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Page 117

propensity toward violence against Nicole. Prosecutors spent the first ten days of

the trial entering evidence of his history of abusing her and claimed that this

alone was a good reason to suspect him of her murder. As they put it, “a slap is a

prelude to homicide.”14 The defense attorneys used this strategy as a launchpad

for their accusations of duplicity, arguing that the prosecution had spent two

weeks trying to mislead the jury and that the evidence that O. J. had battered

Nicole on previous occasions meant nothing. Here is Dershowitz’s reasoning: 4

million women are battered annually by husbands and boyfriends in the United

States, yet in 1992, according to the FBI Uniform Crime Reports, a total of

1,432, or 1 in 2,500, were killed by their husbands or boyfriends.15 Therefore,

the defense retorted, few men who slap or beat their domestic partners go on to

murder them. True? Yes. Convincing? Yes. Relevant? No. The relevant number

is not the probability that a man who batters his wife will go on to kill her (1 in

2,500) but rather the probability that a battered wife who was murdered was

murdered by her abuser. According to the Uniform Crime Reports for the United

States and Its Possessions in 1993, the probability Dershowitz (or the

prosecution) should have reported was this one: of all the battered women

murdered in the United States in 1993, some 90 percent were killed by their

abuser. That statistic was not mentioned at the trial.

As the hour of the verdict’s announcement approached, long-distance call

volume dropped by half, trading volume on the New York Stock Exchange fell

by 40 percent, and an estimated 100 million people turned to their televisions

and radios to hear the verdict: not guilty. Dershowitz may have felt justified in

misleading the jury because, in his words, “the courtroom oath—‘to tell the

truth, the whole truth and nothing but the truth’—is applicable only to witnesses.

Defense attorneys, prosecutors, and judges don’t take this oath…indeed, it is fair

to say the American justice system is built on a foundation of not telling the

whole truth.”16

THOUGH CONDITIONAL PROBABILITY represented a revolution in ideas

about randomness, Thomas Bayes was no revolutionary, and his work

languished unattended despite its publication in the prestigious Philosophical

Transactions in 1764. And so it fell to another man, the French scientist and

Page 118

mathematician Pierre-Simon de Laplace, to bring Bayes’s ideas to scientists’

attention and fulfill the goal of revealing to the world how the probabilities that

underlie real-world situations could be inferred from the outcomes we observe.

You may remember that Bernoulli’s golden theorem will tell you you

conduct a series of coin tosses how certain you can be, if the coin is fair, that you

will observe some given outcome. You may also remember that it will not tell

you you’ve made a given series of tosses the chances that the coin was a

fair one. Along the same lines, if you know that the chances that an eighty-five-

year-old will survive to ninety are 50/50, the golden theorem tells you the

probability that half the eighty-five-year-olds in a group of 1,000 will die in the

next five years, but if half the people in some group died in the five years after

their eighty-fifth birthday, it cannot tell you how likely it is that the underlying

chances of survival for the people in that group were 50/50. Or if Ford knows

that 1 in 100 of its automobiles has a defective transmission, the golden theorem

can tell Ford the chances that, in a batch of 1,000 autos, 10 or more of the

transmissions will be defective, but if Ford finds 10 defective transmissions in a

sample of 1,000 autos, it does not tell the automaker the likelihood that the

average number of defective transmissions is 1 in 100. In these cases it is the

latter scenario that is more often useful in life: outside situations involving

gambling, we are not normally provided with theoretical knowledge of the odds

but rather must estimate them after making a series of observations. Scientists,

too, find themselves in this position: they do not generally seek to know, given

the value of a physical quantity, the probability that a measurement will come

out one way or another but instead seek to discern the true value of a physical

quantity, given a set of measurements.

I have stressed this distinction because it is an important one. It defines the

fundamental difference between probability and statistics: the former concerns

predictions based on fixed probabilities; the latter concerns the inference of

those probabilities based on observed data.

It is the latter set of issues that was addressed by Laplace. He was not aware

of Bayes’s theory and therefore had to reinvent it. As he framed it, the issue was

this: given a series of measurements, what is the best guess you can make of the

true value of the measured quantity, and what are the chances that this guess will

be “near” the true value, however demanding you are in your definition of ?

Page 233

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propensity toward violence against Nicole. Prosecutors spent the first ten days of

the trial entering evidence of his history of abusing her and claimed that this

alone was a good reason to suspect him of her murder. As they put it, “a slap is a

prelude to homicide.”14 The defense attorneys used this strategy as a launchpad

for their accusations of duplicity, arguing that the prosecution had spent two

weeks trying to mislead the jury and that the evidence that O. J. had battered

Nicole on previous occasions meant nothing. Here is Dershowitz’s reasoning: 4

million women are battered annually by husbands and boyfriends in the United

States, yet in 1992, according to the FBI Uniform Crime Reports, a total of

1,432, or 1 in 2,500, were killed by their husbands or boyfriends.15 Therefore,

the defense retorted, few men who slap or beat their domestic partners go on to

murder them. True? Yes. Convincing? Yes. Relevant? No. The relevant number

is not the probability that a man who batters his wife will go on to kill her (1 in

2,500) but rather the probability that a battered wife who was murdered was

murdered by her abuser. According to the Uniform Crime Reports for the United

States and Its Possessions in 1993, the probability Dershowitz (or the

prosecution) should have reported was this one: of all the battered women

murdered in the United States in 1993, some 90 percent were killed by their

abuser. That statistic was not mentioned at the trial.

As the hour of the verdict’s announcement approached, long-distance call

volume dropped by half, trading volume on the New York Stock Exchange fell

by 40 percent, and an estimated 100 million people turned to their televisions

and radios to hear the verdict: not guilty. Dershowitz may have felt justified in

misleading the jury because, in his words, “the courtroom oath—‘to tell the

truth, the whole truth and nothing but the truth’—is applicable only to witnesses.

Defense attorneys, prosecutors, and judges don’t take this oath…indeed, it is fair

to say the American justice system is built on a foundation of not telling the

whole truth.”16

THOUGH CONDITIONAL PROBABILITY represented a revolution in ideas

about randomness, Thomas Bayes was no revolutionary, and his work

languished unattended despite its publication in the prestigious Philosophical

Transactions in 1764. And so it fell to another man, the French scientist and

Page 118

mathematician Pierre-Simon de Laplace, to bring Bayes’s ideas to scientists’

attention and fulfill the goal of revealing to the world how the probabilities that

underlie real-world situations could be inferred from the outcomes we observe.

You may remember that Bernoulli’s golden theorem will tell you you

conduct a series of coin tosses how certain you can be, if the coin is fair, that you

will observe some given outcome. You may also remember that it will not tell

you you’ve made a given series of tosses the chances that the coin was a

fair one. Along the same lines, if you know that the chances that an eighty-five-

year-old will survive to ninety are 50/50, the golden theorem tells you the

probability that half the eighty-five-year-olds in a group of 1,000 will die in the

next five years, but if half the people in some group died in the five years after

their eighty-fifth birthday, it cannot tell you how likely it is that the underlying

chances of survival for the people in that group were 50/50. Or if Ford knows

that 1 in 100 of its automobiles has a defective transmission, the golden theorem

can tell Ford the chances that, in a batch of 1,000 autos, 10 or more of the

transmissions will be defective, but if Ford finds 10 defective transmissions in a

sample of 1,000 autos, it does not tell the automaker the likelihood that the

average number of defective transmissions is 1 in 100. In these cases it is the

latter scenario that is more often useful in life: outside situations involving

gambling, we are not normally provided with theoretical knowledge of the odds

but rather must estimate them after making a series of observations. Scientists,

too, find themselves in this position: they do not generally seek to know, given

the value of a physical quantity, the probability that a measurement will come

out one way or another but instead seek to discern the true value of a physical

quantity, given a set of measurements.

I have stressed this distinction because it is an important one. It defines the

fundamental difference between probability and statistics: the former concerns

predictions based on fixed probabilities; the latter concerns the inference of

those probabilities based on observed data.

It is the latter set of issues that was addressed by Laplace. He was not aware

of Bayes’s theory and therefore had to reinvent it. As he framed it, the issue was

this: given a series of measurements, what is the best guess you can make of the

true value of the measured quantity, and what are the chances that this guess will

be “near” the true value, however demanding you are in your definition of ?

Page 233

http://www.pantheonbooks.com