Steelman
Prosecutor’s fallacy
Also called transposed conditional, confusion of the inverse.
Confusing “the chance of this evidence if innocent” with “the chance of innocence given this evidence”.
What it is
Mistaking the probability of seeing some evidence if a hypothesis is false (e.g. a one-in-a-million chance that a random person’s DNA matches) for the probability that the hypothesis is false given the evidence (a one-in-a-million chance the suspect is innocent).
The pattern
P(evidence | innocent) is tiny. Therefore P(innocent | evidence) is tiny. (invalid)
An example
“The chance that an innocent person would match this blood type is 1 in 1,000. So there’s only a 1-in-1,000 chance the defendant is innocent.”
In a city of a million, about a thousand people would match. The match narrows the field; it doesn’t single out the defendant.
Why it fails
The two probabilities can be wildly different. In a city of 5 million people, a one-in-a-million match would be expected for about five innocent people. Without other evidence, a matching suspect might be just one of them.
When it’s not a fallacy
Most lists skip this part. Calling a fair point a fallacy is a mistake too.
It can be fair when
- The match probability is properly combined with the other evidence and the prior probability, for example using Bayes’ theorem.
Try one
A question from the app. The wrong answers are its usual look-alikes.
Gaming forum, about a top player’s sky-high headshot numbers. Analyst: “Only 1 in 10,000 honest players ever hits numbers like Vex’s. The ranked ladder has about 3 million players.” Top reply: “So it’s 10,000 to 1 he’s cheating. Ban him and move on.”
What’s the flaw?
“1 in 10,000 honest players” is the chance of numbers like his if he’s honest, not the chance he’s honest given the numbers. With 3 million players, about 300 honest ones would hit numbers like that, so the odds he’s cheating are nowhere near 10,000 to 1.
A fair reply
“With 3 million players, about 300 honest ones would put up numbers like that, so we need more than the numbers to ban him.”
Often confused with
- Base rate fallacy
The prosecutor’s fallacy is a specific, courtroom form of base-rate neglect.
Where the name comes from
It’s named for prosecutors, the lawyers who argue a case against the accused, because it makes evidence sound more damning than it is. Anyone can make it, though. “Transposed conditional” names the swap: a conditional is a “chance of this, given that”, and transposed means switched around. “Confusion of the inverse” says the same: mixing up a probability with its flipped version.
The term was introduced by William Thompson and Edward Schumann in 1987.
Sources
- Base rate fallacy (prosecutor’s fallacy, Sally Clark case), Wikipedia
- Fallacies, Bradley Dowden, Internet Encyclopedia of Philosophy
In the app
Practice spotting it on arguments that sound real.
Steelman has more examples of prosecutor’s fallacy, how to answer it in a real conversation, and practice rounds that mix it with its look-alikes, so you learn the difference, not just the name. Coming soon to iPhone and Android.
You’re on the list.
We’ll email you the day Steelman is out.
Thanks for offering to test. We’ll write before the beta with how to join.