Predicting the improbable

Very interesting research on how we behave to certain recurring and/or major events; paper here, excerpt below:

Japan’s trio of tsunami, earthquake, and nuclear disaster has left the world stunned. As this column points out, even the experts were shocked. But while these events were highly unlikely, they were still possible. This column uses evidence from the Danish lottery to show that people tend to adjust their expectations of future events based on only small pockets of recent experience, often at their cost.

Important events are hard to predict – a fact that is particularly hard-felt when it comes to low probability events with dramatic consequences. Nuclear catastrophe, financial crisis and the like are things that even experts struggle to predict. The difficulty stems from a lack of understanding of the underlying factors and complex interactions among causes (probabilities are not independent but conditional on other events).

Experts are thus to some extent forced to base their predictions on inference from observing the past. A difficult issue is to know when a model should be revised given that an event that has been deemed to be highly improbable happens to occur. The issue is most relevant for policy recommendations. For example, what recommendations should experts provide for the regulation of nuclear power in the wake of the Fukushima disaster or for the regulation of banks in the light of the recent financial crisis?
While experts struggle to predict such events accurately, the average person is often simply baffled. They tend to misperceive randomness in a variety of ways, especially when it comes to rare events.

• One common tendency is to see patterns in random data when there are none.

This can lead to a tendency to overreact to recent events, allowing their occurrence to change beliefs about future events in exaggerated ways. More specifically, many people tend to over-infer characteristics of the underlying probability distribution when observing a small number of random events. A literature pioneered by Tversky and Kahneman (1971) has identified the belief in the “law of small numbers” as the source of such over-inference.
Why do people “over infer” from recent events?
There are two plausible but apparently contradicting intuitions about how people over-infer from observing recent events.

• The “gambler’s fallacy” claims that people expect rapid reversion to the mean.

For example, upon observing three outcomes of “red” in roulette, gamblers tend to think that “black” is now due and tend to bet more on “black” (Croson and Sundali 2005).

• The “hot hand fallacy” claims that upon observing an unusual streak of events, people tend to predict that the streak will continue.

The “hot hand” fallacy term originates from basketball where players who scored several times in row are believed to have a “hot hand”, i.e. are more likely to score at their next attempt (e.g. Camerer 1989).
Recent behavioural theory has proposed a foundation to reconcile the apparent contradiction between the two types of over-inference (Rabin and Vayanos 2010). The intuition behind the theory can be explained with reference to the example of roulette play.

A person believing in the “law of small numbers” thinks that small samples should “look like” the parent distribution, i.e. that the sample should be representative of the parent distribution. Thus, the person believes that out of, say, 6 spins 3 should be red and 3 should be black (ignoring green). If observed outcomes in the small sample differ from the 50:50 ratio, immediate reversal is expected. Thus, somebody observing 2 times red in 6 consecutive spins believes that black is “due” on the 3rd spin to restore the 50:50 ratio.