nobels

So it's Pinter this year. Well-deserved.

I was reading about Kahneman's work the other day, and have been showing it about ever since as an example of how winning the Nobel prize can just be a matter of expressing obvious truths in elegant ways.

Prospect theory, Kahneman and Tversky's brainchild, has to do with how we make decisions under conditions of risk and uncertainty. It begins with the observation that expected value theory does not explain a lot of real life behaviour - for example, if you walked up to an average person on the street and offered them either (a)$49, or (b) a coin toss where he could win $100 if the coin comes up heads but nothing if it comes up tails, most people would choose (a), this despite the fact that (b) offers the better expected return.

The point: value is not equal to utility - and risky decisions are weighted by the utilities we associate with their various outcomes. Humans have a fairly predictable set of risk attitudes that colour our decisions. We overweight low probabilities and underweight high probabilities; in other words, we are risk seeking for low-probability gains and high-probabiliy losses, and risk averse when we stand a good chance of winning something, or a low probability of losing. On top of this, we are in general loss averse, we need a far greater amount to compensate us when there is the potential that we may lose something we already have.

Thus, the cornerstone of prospect theory is the one equation:

V (x,p) = v(x).w(p)
where v measures the subjective value of the consequence x, and w measures the impact of probability p on the attractiveness of the prospect.

After which you're off to the races. Neat.

A couple of years ago, I had a few conversations with Justin about the wisdom of buying Toto (or any lottery ticket for that matter), and why playing a negative expectation game still felt like it might not be an irrational decision. And -- with no prior knowledge of Kahneman's work -- we constructed, verbally, a pretty good approximation of what (in theory) he would say (i.e. that the utility of having a 1 in 4 million chance of winning 1.5 million dollars can be more than the utility of having 1 dollar, even in a repeated game situation)

It pleases me that we thought of that, and that it's important, and I admire how prospect theory has been constructed because it articulates so cleanly all the ideas about value and utility that have been swimming around in my head for a while now. This has to be the first time a mathematical model has given me a warm tingly feelnig inside. More people need to win Nobel prizes for things like that.