one such measure. To be sure, it does have disadvantages. It runs the risk that parents who remain opposed to vaccination will remove their children from the school system instead of complying with mandates. The alternative to public or private schooling is home schooling. If unvaccinated children are homeschooled together, this may jeopardize herd immunity, especially given clustering effects, whereby unvaccinated individuals tend to pool together, which increases the probability of a disease outbreak.^{Footnote 17} Furthermore, this alternative runs the danger of disadvantaging the unvaccinated children by depriving them of an education to which they are entitled. Children who are homeschooled may also be deprived of socialization that they would receive in the school system.

There are alternatives to California’s proposed legislation. Australia, for example, has recently announced its “no jab, no pay” policy, which prevents parents who refuse vaccination for philosophical or religious reasons from receiving annual tax and childcare benefits.^{Footnote 18} The benefits forgone by parents who refuse immunization may amount to as much as $11,000 per child.^{Footnote 19} Whether this intervention will be effective in boosting vaccination compliance is yet to be seen. However, independently of its effectiveness, the main drawback to Australia’s policy—or, for that matter, to any kind of intervention that relies on economic incentives to generate the desired result—is that it privileges those who can afford to forgo the state-sponsored financial benefit. Consequently, the burdens of securing the public good of herd immunity may not be equally shared across the population because of disparities in wealth. The rich can free ride off of the efforts of the poor.