Proofiness - Charles Seife [100]
For example, Alan Dershowitz argued that O. J. Simpson was innocent because there was only a one in a thousand chance that a wife-beater kills his wife. This number, he implies, means that there’s only a one in a thousand chance that O. J. is guilty. This is the prosecutor’s fallacy in action, because Dershowitz doesn’t put the number into the proper context. The one in a thousand figure doesn’t take into account that there is an extremely low probability that a thirty-five-year-old woman like Nicole Brown is murdered in a given year—about 1 in 40,000. Just as the one in a billion chance of disease made the one in a million chance of test error loom very large in comparison, the 1 in 40,000 chance of murder makes the 1 in 1,000 chance of a wife-beater turning murderer seem huge. When statisticians crunched the numbers in the proper way, their estimates of the probability of O. J.’s guilt turned out to be quite large—better than 50 percent. The fact that O. J. had previously battered his wife made it much more probable that he was the murderer, as would have been clear had Dershowitz put the number in the proper context.
Similarly, even if the probabilities Sir Roy Meadow used to convict Sally Clark of killing her children were in the ballpark (which they weren’t), they would be deceptive on their own. Meadow didn’t take into account that the probability of being a murderer—much less a serial murderer—in the United Kingdom is quite small. Any probability that Meadow used should have been put in the context of that very small probability, which would have made it look a lot less impressive to a jury. Indeed, a mathematician estimated the real probability to be closer to nine in ten that Sally Clark was not guilty based solely upon the deaths of her two children—a far, far cry from the 1 in 73 million chance that Meadow claimed.
The prosecutor’s fallacy is powerful because it appeals to our innate misunderstanding of probabilities. It’s counterintuitive that a tiny probability (a one in a million chance of a test’s going wrong, for example) can, in certain contexts, wind up being extremely large. As a result, few people notice when a prosecutor ignores the context and, through a little numerical hanky-panky, makes a shaky case seem like a rock-solid one.
Notes
Introduction: Proofiness
1 “In my opinion” Joseph McCarthy quoted in Robert G. Torricelli and Andrew Carroll, In Our Own Words (New York: Washington Square Press, 1999), 174.
2 “we have been able to compile” “M’Carthy Insists Truman Oust Reds,” New York Times, February 12, 1950, 5.
2n “205 or 207?” Quoted in David M. Oshinsky, A Conspiracy So Immense (New York: Free Press, 1983), 112.
3 “Joe never had any names” Ibid., 117.
1: Phony Facts, Phony Figures
7 The second chapter epigraph is drawn from Ronald Reagan, Address to the Republican National Convention, August 15, 1988. See, e.g., http://www.reagansheritage.org/html/reagan_rnc_88.shtml.
7 “will become extinct by 2202” “Blondes ‘to die out in 200 years,’” BBC News, September 27, 2002, http://news.bbc.co.uk/2/hi/health/2284783.stm.
8 “vanish from the face of the earth within two hundred years” Quoted in Lawrence Altman, “Stop Those Presses! Blondes, It Seems, Will Survive After All,” New York Times, October 2, 2002, A5.
8 “WHO wishes to clarify” “Clarification of erroneous news reports indicating WHO genetic research on hair color,” World Health Organization, October 1, 2002, http://www.who.int/mediacentre/news/statements/statement05/en/.
8 “Fifty-eight percent of all the exercise” Deborah Norville Tonight, March 12, 2004, transcript at http://www.msnbc.msn.com/id/4533441/.
9n “a five-year study” Countdown with Keith Olbermann, September 8, 2004, transcript at http://www.msnbc.msn.com/id/5953239/.
13 “40 per cent cleverer” Denis Campbell, “Simple ways to make yourself far cleverer,” Observer (UK), March 5, 2006.
14 “twelve times more impact