Wednesday, 8 November 2017

Here's Someone Who Should Know Better!

Having once read Daniel Kahneman's very good book "Thinking, Fast and Slow", and being no stranger to Thomas Nagel (you know Thomas Nagel, the writer of the hugely famous "What Is It Like To Be a Bat?" essay), I was interested to stumble on Nagel's review of the book here.

It's generally a good review, but what struck me from Nagel's review is the bit where he gets on to economics, and in that section makes the audacious claim that a 10% chance of $1,000 is better than a 50% chance of $150. This is a basic GCSE-type error Nagel is making, because one of the quintessential tenets of economics is that we don't get to say what other people value, we let their own decisions provide the signals.

Mathematically it's certainly true that the value of such choices is possible outcomes x probabilities, and economics doesn't disagree with that. But there are no grounds in economics for claiming that a 10% chance of $1,000 is better than a 50% chance of $150, because 'better' depends entirely on the individual's trade off of expected value when measured against the risk.

If Betty is pretty well off and has no disposable income issues she might well prefer a 10% chance of $1,000, in the knowledge that she can treat herself to something nice if she wins, but not worry at all if she doesn't. On the other hand, Joan, who is struggling to pay her food bill this month would be well advised to go for the 50% chance of $150 rather than just 10% chance of $1,000, as the higher probability of $150 is of much more immediate value to her. This is basic stuff, and Nagel should know better.

What Nagel is missing, so it would appear, is that in economics rational expectations theory is not the same as expected utility theory - even though he is talking about them in the same breath. Expected utility deals with already extant probabilities, whereas rational expectations are about decisions and outcomes where interaction generates probabilities and explains why they are so.

The above decision regarding the money is not about expected utility, it is about a forecast of value measured against risk. For that reason, it would not be at all unnatural for two different people to be faced with the same probabilistic circumstances, yet perfectly rationally opt for different risks, based on the immediacy of their need.