How Two People’s Rights Can Do Both People Wrong: Vaccines & (Anti-)Social Choice Theory

Vaccination, both in terms of its social good and the role of government in securing that social good while respecting individual liberty, has been a hot topic lately.  In fact, it’s gone viral. (HAHAHAHA.  Sorry.)  In this short post, I link the debate about vaccination, liberty, and social welfare, with the work of Amartya Sen, a preeminent social choice theorist who won the 1998 Nobel Memorial Prize in Economic Sciences.

The Vaccination Paradox. Suppose that—due to there only being one dose of the measles vaccine available—two families, A and B, each with a single child, a and b, are confronted with choosing which child (if any) to vaccinate against measles.  The choices are “a: vaccinate child a,” “b: vaccinate child b,” “n: vaccinate neither child.”

Family would prefer that child b get vaccinated because child a has a compromised immune system, but would prefer that child a get vaccinated rather than neither child gets vaccinated.  In other words, Family A‘s preference over the three outcomes is:

b > a > n.

Due to personal beliefs, Family B is opposed to vaccination for anyone, but due to child a‘s situation, prefers that child b get vaccinated rather than child a.  Thus, Family B’s preference over the three outcomes is:

n > b > a.

Now, suppose that a government agency is tasked with choosing whether to vaccinate a child and, if so, which one.  Furthermore, suppose that the government agency is required to respect the families’ wishes with respect to their own children.  That is, if either family prefers having nobody vaccinated to having their own child vaccinated, then their child is not vaccinated (i.e., the government agency is required to grant an “opt-out” exemption to each family).

What would the result be?  The opt-out exemption requirement implies that Family A is decisive with respect to a versus n, so that n will not occur: child a will be vaccinated if child b is not.  Similarly, Family B is decisive with respect to b versus n, so that b will not occur: child b will not be vaccinated. Accordingly, because the government agency can not choose n, and it can not choose b, it must choose a.  Because the government agency is required to respect individual rights to opt-out, child a will receive the vaccine.

Okay.  But, wait… the government agency has (implicitly) ranked the three possible vaccination choices as

a >> n >> b,

so that in spite of both families agreeing that they prefer that child b be vaccinated rather than child a:

b > a,

The government agency—because it is respecting individual rights—must vaccinate child a instead of child b.

This is an example of the Liberal Paradox (or Sen’s Paradox), which states that no policymaking system can simultaneously

  1. be committed to individual rights and
  2. guarantee Pareto efficiency.

This paradox is at the heart of a surprising number of political/social conundrums. One basic reason it emerges is that individual rights are in a sense absolute and not conditioned on the preferences of others.  That is, if Families A and B could somehow write a binding contract and Family B knew/believed Family A‘s preferences, then Family B would agree to sign away their right to decline the vaccination for child b.

I’ll leave this here, but my limited take-away point is this: individual rights are important, but even in situation in which their definition seems straightforward, there’s no free lunch here: individual rights invariably come into conflict with social welfare.  That’s not saying that individual rights should be sacrificed, of course.  But it is saying that preserving individual rights does not always maximize social welfare.