Category Archives: Risk

Innumeracy

In one study, Gigerenzer and his colleagues asked doctors in Germany and the United States to estimate the probability that a woman with a positive mammogram actually has breast cancer, even though she’s in a low-risk group: 40 to 50 years old, with no symptoms or family history of breast cancer.  To make the question specific, the doctors were told to assume the following statistics — couched in terms of percentages and probabilities — about the prevalence of breast cancer among women in this cohort, and also about the mammogram’s sensitivity and rate of false positives:

The probability that one of these women has breast cancer is 0.8 percent.  If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram.  If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram.  Imagine a woman who has a positive mammogram.  What is the probability that she actually has breast cancer?

Gigerenzer describes the reaction of the first doctor he tested, a department chief at a university teaching hospital with more than 30 years of professional experience:

“[He] was visibly nervous while trying to figure out what he would tell the woman.  After mulling the numbers over, he finally estimated the woman’s probability of having breast cancer, given that she has a positive mammogram, to be 90 percent.  Nervously, he added, ‘Oh, what nonsense.  I can’t do this.  You should test my daughter; she is studying medicine.’  He knew that his estimate was wrong, but he did not know how to reason better.  Despite the fact that he had spent 10 minutes wringing his mind for an answer, he could not figure out how to draw a sound inference from the probabilities.”

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Risk: The Neural Basis of Decision Making

“Lecture presented by Professor John O’Doherty for the Darwin College Lecture Series 2010.

A deeper understanding of how the brain makes decisions will not only inspire new theories of decision making, it will also contribute to the development of genuine artificial intelligence, and it will enable us to understand why some humans are better than others at making decisions, why humans with certain psychiatric and neurological disorders are less capable of doing so, and why under some circumstances humans systematically fail to make rational decisions. Most decisions made in everyday life are taken for the purposes of increasing our well-being, whether it is deciding what item to choose off a restaurant menu, or deliberating over what career path to follow. Prominent amongst these is the value or utility of each decision option, which indicates how advantageous a particular option is likely to be for our future well-being. Another relevant signal present in the brain is the riskiness attached to a particular decision option, which can influence the decision making mechanism according to ones own individual preferences (whether one is risk-seeking or risk-averse).”

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