Vsauce! Kevin here -- with the dumbest math ever used to convict an innocent
person in a court of law. It all started with a little old lady in an alleyway,
and it ended by defining how we use probabilistic evidence in trials, with
the California Supreme court warning that bad math could become a “veritable sorcerer” to ruin law.
Almost 60 years ago, a petty neighborhood robbery you've never heard of changed everything.
An elderly woman named Juanita Brooks was walking down an alleyway
when someone shoved her to the ground. She looked up to see
a blonde woman running away -- and that woman had taken Juanita’s purse.
At the end of the alley, a man named John Bass witnessed a white blonde woman with a ponytail
get into a yellow car and drive past him. He saw that the driver was a black man with a beard and
a mustache. These SOUND LIKE the basic facts of the case -- but they ended up becoming numbers.
And it happened because of total uncertainty. John Bass saw that the woman had a ponytail;
Juanita Brooks couldn’t remember if she did. A police officer asked around local
gas stations until he found someone who said that an interracial couple filled
up their yellow car there frequently -- Janet Collins and her husband Malcolm.
They’d only been married for 2 weeks, and now they were being arrested for robbery.
When Juanita Brooks and John Bass were asked to identify Janet and Malcolm from photos,
neither one could do it. Juanita completely blanked, and Bass only saw a resemblance in
the ponytail. The police still had some case -- their alibi was a little shaky,
Malcolm had a criminal record, and a recorded conversation with police showed Janet’s desire
to take the blame to protect her husband. And that’s when desperation kicked in.
The prosecution turned Juanita Brooks’ assault and theft into a probability problem.
Prosecutor Ray Sinetar brought in a professor from Cal State Long Beach to help him prove
to the jury mathematically that Janet and Malcolm Collins were guilty. The professor
testified to the validity of the product rule -- which is that if events are independent,
you can multiply the probabilities of each to find the chance that they happen together. For example,
if Thing A has a 1 in 5 chance of happening, and Thing B has a 1 in 10 chance of happening,
then both of them happening separately-but-together is 1 in 50, or 2%.
So what did Sinetar do next? He started literally making up numbers. I’LL EXPLAIN IN A SECOND.
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Okay. Sinetar invented 6 vague estimates touching on the only details that John Bass
and Juanita Brooks could provide. Here’s what he said. He said the chances of:
-- A black man having a beard were 1 out of 10. -- That a man would have a mustache? 1 out of 4.
-- That a white woman had blonde hair: 1 out of 3. -- That a woman had a ponytail:
1 out of 10. -- That an
interracial couple would be in a car: 1 in 1,000. -- And that the car would be yellow? 1 in 10.
Sure. The professor was given a pencil and paper to work out the probability of all those
6 events happening together using the product rule,
and he did: the answer was 1 in 12,000,000. And that was it. He left the witness stand. Yeah.
If you watched my video about Sally Clark, you know exactly what’s happening here.
The prosecutor explained to the jury that this sort of mathematical proof
was actually better than the concept of proof beyond a reasonable doubt,
because it dealt with hard numbers instead of vague beliefs. He called it the “new math,”
and he said it would help convict the people who “push old ladies down and
take their money. “ He said that Malcolm and Janet Collins were the only two people in Los
Angeles who could satisfy all the elements of probability in this case. He suggested that they
had to be the 1 in 12 million -- because with all those pieces matching up, how could they NOT be?
But this wasn’t new math. It was bad math. And it was still enough to convict the Collinses
of second degree robbery. And in Jim Crow-era
Los Angeles, there was almost certainly an element of racial bias supporting it.
Malcolm Collins appealed his conviction, and it went to California's Supreme Court -- and they
finally obliterated the prosecutor’s stupidity.
The math was obviously wrong -- starting with the completely made-up odds for each
characteristic. It’s not like the prosecutor analyzed the vehicle registrations of all
California automobiles to determine that 10% of the state’s cars were yellow.
He didn’t conduct a massive survey of hairdressers to find out what percentage of their clients
pulled their hair back into a pontail. He just guessed.
Then he failed to acknowledge that these events are NOT independent -- like beards and mustaches.
Ya know, they kinda tend to come as a pair… a lot. Not always, but a lot. So,
you can’t just straight up multiply them like they’re coin flips.
But here’s the big one. Let’s say the math is accurate -- which it isn’t. You’ve found
a couple who satisfy all the conditions to be the 1 in 12 million. Great. How do you know THEY
are the couple who committed the crime?! Are they the only two people in the greater
Los Angeles metropolitan area who were a blonde ponytail and black mustached-and-bearded couple
in a yellow car?? Surely there weren’t MANY -- but there’s a decent chance there’s a few.
The Supreme Court actually calculated the probability that another couple
fitting the same exact description at over 40%. 40%! So even if the math checked out,
there’s pretty close to even odds that Janet and Malcolm were the wrong couple.
3 years later, Malcolm’s conviction was overturned and he was released -- Janet
had been given a short sentence, and she’d already served it. The Collinses never
really got justice. Janet served her time and Malcolm lost a few years of
his life -- but the biggest loser was the validity of probabilistic evidence.
It’s the most glaring example of the prosecutor’s fallacy -- and
it’s taken decades to undo the damage Ray Sinetar caused to the use of math in the courtroom.
But the fallout wasn’t ALL bad. It did lead to the “Collins test,” a set of conditions
the introduction of probability needs to satisfy for the math to be relevant and valid in a trial:
1) The probability factors need to be accurate -- you can’t just make them up;
2) The calculations are done correctly and formulas are applied appropriately -- like…
not abusing the product rule to get the result you want;
3) All the factors being calculated actually apply to the parties involved,
4) And the evidence proves there could be only ONE result -- so,
that the Collinses could be the ONLY possible couple capable of satisfying every condition.
The police never did figure out who knocked Juanita Brooks down and stole her purse. In 1965,
two criminals in Los Angeles got $40 richer, and math got a lot less trustworthy in the courtroom.
But without it we don’t have the Collins test, or an ever-evolving debate about how we can
leverage what we know about math to find out what we don’t know about everything else. Proving that
sometimes things have to get really dumb before we can even start to get… smart.
And as always - thanks for watching.