The prosecutor’s fallacy is when someone wrongly assumes that a rare match (like DNA) means a person is almost surely guilty, ignoring how many people could also match.
It’s another name for the base rate fallacy, which is when someone considers only a small aspect of a circumstance and ignores the broader reality.
For example, if you know someone is bookish, quiet, thorough, and has a degree in library science are they more likely to be a librarian or work at a supermarket? Many people will jump to them being a librarian because the description sounds like one, but statistically speaking, they probably work at a supermarket, because there are a lot of jobs at supermarkets, and not very many as librarians
It’s when a person takes one observation about one thing and uses it as proof to conclude something else without proving the connection.
For example, if a witness in court shares a description of a criminal who wore a specific outfit, was a specific race, weight, size, etc. The prosecutor uses as evidence that out of 100,000 people in the area that day, only the accused matches that description perfectly.
Therefore they conclude that if this person is the 1/100,000 to match the description, there is a 1/100,000 chance they did not commit the crime, in other words there is a 99.999999% chance they commit the crime, case closed.
It’s linking the improbability of obtaining a result AS PROOF of something else.
If the defendant is innocent, then it is unlikely that this evidence will match. That must mean the opposite, where if the evidence matches, that must mean the defendant is guilty.
There’s one famous example, where a mother had two children die of SIDS. The prosecutor argued that the probability of both kids dying from SIDS was low, so something else must have happened and mom was guilty.
I just rolled ten dice on Google (TIL you can do that from the search bar) and got 1222346666. So, wow, eight of the ten rolls were even. What are the odds of that, and can you conclude that Google’s random number generator is broken based on the answer?
The answer is no, because I rolled the dice before deciding what criterion I would use as evidence for Google’s RNG being broken. You can well imagine that any roll of ten dice would have something “unusual” about the distribution, and if you didn’t find anything the ordinariness of the roll would itself be unusual! So the moral of the story is that you shouldn’t be overly impressed by a rare event happening unless it was the result of an unbiased test that you had actively initiated.
The reason this phenomenon gets tagged as the Prosecutor’s fallacy is because you can think of it in terms of a court case. Imagine someone was found dead and some DNA of the murderer was found. If the DNA matched an obvious suspect like the last person known to see the victim alive or the beneficiary of the victim’s estate with one-in-a-million accuracy, then the prosecutor is on solid ground promoting this as conclusive evidence. But if the prosecutor trawled the DNA database and found a former criminal with a similarly close match but that person had no connection to the victim, then presenting the DNA evidence as one-in-a-million clinching evidence is unwarranted. The defense could and should counter that there are ten million former criminals in the DNA database so finding a one-in-a-million hit who also has a criminal record is not surprising at all.
It is a statistical fallacy that says “if it is very likely to be true, then it must be true” (gross oversimplification, I know.)
It is named as such for the fact that prosecutors have a job to do, and that job is to make the accused seem guilty through the evidence, so they usually go about demontrating that it is very likely that the evidence demonstrates the guilt of the accused, then draw the conclusion that “the evidence shows that it is very likely that this person committed the crime, therefore, this person committed the crime”. This conlusion may not be reflective of the truth of the matter.
To draw an example: One night, a 5’10” male-looking person who wears a Dallas Stars jacket, breaks into a restaurant, cleans the safe and registers, and disappears before anyone can arrive and arrest them. A regular customer to this restaurant has the same jacket, is male, 5’10”. It is not a stretch to say that this customer could have overheard the boss training a new employee and tell them the safe combination, since his favorite spot was at the counter itself.
It seems very likely that this man is guilty. His fingerprints can be found on site, some of his hair was found on top of the safe itself. Everything matches. Except his alibi, which says that he was sleeping next to his dog at home, with no witnesses, a convenient, yet weak alibi.
You don’t know for 100% sure that this man is guilty of that break in and burglary, but you know for 100% sure that all the evidence points towards him, so you just assume he is guilty. As a prosecutor, you have to assume that this is true.
This assumption is the prosecutor’s fallacy, as every bit of evidence listed is not exclusively pointing to him. His fingerprints should be there: he’s a regular. A single lost hair flying through the air and landing on top of the safe, a spot likely less cleaned than the rest of the place, is not only possible, but probable. Dallas Stars vests aren’t rare, and I can order one online right now. 5’10” is a common height for men. The Lockpicking Lawyer on youtube shows you very easy ways to bypass smaller safes, and it is easy to make it look like you knew the combination. Most cash registers aren’t hard to open either, and even with a lock, refer to the previous Lockpicking Lawyer point about smaller safes.
At the end of the day, all the evidence says, is that he is a very likely suspect, but what if the guy is right, and it is someone else?
Comments
The prosecutor’s fallacy is when someone wrongly assumes that a rare match (like DNA) means a person is almost surely guilty, ignoring how many people could also match.
It’s another name for the base rate fallacy, which is when someone considers only a small aspect of a circumstance and ignores the broader reality.
For example, if you know someone is bookish, quiet, thorough, and has a degree in library science are they more likely to be a librarian or work at a supermarket? Many people will jump to them being a librarian because the description sounds like one, but statistically speaking, they probably work at a supermarket, because there are a lot of jobs at supermarkets, and not very many as librarians
It’s when a person takes one observation about one thing and uses it as proof to conclude something else without proving the connection.
For example, if a witness in court shares a description of a criminal who wore a specific outfit, was a specific race, weight, size, etc. The prosecutor uses as evidence that out of 100,000 people in the area that day, only the accused matches that description perfectly.
Therefore they conclude that if this person is the 1/100,000 to match the description, there is a 1/100,000 chance they did not commit the crime, in other words there is a 99.999999% chance they commit the crime, case closed.
It’s linking the improbability of obtaining a result AS PROOF of something else.
The argument goes as follows…
If the defendant is innocent, then it is unlikely that this evidence will match. That must mean the opposite, where if the evidence matches, that must mean the defendant is guilty.
There’s one famous example, where a mother had two children die of SIDS. The prosecutor argued that the probability of both kids dying from SIDS was low, so something else must have happened and mom was guilty.
I just rolled ten dice on Google (TIL you can do that from the search bar) and got 1222346666. So, wow, eight of the ten rolls were even. What are the odds of that, and can you conclude that Google’s random number generator is broken based on the answer?
The answer is no, because I rolled the dice before deciding what criterion I would use as evidence for Google’s RNG being broken. You can well imagine that any roll of ten dice would have something “unusual” about the distribution, and if you didn’t find anything the ordinariness of the roll would itself be unusual! So the moral of the story is that you shouldn’t be overly impressed by a rare event happening unless it was the result of an unbiased test that you had actively initiated.
The reason this phenomenon gets tagged as the Prosecutor’s fallacy is because you can think of it in terms of a court case. Imagine someone was found dead and some DNA of the murderer was found. If the DNA matched an obvious suspect like the last person known to see the victim alive or the beneficiary of the victim’s estate with one-in-a-million accuracy, then the prosecutor is on solid ground promoting this as conclusive evidence. But if the prosecutor trawled the DNA database and found a former criminal with a similarly close match but that person had no connection to the victim, then presenting the DNA evidence as one-in-a-million clinching evidence is unwarranted. The defense could and should counter that there are ten million former criminals in the DNA database so finding a one-in-a-million hit who also has a criminal record is not surprising at all.
It is a statistical fallacy that says “if it is very likely to be true, then it must be true” (gross oversimplification, I know.)
It is named as such for the fact that prosecutors have a job to do, and that job is to make the accused seem guilty through the evidence, so they usually go about demontrating that it is very likely that the evidence demonstrates the guilt of the accused, then draw the conclusion that “the evidence shows that it is very likely that this person committed the crime, therefore, this person committed the crime”. This conlusion may not be reflective of the truth of the matter.
To draw an example: One night, a 5’10” male-looking person who wears a Dallas Stars jacket, breaks into a restaurant, cleans the safe and registers, and disappears before anyone can arrive and arrest them. A regular customer to this restaurant has the same jacket, is male, 5’10”. It is not a stretch to say that this customer could have overheard the boss training a new employee and tell them the safe combination, since his favorite spot was at the counter itself.
It seems very likely that this man is guilty. His fingerprints can be found on site, some of his hair was found on top of the safe itself. Everything matches. Except his alibi, which says that he was sleeping next to his dog at home, with no witnesses, a convenient, yet weak alibi.
You don’t know for 100% sure that this man is guilty of that break in and burglary, but you know for 100% sure that all the evidence points towards him, so you just assume he is guilty. As a prosecutor, you have to assume that this is true.
This assumption is the prosecutor’s fallacy, as every bit of evidence listed is not exclusively pointing to him. His fingerprints should be there: he’s a regular. A single lost hair flying through the air and landing on top of the safe, a spot likely less cleaned than the rest of the place, is not only possible, but probable. Dallas Stars vests aren’t rare, and I can order one online right now. 5’10” is a common height for men. The Lockpicking Lawyer on youtube shows you very easy ways to bypass smaller safes, and it is easy to make it look like you knew the combination. Most cash registers aren’t hard to open either, and even with a lock, refer to the previous Lockpicking Lawyer point about smaller safes.
At the end of the day, all the evidence says, is that he is a very likely suspect, but what if the guy is right, and it is someone else?