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Wednesday 19 December 2012

Experience, Rare Events and Risky Choice

Choice, Education and Experience

Decision making, the challenge of choice, is often discussed as though it’s a single, invariant type of event.  Perhaps this is most strongly presented in the idea of stable preferences, the idea that if we choose to eat the fish at a restaurant one day then we should choose it the next day as well, always assuming we liked it.  People don’t actually behave like this, and decision making is much more complex than economics often makes out.

However, we can roughly divide our choice processes into two – decisions we make from personal experience and decisions we make from education.  We may invest in banks because we've had a good experience doing so, but we may choose to limit our investments based on third-party knowledge that financial institutions are inherently risky.  But how we decide which model to follow can change the course of our lives; and certainly determine the health of our wealth.

The Prospect of Choice

The cornerstone of behavioral economics is Prospect Theory, which applied weightings to the traditional expected-utility models of standard economics.  We've looked at the historical development of this a few times, but we can recap quickly (and if you want a fuller treatment you’ll need to go to the sourced articles).

As we saw in Utility, the Deus Ex-machina of Economics the key to modern economic theory is the idea that people make rational choices – and the definition of rational choice goes way back to discussions between Blaise Pascal and Pierre Fermat in the seventeenth century.  In essence this argues that people should always choose the option that maximizes their expected return, a definition based in probability theory.  However, in the St Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price. 

However, this is a statement about probabilities - we may be likely to win, but we're not certain to and this uncertainty means that people won't enter the game once the entry fee is above a certain price.  The point is that people don’t really make rational assessments based on probability – there comes a point when the possibility of losing your winnings, even if the probability is low, is too great to be willing to take the chance.  Daniel Bernoulli’s solution to the problem was the idea of expected utility, a subjective form of expected value.  A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.

Risk and Uncertainty

The idea of expected utility became the central principle of modern economics in the twentieth century but started to run into serious problems when a series of experiments showed that people violated the underlying axioms – so issues such as the Allias Paradox and the Ellsburg Ambiguity Paradox showed that peoples’ choices choices are not independent of the other options available to us (see: Ambiguity Aversion: Investing Under Conditions of Uncertainty).  Choice is affected by uncertainty: people prefer a defined risk to an undefined one.  

This problem was solved in Prospect Theory by Tversky and Kahneman who argued from experimental evidence that people underweight large probability events and overweight small probability ones.  By weighting the probabilities associated with such events Prospect Theory retains the core of Daniel Bernoulli’s great idea of subjective expected utility: and this modification rescued economics by providing an explanation for the various paradoxes that were otherwise so difficult to explain.

All then is well, you would think, in the world of modern economics.  Behavioral psychology has been enlisted to rescue the concept of expected utility and provides an integrated theory for us all to move forward with.  Well, that’s the idea.  However, as we saw in Behavioral Finance’s Smoking Gun, it's possible to set up experiments in a way that shows violations of Prospect Theory – situations where people underweight small probability events rather than overweighting them, for instance.

Experience and Choice

This is a puzzle and one that potentially undermines the whole concept of subjective utility – which would also undermine Prospect Theory and the traditional approach to behavioral economics.  Gerd Gigerenzer has suggested that this can be explained by abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic.  Instead he argues that we should focus on how the brain actually makes decisions.

As an example, Hertwig, Barron, Weber and Erev in Decisions From Experience and the Effect of Rare Events in Risky Choice argue that the inversion of the weighting of small probability events can be explained by looking at how people learn about the likelihood of the occurrence of rare events:
“Decisions from experience and decisions from description can lead to dramatically different choice behavior. In the case of decisions from description, people make choices as if they overweight the probability of rare events, as described by prospect theory. We found that in the case of decisions from experience, in contrast, people make choices as if they underweight the probability of rare events”.
So, for example, if your experience of investing is twenty years of happy share price rises you’ll likely underestimate the chance of a market calamity.  On the other hand if you spend your time reading books about the constantly recurring crashes that dog financial markets you’ll probably overweight the chances of such events. 

Underweighting and Choice

The issue of underweighting from experience is easily drawn out of probability theory.  We will each only experience a relatively small number of events, relative to those in the wider markets.  It's a facet of statistics  that if we only experience a small sample of events relative to the total then we are more than likely to miss the rare event completely – so our experience will not be representative of the probability of the actual event occurring.  Even in large samples recency effects are suspected of causing a similar bias – we’re less likely to have experienced the total failure of one of our investments recently and we’ll tend to discount past events more than recent ones (see: Recency: Hot Hands and the Gambler's Fallacy).

Yet where the researchers examined the effects of decision making from description – i.e. from symbolic information (aka “writing”) – the results obtained matched those found in Prospect Theory.  This fundamental difference in decision making processes based on either experience from limited numbers of samples or from descriptions that require more conscious processing may well be fundamental to understanding the discrepancies at the heart of economics and behavioral finance.

Bifurcated Choice

What’s really interesting, of course, is that neither route actually provides an optimal answer.  The fact that education leads us into a set of biases which can be described by Prospect Theory, while relying on gut instinct leads us into a set of different biases which can’t be, only shows that the underlying theories aren’t very robust: but it doesn’t take us very far down the road of greater understanding.

Still, it’s a start. 

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