Drunkard's Walk - Leonard Mlodinow [20]
This is not an isolated issue. The use of mathematics in the modern legal system suffers from problems no less serious than those that arose in Rome so many centuries ago. One of the most famous cases illustrating the use and misuse of probability in law is People v. Collins, heard in 1968 by the California Supreme Court.22 Here are the facts of the case as presented in the court decision:
On June 18, 1964, about 11:30 a.m. Mrs. Juanita Brooks, who had been shopping, was walking home along an alley in the San Pedro area of the city of Los Angeles. She was pulling behind her a wicker basket carryall containing groceries and had her purse on top of the packages. She was using a cane. As she stooped down to pick up an empty carton, she was suddenly pushed to the ground by a person whom she neither saw nor heard approach. She was stunned by the fall and felt some pain. She managed to look up and saw a young woman running from the scene. According to Mrs. Brooks the latter appeared to weigh about 145 pounds, was wearing “something dark,” and had hair “between a dark blond and a light blond,” but lighter than the color of defendant Janet Collins’ hair as it appeared at the trial. Immediately after the incident, Mrs. Brooks discovered that her purse, containing between $35 and $40, was missing.
About the same time as the robbery, John Bass, who lived on the street at the end of the alley, was in front of his house watering his lawn. His attention was attracted by “a lot of crying and screaming” coming from the alley. As he looked in that direction, he saw a woman run out of the alley and enter a yellow automobile parked across the street from him. He was unable to give the make of the car. The car started off immediately and pulled wide around another parked vehicle so that in the narrow street it passed within six feet of Bass. The latter then saw that it was being driven by a male Negro, wearing a mustache and beard…. Other witnesses variously described the car as yellow, as yellow with an off-white top, and yellow with an egg-shell white top. The car was also described as being medium to large in size.
A few days after the incident a Los Angeles police officer spotted a yellow Lincoln with an off-white top in front of the defendants’ home and spoke with them, explaining that he was investigating a robbery. He noted that the suspects fit the description of the man and woman who had committed the crime, except that the man did not have a beard, though he admitted that he sometimes wore one. Later that day the Los Angeles police arrested the two suspects, Malcolm Ricardo Collins, and his wife, Janet.
The evidence against the couple was scant, and the case rested heavily on the identification by the victim and the witness, John Bass. Unfortunately for the prosecution, neither proved to be a star on the witness stand. The victim could not identify Janet as the perpetrator and hadn’t seen the driver at all. John Bass had not seen the perpetrator and said at the police lineup that he could not positively identify Malcolm Collins as the driver. And so, it seemed, the case was falling apart.
Enter the star witness, described in the California Supreme Court opinion only as “an instructor of mathematics at a state college.” This witness testified that the fact that the defendants were “a Caucasian woman with a blond ponytail…[and] a Negro with a beard and mustache” who drove a partly yellow automobile was enough to convict the couple. To illustrate its point, the prosecution presented this table, quoted here verbatim from the supreme court decision:
Characteristic
Individual Probability
Partly yellow automobile
1/10
Man with mustache
1/4
Negro man with beard
1/10
Girl with ponytail
1/10
Girl with blond hair
1/3
Interracial couple in car
1/1,000
The math instructor called by the prosecution said that the product rule applies to this data. By multiplying