People v. Collins
Encyclopedia
The People of the State of California v. Collins was a 1968 jury trial
in California
, USA that made notorious forensic use of mathematics
and probability
.
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 fitted 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:
The jury returned a verdict of guilt
y.
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:
It has also been criticised as an example of the prosecutor's fallacy
.
The original decision has been supported by a minority of writers.
Jury trial
A jury trial is a legal proceeding in which a jury either makes a decision or makes findings of fact which are then applied by a judge...
in California
California
California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...
, USA that made notorious forensic use of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
.
Trial at first instance
Bystanders to a robberyRobbery
Robbery is the crime of taking or attempting to take something of value by force or threat of force or by putting the victim in fear. At common law, robbery is defined as taking the property of another, with the intent to permanently deprive the person of that property, by means of force or fear....
in Los Angeles
Los Ángeles
Los Ángeles is the capital of the province of Biobío, in the commune of the same name, in Region VIII , in the center-south of Chile. It is located between the Laja and Biobío rivers. The population is 123,445 inhabitants...
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
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, the prosecutor
Prosecutor
The prosecutor is the chief legal representative of the prosecution in countries with either the common law adversarial system, or the civil law inquisitorial system...
invited the jury
Jury
A jury is a sworn body of people convened to render an impartial verdict officially submitted to them by a court, or to set a penalty or judgment. Modern juries tend to be found in courts to ascertain the guilt, or lack thereof, in a crime. In Anglophone jurisdictions, the verdict may be guilty,...
to consider the probability that the accused pair, who fitted the description of the witnesses, were not the robbers. Even though the "instructor" had not discussed conditional probability
Conditional probability
In probability theory, the "conditional probability of A given B" is the probability of A if B is known to occur. It is commonly notated P, and sometimes P_B. P can be visualised as the probability of event A when the sample space is restricted to event B...
, the prosecutor suggested that the jury would be safe in estimating:
| Black man with beard | 1 in 10 |
| Man with moustache | 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 guilt
Guilt
Guilt is the state of being responsible for the commission of an offense. It is also a cognitive or an emotional experience that occurs when a person realizes or believes—accurately or not—that he or she has violated a moral standard, and bears significant responsibility for that...
y.
Appeal
The Supreme Court of CaliforniaSupreme Court of California
The Supreme Court of California is the highest state court in California. It is headquartered in San Francisco and regularly holds sessions in Los Angeles and Sacramento. Its decisions are binding on all other California state courts.-Composition:...
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.
Discussion
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.It has also been criticised as an example of the prosecutor's fallacy
Prosecutor's fallacy
The prosecutor's fallacy is a fallacy of statistical reasoning made in law where the context in which the accused has been brought to court is falsely assumed to be irrelevant to judging how confident a jury can be in evidence against them with a statistical measure of doubt...
.
The original decision has been supported by a minority of writers.