The Optimal Free Rider Problem

It occurred to me this morning that the optimal state of compliance with many programs is not 100%. Society is better off, in essence, with some free riders.

Take vaccines. Immunity is good. Herd immunity is good. Herd immunity in general goes up as vaccination rates go up, but by its very nature, herd immunity does not require 100% vaccination.

But vaccines also have side effects; there are people who, for medical reasons, probably shouldn’t have vaccines.

Let’s take measles, an unpleasant and highly contagious disease. A vaccination rate of 90-95% is required to achieve herd immunity against measles–let’s just play it safe and say 95%.

Since every vaccine (and medications generally) carries some risk of side effects, that last 5% of people is not necessarily any better off getting the vaccine than not getting it. In fact, if they can coast along on herd immunity without taking any of the risk of vaccine side effects, they are personally better off. From a herd standpoint, there’s no point in spending resources on unneeded vaccines, finding the last few non-compliant people, or killing people with compromised immune systems who can’t handle vaccination–beyond 95%, these activities may be lowering the herd’s collective health, not raising it.

Of course, this opens a Prisoners’ Dilemma-type situation: Everyone would like to enjoy more herd immunity with less personal risk of vaccine side effects (not to mention cost, inconvenience, etc), which means everyone has an incentive to defect, claim a medical exemption, and let everyone else take the jab for them.

If too many people start claiming exemptions, of course, herd immunity breaks down. People claiming religious, ethical, or “I just don’t want to have vaccines” exemptions aren’t really in the former category of people whose health would be actually harmed by vaccines. Some of them might still fit in that 5%, but beyond that, we have a problem.

Then society starts cracking down on the freeloaders. This leads to “policies,” procedures, gate keepers, and red tape. Now people who actually shouldn’t get vaccines have to go through a bunch of trouble to prove they aren’t freeloaders, and people are generally shamed for non-vaccination.

Parking spots are another case where a few freeloaders is probably optimal.

Most parking lots set aside a few spaces for the disabled, but most of the time, these spaces are not completely filled. There are usually a few empty spaces that could be optimally allocated to people in a special hurry, making deliveries, pregnant women, people nervous about crime at night, etc.

Of course, if more than one or two people cheat, then very quickly we don’t have any disabled parking spots, so there’s a lot of social pressure on people not to abuse the disabled parking.

Disabled assistance animals are also exceptions to a general rule. We usually declare that dogs and other animals aren’t allowed inside places like grocery stores and restaurants for hygienic reasons/other people’s allergies, but 100% compliance with the “no dogs” rule isn’t optimal. We make exceptions for seeing eye dogs because obviously everyone is better off with blind people being able to get around town and buy food. The general category of assistance animal has been expanded to include other useful abilities, like hearing dogs for the deaf and mobility for people in wheelchairs.

These are clear-cut cases, but the water becomes muddier when we enter the realm of psychiatric or emotional assistance animals. Does someone with PTSD who disappears under a car every time there’s a loud noise need an assist animal? What about a child with autism who will be much quieter and calmer on a plane if his dog is there? How about an anxious older woman who feels calmer with her cat?

At some point we run into the fact that most pet owners have a pet in the first place because it makes them happy. Many people would be happier or less anxious with their pet with them (or at least think they would). 

Allowing a broadened definition of self-declared assist animals leads quickly down a path to someone’s “emotional support pitbull” mauling a five year old at the airport:

The traumatic incident for the young girl is just one of numerous high-profile allegations of bad support-animal behavior at airports as airlines and the federal government have scrambled to respond to a growing pile of complaints, ranging from poor potty training to nasty bites.

The episodes have proliferated over the past two years, fueling a debate over how the animals should be regulated while traveling. In June 2017, a 70-pound emotional support dog bit a man in the face just as he sat down in his window seat on a Delta Air Lines flight departing Atlanta, leaving him with 28 stitches. In February 2018, another emotional support dog chomped at a little girl’s forehead on a Southwest Airlines flight departing Phoenix, leaving her with only a scrape but causing panic.

In Gabriella’s case, she had to undergo tear-duct surgery, leaving her with permanent scars, her attorney, Chad Stavley, told The Washington Post. The pit bull severed her tear duct and disfigured her upper lip, leaving a chunk of it missing, according to a graphic photo of her injuries provided by Stavley. …

All of these bad incidents amount to businesses and lawmakers cracking down on “support” animals and passing stricter laws about which ones qualify–in other words, people who have a legitimate need for real support animals get inconvenienced because of people taking advantage of the system.

Firefighting is another case where there’s probably an optimal number of free riders–not in the fighting of fires, but in the paying taxes to pay the firefighters. Suppose a system where everyone pays their taxes to the fire department and the department puts out all fires: good. But some people are poor and don’t have any money for taxes. Even if we don’t care about their houses, their neighbors do, and their neighbors don’t want fire jumping from their houses to the houses of taxpayers. It makes sense for the fire department to put out all of the fires, even of people who haven’t paid. But if people can get their fires put out without paying, there stops being any incentive to pay the fire tax, and soon the fire department can’t afford trucks.

These cases suggest an overall pattern: First, a rule that needs to be nearly universally followed. Second, a few legitimate exceptions that people generally recognize. Third, too many people taking advantage of the exceptions. Fourth, increased institutional/legal rigidity in an attempt to define just who exactly gets the exceptions.

A hopeful note on ability distributions

I read recently (my apologies, I can’t find the link) that in every country where we have reliable testing data, a consistent pattern emerges: girls tend to do slightly better on reading/writing tasks than mathematical tasks, and boys slightly better on mathematical than language-tasks.

This is an interesting dynamic because it creates different “optimal” outcomes depending on what you are trying to optimize for. 

If you optimize for individual achievement–that is, get each student to go into the field where they, personally, can do the best–the vast majority of girls will go into language-related fields and the vast majority of boys will go into math-based fields. This leaves us with a strongly gender-divided workforce.

But if we optimize instead for getting talented people into a particular field, the gender divide would be narrower. Most smart students are good at both math and language, and could excel in either domain. You could easily have a case where the best mathematician in a class is even more talented in language, or where the most verbally talented person is even more talented at mathematical tasks (but not both at once).

If we let people chose the careers that best suit them, some fields may end up sub-optimally filled because talented people go elsewhere. If we push people into particular fields, some people will end up sub-optimally employed, because they could have done a better job elsewhere.

Relatedly, we find that people show more gendered job preferences in developed countries, and less gendered preferences in undeveloped countries. In Norway, women show a pretty strong preference, on average, for careers involving people or language skills, while in the third world, they show a stronger preference for “masculine” jobs involving math, science, or technical skills. This finding is potentially explained by different countries offering different job opportunities. In Norway, there are lots of cushy jobs, and people feel comfortable pursuing whatever makes them happy or they’re good at. In the third world, technical skills are valued and thus these jobs pay well and people strive to get them.

People often ascribe the gender balance in different jobs to nefarious social forces (ie, sexism,) but it is possible that they are an entirely mundane side effect of people just having the wealth and opportunity to pursue careers in the things they are best at.