Why we Misestimate Probabilities

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Professor Simon Gandevia, a neurologist from the Prince of Wales Medical Research Institute explains in this podcast why we often literally 'jump' to the wrong conclusion;

“Suppose there was a stabbing outside a nightclub. In court, the one eyewitness testifies that the assailant fled in a silver-coloured taxi. On the night of the offence, it is known that only 15% of taxis on the road were silver. Furthermore, when the crime scene is recreated, it is established that the witness is 80% accurate at picking silver from non-silver taxis. You are the judge. What is the probability that the taxi involved in the crime was silver? Initially, it might seem, given the eyewitness is 80% accurate, that the probability the taxi was silver, as claimed, is also 80%. But this ignores the error the witness makes when observing the much more common, non-silver taxis. In fact, to work out the correct probability, we need to invoke a theorem devised by the Reverend Thomas Bayes, published in 1763, two years after his death. This theorem allows probabilities to be calculated accurately on the basis of full knowledge of all initial possibilities. When this non-intuitive, but mathematically simple, theorem is applied, the true probability that the taxi at the crime was silver is found to be only 41%; less than a one in two chance. In the Australian tradition, you should therefore bet that the taxi at the crime was actually not silver. We jump to the wrong conclusion unless the Reverend Bayes’ approach is applied.

What is happening here? The fact is that we are all victims of cognitive illusions. They are potent and almost impossible to ‘unlearn’, just like visual illusions, such as the ones in which two parallel lines with different cross hatchings seem not to be parallel, or two identical parallel lines with differently pointing arrowheads suddenly seem different in length. Just as these sensor y illusions expose the unconscious brain processes involved in perception, so cognitive illusions reveal the brain processes involved in thinking.

Why do these illusions exist? In the evolutionary world of predator and prey, snap decisions are quite literally vital. It has been argued that because we need time to evaluate probabilities before making a decision, a default system has evolved that rapidly evaluates choices. The Nobel laureate, Francis Crick, is well known for his discoveries about the double helix of our genes, but he later worked in the field of neuroscience. He and his colleagues postulated that humans needed to develop what he termed ‘zombie thinking’ in order to deal efficiently with the massive sensory input we continuously receive about the external world. This mode of thinking is thus necessary to allow us to react rapidly to external events, so that these cognitive illusions are ‘built in’ to us, almost certainly for evolutionary reasons. None of us is immune to them, not even those trained as scientists or judges. Our capacity for rational thinking is limited. Propagandists and advertisers are all too well aware of this.”

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Bayesian estimation tends to justify stereotyping.

For example, suppose a white and a black student both score 1300 on the SAT. Which student is more qualified?

Most people will say they are equally qualified, but because we know that the median black SAT score is a whole standard deviation below the median white SAT score, the real answer is that the black student is probably less qualified because there is a greater chance that measurement error skewed his score higher.

This may partially explain why SAT scores overpredict black college performance compared to whites.


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This page contains a single entry by Paul published on May 29, 2006 11:55 PM.

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