Science, Evidence and Logic

Modem debates about the role of mathematical models in adjudicative fact-finding are commonly traced back to People v Collins.' The Collinses were accused of robbery, the case against them being largely that they fitted eyewitness descriptions of the robbers. The prosecutor identified several characteristics of the defendants, such as that the man had a moustache and that they drove a yellow car, which matched the eyewitness descriptions. The prosecutor assigned probabilities to the occurrence of each of the characteristics and, relying on the testimony of a mathematics instructor who had described the product rule, multiplied these probabilities together. He claimed that the resulting figure of 1/12,000,000 represented the probability of any couple possessing all of the characteristics of the defendants. The jury convicted. While the newspapers triumphantly announced that 'Law of Probability Foils 2 Robbers in Tough Case,'2 the Collinses appealed and their convictions were overturned by the Supreme Court of California. There were two main problems with the prosecutor's strategy. First, the figures he used seemed to have been plucked out of thin air: they lacked any objective grounding, while some of the characteristics chosen were not independent, making use of the product rule for independent events untenable. Secondly, even if the prosecutor could have proved the validity of the calculations underlying the 1/12,000,000 figure, it was not obvious what the figure meant: it does not necessarily follow that there was only a 1/12,000,000 probability that the Collinses were innocent.3