People v. Collins
Trial at first instance
Bystanders to a robbery in Los Angeles testified that the perpetrators had been a black male, with a beard and moustache, and a caucasian female with blonde hair tied in a ponytail. They had escaped in a yellow motor car.
After testimony from an "instructor in mathematics" about the multiplication rule for probability, the prosecutor invited the jury to consider the probability that the accused pair, who fit the description of the witnesses, were not the robbers. Even though the "instructor" had not discussed conditional probability, the prosecutor suggested that the jury would be safe in estimating:
|Black man with beard||1 in 10|
|Man with mustache||1 in 4|
|White woman with pony tail||1 in 10|
|White woman with blonde hair||1 in 3|
|Yellow motor car||1 in 10|
|Interracial couple in car||1 in 1000|
The jury returned a verdict of guilty.
The Supreme Court of California set aside the conviction, criticising the statistical reasoning and disallowing the way the decision was put to the jury. In their judgment, the justices observed that mathematics:
- ... while assisting the trier of fact in the search of truth, must not cast a spell over him.
The statistical reasoning at first instance was criticised as it failed to take into account the probable dependencies between the characteristics, for example, bearded men commonly sport moustaches.
The original decision has been supported by a minority of writers.
- People v. Collins, 438 P. 2d 33 (68 Cal. 2d 319 1968)
- Michael O. Finkelstein & William B. Fairley, A Bayesian Approach to Identification Evidence, 83 HARV. L. REV. 489 (1970).
- Kreith, K. (1976) "Mathematics, Social Decisions and the Law", International Journal of Mathematical Education in Science and Technology vol.7 p315
- Laurence H. Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 HARV. L. REV. 1329 (1971).
- Leila Schneps and Coralie Colmez, Math on trial. How numbers get used and abused in the courtroom, Basic Books, 2013. ISBN 978-0-465-03292-1. (Second chapter: "Math error number 2: unjustified estimates. The case of Janet Collins: hairstyle probability").