Gaming America: the philosophy and math behind choices we make

It's been said before, and it'll be said again, but the USA is a remarkably paternalistic nation. We have this idea, right now, that instead of doing what the Iraqis want us to do (leave), we must instead do the thing which is best for them, even in circumstances where no one knows what that thing may be. I started thinking about this yesterday while reading a philosophy paper on game theory, and it occurred to me that what America is facing right now is an optimization problem. Optimization problems in game and decision theory literature are most often solved with equations that weigh participants' beliefs against foreseen possible outcomes. This is an elegant way of addressing such problems, and it has produced a number of fascinating insights into human behavior in game situations, but it has an acknowledged fault: one cannot calculate the potential utility of an outcome that is vague or indeterminate. And that is the dilemma that America presently faces. We are trying to weigh the incalculable utility of a vague outcome (what might happen if we withdraw troops from Iraq) against the calculable utility of a known outcome (what happens if we leave troops in Iraq).

Why would I call the outcome of withdrawal vague? Well, it might help first to talk about what an un-vague, or defined, utility value would be. A defined utility is a utility that can be assigned numerical value, or assigned to a range of numerical values. An example is in order. Suppose I have an envelope in one hand that contains $10, and an identical envelope in the other that contains no money. If I ask my friend Jane to assign a value to the envelope in my right hand, according to decision theory the unopened envelope is worth $5, because Jane knows there is a 1/2 certainty that it contains $10. Once the envelope is opened, it will either be worth $10 or no money, and there is no outcome on which it will be worth $5, but while it remains unopened, its expected value is $5. Another way of looking at the question is to ask Jane how much she would pay for the unopened envelope in my right hand. Her expected answer would be $5, which is the value that balances her negative risk (the amount she loses if the envelope is empty) with her potential gain (the amount she wins if the envelope contains money). Jane's preferences can be converted to percentages easily: there is a 50% chance that she should prefer the envelope in the right hand. In this highly simplified situation, Jane can assign a defined value to the expected utility of the envelopes. A 'vague' or 'indeterminate' utility is one which cannot be evaluated in that manner. For example, the Jane situation would become vague if I informed Jane that there was no money in one envelope and some money in the other envelope, then asked her how mush she would pay. She cannot make an educated guess about how much to pay, because she doesn't know the expected value of the second envelope.

Much in the same way, no one knows what will happen if we withdraw troops. It seems likely that Iraq would fracture, but along what fault lines no one is certain. The resulting power struggles might leave Iran in power across large parts of the Iraqi oilfield, or it might not. The end result might be favorable for the US, or it might not. If zero represents the status quo and one represents the best possible outcome of withdrawal, it's impossible to assign a number or range of numbers that encompasses the 'most likely' outcome of withdrawal, because there is no 'most likely set of outcomes'. Since there is no 'most likely outcome', the value of withdrawal is indeterminate, and the choice between the status quo and withdrawal weighs a known option against an unknown option. The choice is "vague," as the philosophical jargon goes. At this point in time, most Democrats in Congress believe that the expected value of some sort of withdrawal plan is higher than that of the status quo, while most Republicans believe the opposite. Because of the vagueness involved, however, there is no truely 'rational' decision to be made, and this is the root of the dilemma in which the nation currently finds itself.

What in the world does this have to do with Christianity, one might well ask. Well, the answer is that it explains other political-religious divides in our nation. If one is a fundamentalist Christian, the expected utility of heaven is infinitely high. There is no decision on which the 'do this and go to heaven' outcome is not better that any other situation. This is the root of all moral absolutism. If there is a set of rules and one believes that they are inflexible (ie, if one believes that the word of God is infallible), then there is no higher expected utility to be found than in following those rules exactly and getting the expected outcome from them: heaven. This is why the religious right campaigns so hard on issues like abortion. The amount of utility that can be expected from the ease gained in a prospective mother's life by aborting a child (even if that is a large amount of utility, since the mother won't have financial troubles in the future, can get an education, won't be forced into a marriage to the child's father, etc) is trumped by the expected utility of going to heaven. An envelope containing the benefits of the abortion will never be more utile than an envelope containing heaven, so our hypothetical Christian will assert for the person's own good that getting the abortion is categorically wrong.

The flaw in this reasoning is the assumption that the rules are absolute. This game only plays out correctly if one assumes that changing social times don't affect what is morally right. If changing social times do somehow affect what is morally correct, then the expected value of getting the abortion increases dramatically, because there is a chance that the abortion envelope will outweigh the heaven one (benefits of abortion+heaven > just heaven). There is no certainty about the will of God, however, in this situation, so the game becomes much like the one that America is currently playing over Iraq. Maybe morality in this particular social climate will be conducive to abortions, and maybe it won't, but if the rules are uncertain there's no sure way to know the value of that envelope. Maybe withdrawal from Iraq will end favorably for America, and maybe it won't, but since the future is uncertin there's no sure way to know the value of that envelope either.

In situations of vague or indeterminate values, like the Iraq war or the question of morality if one believes that the scripture is not completely inerrant, there is no 'right' answer in decision theory. All that the math prescribes is that we all consult our moral intuitions and do as we personally see fit, with the understanding that we may well be making the wrong choice. The real problem arises when, as now with Iraq, people refuse to make the choice at all. As we refuse to make the choice, the expected utility for both options decreases. Sometimes it's better to commit to an indeterminate future than to not commit at all.


Note: the Stanford Encyclopedia of Philosophy will explain game theory more rigorously than I did here, if you're interested. It's a field that intersects economics, mathematics, and philosophy, and it's very worth learning about.