fidesquaerens (marta_bee) wrote,

The Prisoner's Dilemma + Obamacare insurance mandate

Next week, I'm teaching egoism and the Prisoner's Dilemma. Egoism is the theory we should all do what's in our own best interests. Which isn't quite the same as acting selfishly; sometimes it's in our own best interest to have others owe us a favor or to uphold a social institution (like the idea of trust).

The Prisoner's Dilemma basically says that sometimes our best interests are served by doing what's in the common good. Take the following scene from A Beautiful Mind:

Here, Nash realizes that if he and his friends all go after the same woman (that they all fancy), none of them will get her. What's more, they won't even get their second-choice women (the blonde's friends), since "nobody likes being second choice." But if they coordinate their actions, then they'll all get a date for the night - not their first-choice woman, but definitely a better consequence than if they all went for the woman they all wanted. The trick is getting other people to go along, and trust that someone won't trick other people so he can take advantage. (Imagine Nash getting all the people to not go for the blonde, and then swooping in himself.)

Anyway, this has me thinking about healthcare and in particular the insurance mandate. Let me make a few hypothetical assumptions to make things interesting:
  • Assume I could guarantee you that your healthcare costs would be somewhere between $0 and $5,000.
  • Assume these costs are evenly distributed, so you have an equal chance of spending $117 and $4,803.
  • ... but, some years you are guaranteed to have a high health care costs and other years a low cost
  • Assume that the doctors will not treat you (or will provide only minimal care) unless you can pay the full cost of treatment when you get sick or injured.
  • Assume that the cost to you is truly random (i.e., this doesn't cover optional procedures or things related to personal behaviors like smoking).
I know this isn't how healthcare works, but I think it simplifies things to make an important point. Under a system like this, most people would set aside $5,000 at the beginning of the year, because whatever they would spend it on probably isn't worth the chance of needless suffering. Some people might set aside just enough to pick up the slack for whatever "give" they have in their paycheck (what they can afford to spend on an unexpected expense). That money represents lost opportunities, because no rational person is going to invest in a company or buy their kid that new computer at the very real risk of someone breaking an arm and you not being able to afford care for it. You might buy them at the end of the year, but quite often the opportunity would have slipped by or the purchase would be less valuable

Now, say a company comes along and says for $3,500 it will cover whatever healthcare costs you have that year. If you paid for your own health care over any length of time, it should average out at $2,500 but you'd have to set double that aside if you wanted to be sure you'd get coverage you need. Maybe you're not willing to fork over an extra $1,000 just to have control over that $2,500 you had to set aside on the chance you'd get sick. But I'm willing to bet there's some amount you'd be willing to pay this company if it meant having immediate access to that extra $2,500 you had to save but on average wouldn't end up using.

RL is more complicated than this because peoples' health care gets more expensive as they age. So let's say that younger people have a greater chance of spending at the low end of the spectrum, and older people at the high end. I'm imagining something like an equal distribution over a different range for each age: say, between $0 and $5,000 for a 0-10 year old, between $500 and $5,000 for a 11-20 year old, $1,000 and $5,000 for a 21-30 year old, and so on. Now, let's say the company somehow adjusts for this by setting its premium at 60% of the possible costs of health care for the enrollee's age-range. Those are scary words, but what I mean is it would cost $3,000 to enroll at birth but by the time you're my age (21-30) it would cost you $3,400, and by the time you're eighty-three (when your costs range between $4,000 and $5,000) it would cost you $4,600 join up. Also, assume that whatever price you join in at, that's your price your entire life. So if you enroll your three-year-old in with a $3,000/yr premium , he'll still only be paying a $3,000/yr premium when he's an octogenarian. The point here is that kid has been paying into the system throughout his life, subsidizing the older people who had a greater chance than he did of needing more care, and in his twilight years others would be subsidizing him.

Alternately, a much simpler proposal: require everyone to sign up at birth and everyone pays $3,000/yr. Or if you want to eliminate the profit motive, $2,500 (or whatever the midway point is, since you often have less elderly than young people) + whatever your share of the administrative costs is.

Everybody gets sick and we don't generally blame people for being ill or injured (I hope not!). But we do charge those people who are unlucky enough to be sick the cost of their treatment. That strikes me as an unjust way to handle things, personally, since I don't like penalizing people for things that aren't their fault; I'd rather share the costs between the lucky and unlucky alike. But on top of that, it's just not the best system for people to have to set aside more money than they need, year after year. This strikes me as just the kind of situation the Prisoner's Dilemma is made for. We do best by ourselves when we eliminate that waste.

In this particular situation I found a set-up that didn't require everyone enroll. The Thing is, real life isn't nearly this neat. Over the last few years I've heard a lot of people say it isn't fair to require young people who don't need health insurance to buy a service they won't use. The thing is, everyone uses healthcare (to varying degrees, and at varying times), and we have no way of knowing how much until we actually need it - so the more people who wait until they get sick to buy insurance, the more it costs and the less benefit there is to it.

It's not exactly the Prisoner's Dilemma, but it has the same basic point, I think: sometimes, the best way to do what's best for you is to set up a system that benefits everyone. I know, this is a rather dry, logical post with lots of numbers and not the emotional appeals you usually get with health care reform. But it's a point worth thinking about, I think.

(Btw: I'm a mathematician, not an economist or accountant. Or a health care provider. Those numbers may not reflect reality as much as I'd like. But my guess is, even if the math isn't so neat, there's still an advantage to only paying the average [or near the average] cost of health care rather than setting aside the maximum you think you'd possibly need.)    

(Btw #2: This in no way props up the existing insurance mandate. It may infringe on freedom or just be a badly structured law. My point is philosophical: it's in a healthy young person's best self-interest to have everyone paying into a health-insurance system of some kind he'll come to rely on more and more, rather than only joining in when he needs it.)
Tags: philosophy, politics, wonkery
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