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Petraeus, Cheating, and Bayes’ Rule

Last Friday (Nov. 9th) CIA Director, and retired four-star general, David H. Patraeus resigned from his position after an F.B.I. investigation uncovered evidence that he was having an extramarital affair with his biographer Paula Broadwell. He is the latest of numerous public figures including former U.S. Senator John Edwards, former California Governor Arnold Schwarzenegger, and former U.S Representative Anthony Weiner to admit to engaging in affairs. He is not the first high ranking military official to stray from his marriage either. WWII Generals George Patton and Douglas MacArthur both had affairs— Patton with his wife’s step-niece and MacArthur with a woman he met in the Phillipines. Former President Dwight D. Eisenhower and WWII general was also suspected of having an affair with his wartime chauffeur. All these instances pose the question: why would men with so much to lose risk everything for sex?

Part of is biological. Military figures like Patraeus tend to be bolder and take more risks than other men because that trait serves them well in combat and when leading soldiers into battle. However this trait is often carried over into their personal lives. It may also come as no big surprise that men in general become more blind to risk at the sight of an attractive woman.   A 2008 study on blackjack players supports this, finding that men who were shown beautiful female faces before playing took more risks than those shown unattractive faces. The evolutionary drive to reproduce often outweighs the risk of losing one’s career.

Moreover people often tend miscalculate risk and underestimate how quickly small risks can add up. This can be related to Bayes’ Rule and conditional probability as we discussed in class. Given that a man cheats, what is the likelihood he gets caught? While the probability of him getting caught may be very small if he only cheats once it can increase rapidly for multiple occurrences. Consider Bayes’ rule applied in a rather simplified world:

P(“gets caught” | “cheats”) = P(“gets caught”)P(“cheats”|”gets caught”)/P(“cheats”)

Assuming that P(“cheats”|”gets caught”)= 1 (i.e. a man will only get caught for cheating if he has indeed cheated) then this can be simplified to:

P(“gets caught” | “cheats”) = P(“gets caught”)/P(“cheats”).

If a man cheats multiple times the numerator in this equation will remain constant while the denominator  can decrease  fairly rapidly (assuming cheating events are treated independently) driving the probability of getting caught upward. Many people are blind to this phenomenon though and so underestimate the risk of getting caught, especially after getting away with it once.

 

http://news.yahoo.com/why-men-petraeus-risk-cheat-210918083.html

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