Drunkard's Walk - Leonard Mlodinow [21]
What is wrong with this picture? For one thing, as we’ve seen, in order to find a compound probability by multiplying the component probabilities, the categories have to be independent, and in this case they clearly aren’t. For example, the table quotes the chance of observing a “Negro man with beard” as 1 in 10 and a “man with mustache” as 1 in 4. But most men with a beard also have a mustache, so if you observe a “Negro man with beard,” the chances are no longer 1 in 4 that the man you observe has a mustache—they are much higher. That issue can be remedied if you eliminate the category “Negro man with beard.” Then the product of the probabilities falls to about 1 in 1 million.
There is another error in the analysis: the relevant probability is not the one stated above—the probability that a couple selected at random will match the suspects’ description. Rather, the relevant probability is the chance that a couple matching all these characteristics is the guilty couple. The former might be 1 in 1 million. But as for the latter, the population of the area adjoining the one where the crime was committed was several million, so you might reasonably expect there to be 2 or 3 couples in the area who matched the description. In that case the probability that a couple who matched the description was guilty, based on this evidence alone (which is pretty much all the prosecution had), is only 1 in 2 or 3. Hardly beyond a reasonable doubt. For these reasons the supreme court overturned Collins’s conviction.
The use of probability and statistics in modern courtrooms is still a controversial subject. In the Collins case the California Supreme Court derided what it called “trial by mathematics,” but it left the door open to more “proper applications of mathematical techniques.” In the ensuing years, courts rarely considered mathematical arguments, but even when attorneys and judges don’t quote explicit probabilities or mathematical theorems, they do often employ this sort of reasoning, as do jurors when they weigh the evidence. Moreover, statistical arguments are becoming increasingly important because of the necessity of assessing DNA evidence. Unfortunately, with this increased importance has not come increased understanding on the part of attorneys, judges, or juries. As explained by Thomas Lyon, who teaches probability and the law at the University of Southern California, “Few students take a probability in law course, and few attorneys feel it has a place.”23 In law as in other realms, the understanding of randomness can reveal hidden layers of truth, but only to those who possess the tools to uncover them. In the next chapter we shall consider the story of the first man to study those tools systematically.
CHAPTER 3
Finding Your Way through a Space of Possibilities
IN THE YEARS leading up to 1576, an oddly attired old man could be found roving with a strange, irregular gait up and down the streets of Rome, shouting occasionally to no one in particular and being listened to by no one at all. He had once been celebrated throughout Europe, a famous astrologer, physician to nobles of the court, chair of medicine at the University of Pavia. He had created enduring inventions, including a forerunner of the combination lock and the universal joint, which is used in automobiles today. He had published 131 books on a wide range of topics in philosophy, medicine, mathematics, and science. In 1576, however, he was a man with a past