I remember _thinking_ about it, but can't remember if I saw anyone trying it. Instinctively, I like the symmetry, it just seems to make it less blatant that you're going to say "yes, but with plausible deniability".
I'm interested that it seems to be working.
It also creates ... weird legal implications. It's probably best for the government to turn a blind eye. But with the conditions given, if someone says "yes", there's an 80% chance they're guilty. That's not beyond reasonable doubt, but would it suffice for a balance-of-probabilities civil judgement? We normally don't take someone's unsupported confession as sufficient evidence, but I don't know if someone could try...
But with the conditions given, if someone says "yes", there's an 80% chance they're guilty.
Don't confuse P(A|B) with P(B|A)! If the real proportion of guilty people is p, then 5p/6 of people will truthfully answer yes (that includes the ones who rolled a six and were guilty) and (1-p)/6 of people will falsely answer yes. So out of all the yes answers, the proportion of guilty people is 5p / (4p + 1), which varies monotonically with p, can itself be anything from 0 to 1, and is only equal to 80% if p=4/9.
I can see your reasoning for the 80% figure: if someone says yes, we know they didn't roll a 1, therefore there are five remaining equiprobable things they might have rolled and four of those five mean they're guilty as hell. The flaw is in the word "equiprobable": because rolling a 6 changes your probability of saying yes, it follows that if all you know about someone is that they said yes, it's no longer equiprobable that they rolled 2, 3, 4, 5 or 6.
It's still high-ish, but less than half (if I did the revised calcualtion right, and the percentage of people who actually said yes was accurately deduced and reported in the article)
I would add that we can get a point estimate of p from sufficient samples using:
Prob (Yes) = (1+4p)/6 and Prob (No) = (5-4p)/6
Hence if we know the number of nos and yeses we can estimate the probability of guilt given a yes and a no answer and put confidence intervals on it should we so choose (if we know the sample size.
I think I was subconsciously assuming you were doing this with something where everyone was guilty, whereas that's not true here: it's endemnic, but that still means only 20% of people.
Indeed, if absolutely everyone were guilty and the aim of this exercise was purely to try to trick them into confessing something that could be used in a court of law, your reasoning would be perfectly all right :-)
I seem to recall teh version I heard was something like "do you masterbate" or "have you ever been influenced by a source you failed to cite when writing an essay at school" which applies to almost everyone, but isn't illegal.
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
andrewducker) wrote2011-08-01 12:40 pm
no subject
I'm interested that it seems to be working.
It also creates ... weird legal implications. It's probably best for the government to turn a blind eye. But with the conditions given, if someone says "yes", there's an 80% chance they're guilty. That's not beyond reasonable doubt, but would it suffice for a balance-of-probabilities civil judgement? We normally don't take someone's unsupported confession as sufficient evidence, but I don't know if someone could try...
no subject
Don't confuse P(A|B) with P(B|A)! If the real proportion of guilty people is p, then 5p/6 of people will truthfully answer yes (that includes the ones who rolled a six and were guilty) and (1-p)/6 of people will falsely answer yes. So out of all the yes answers, the proportion of guilty people is 5p / (4p + 1), which varies monotonically with p, can itself be anything from 0 to 1, and is only equal to 80% if p=4/9.
I can see your reasoning for the 80% figure: if someone says yes, we know they didn't roll a 1, therefore there are five remaining equiprobable things they might have rolled and four of those five mean they're guilty as hell. The flaw is in the word "equiprobable": because rolling a 6 changes your probability of saying yes, it follows that if all you know about someone is that they said yes, it's no longer equiprobable that they rolled 2, 3, 4, 5 or 6.
no subject
It's still high-ish, but less than half (if I did the revised calcualtion right, and the percentage of people who actually said yes was accurately deduced and reported in the article)
no subject
I would add that we can get a point estimate of p from sufficient samples using:
Prob (Yes) = (1+4p)/6
and
Prob (No) = (5-4p)/6
Hence if we know the number of nos and yeses we can estimate the probability of guilt given a yes and a no answer and put confidence intervals on it should we so choose (if we know the sample size.
no subject
no subject
no subject