Sunday, March 13, 2011

Definition of Rationality

Many think irrationality is when people make a decision that with hindsight was really dumb, like making a bad investment. A good definition of rationality I found in Gilboa and Schmeidler's nifty treatise A Theory of Case-Based Decisions:

An action, or sequence of actions is rational for a decision maker if, when the decision maker is confronted with an analysis of the decisions involved, but with no additional information, she does not regret her choices.

Stated differently, a decision is rational if it is immune to logical introspection, but no new or different assumptions. Thus, you could show someone not following Bayes's rule they are wrong in real time if all they understood was logic, which is independent of empirical data. People who think 'shy librarians' are more common than 'librarians' are thinking irrationally, whereas people who think tax cuts are good/bad for the economy are rational as long as they understand how their assumptions relate to their conclusion.

Many of Kahneman and Tversky's famous behavioral biases are not robust to instrospection, and people realize that anchoring, framing, and representativeness biases are 'wrong', and thus change their opinions upon learning about their errors.

Interestingly, this implies that bees, lions, babies or morons can never be rational, because they don't understand logic, their instincts simply dominate in certain cases. But that's not most people, so if an educated group of adults believes something, and defends their beliefs vigorously, it's rational even if it's wrong.

You could not show people that NINJA loans were toxic back in 2003--there were academic conferences that basically all agreed Alicia Munell was right and Stan Liebowitz was wrong, so smart people all agreed that the historical data showed trivial mortgage risk from such changes (See Papademetriou and Ray, 2004, which highlights no doc, teaser rate, low down payment loans as efficient and just). We now know they were wrong, but the point is, they argued about this in academic journals, and they all agreed previous underwriting standards were discriminatory. Thus, it wasn't irrational, just wrong.

That's important, because it's trivial to prevent irrational bubbles, but rational ones are by definition immune to greater examination.


Eccdogg said...

This is a very good definition. I find that irrationality is often undefined in discussions of behaivor and ends up standing in for "I disagree with the action that was taken"

By this definition markets can seldom be "irrational". There is nothing irrational about the S&P 500 trading at a 30 P/E because there is no god given value that a stock is worth.

To me markets can only be irrational when there exist arbitrage opportunities and these are exceedingly rare and fleeting.

Even the low volatility higher return relationship cannot be said to be irrational. There is no law that says that people in general can't like lower return lottery tickets over over higher return boring stocks.

Mercury said...

By the same token and with full hindsight you could also argue that discriminatory lending, although ethically wrong, was both rational and right from a risk management perspective.

I'd like to see what exactly this "controlling for the probability of and costs of default and for loan and personal characteristics" involved in these reports.

Also, I understand that "red lining" is the practice of geographical discrimination as a proxy for ethnic/racial discrimination but were banks actively discriminating against ethnic individuals outside these zones? I took out a mortgage around 2000 and I'm pretty sure the loan was approved before anyone ever laid eyes on my skin tone.

Patrick R. Sullivan said...

'...discriminatory lending, although ethically wrong....'

Why is that? What's wrong with choosing to whom you lend YOUR money on YOUR standards?

Mercury said...

Well for the purpose of this discussion of rational actors the relevant point is that discriminatory lending was illegal and its real or perceived practice was no longer a viable option.

Adam Bell said...

Surely this definition of rationality implies that every decision is rational? The 'additional information' qualifier removes the possibility of post-hoc opinion changes from the demonstration of incorrect assumptions, as in your 'behavioural biases' example.

In fact, this definition actually contains another definition within it. 'Analysis' can only refer to the use of reason to unpack decisions, about which one will have to make decisions. Analysis requires decision-making about the mode of analysis, leading - I would expect - to an infinite regress.

Patrick R. Sullivan said...

Mercury, you also said:

'...although ethically wrong, was both rational and right from a risk management perspective.'

Now you've introduced 'illegality', which is a new argument altogether. And, frankly doesn't make much sense, as illegal and unethical aren't synonyms.