Two different questions
The first question is: how rarely does this kind of evidence occur in a random person? The second is: how likely is it that this person is innocent, given that the evidence was found? The answers coincide only when the suspect was not selected at random in advance.
Let's look at the numbers. Suppose the characteristic occurs in 1 person out of a million, and a city has a population of 10 million. That means there are about 10 such people. The match narrows the field to 10 people; it does not prove one person's guilt.
They state how rare the evidence is. 1 chance in a million. It sounds like a conviction.
They forget the size of the pool. How many people could have come under suspicion? The larger the pool, the more random matches there will be.
They reverse the question. They present the rarity of the evidence as the probability of innocence. These are different quantities.
The number decides the case. Jurors hear a confident number and take it as proof.
The name is associated with the prosecution for a reason: it is in the prosecution's interest to make the rarity of the evidence sound like proof. But anyone can make this mistake, including the defense, if it reverses the probabilities to support its case.
If a match occurs 1 time in a million, guilt is proven.
This tells us only how rare the characteristic is. The conclusion also depends on how large the pool of suspects is and what is known beyond this piece of evidence.
A famous case
In Britain, a mother was accused of the deaths of 2 infants. An expert stated that the probability of 2 sudden infant deaths in such a family was 1 chance in 73 million. The number made a strong impression, and the verdict was guilty.
There were 2 errors in the calculation. The probabilities were multiplied as if they were independent, even though cases in one family may be linked by a common cause. And, most importantly, they were not compared with the probability of the alternative explanation: that the mother had committed a double murder, which was also extremely small.
The conviction was later overturned, and statistical organizations officially condemned this method of calculation. The case became a textbook example of how a convincing number can lead a court away from the heart of the matter.
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Sources
- The case of Sally Clark, convicted in 1999 and acquitted in 2003, became a classic example of the misuse of probabilities in court
- the statistical community publicly criticized the calculation presented