Interesting Links for 1-8-2011

[andrewducker]

• Throwing dice gets to the truth about killing leopards. Incredibly smart thinking. I'm impressed
  (tags: random behaviour questions)

Comments

[steer.livejournal.com]

That is really very clever indeed!

[simont]

I have a feeling I've heard of a trick like this before. My memory thinks it was something to do with trying to find out rates of drug use in the US, or possibly the US military, but I can't recall where I might have read that and a quick google didn't find anything that looked like what I was half-remembering. I also have a vague feeling that the one I'm thinking of didn't provide for both false positives and false negatives; it just gave you deniability for giving a "yes" answer, but didn't do anything to turn some real "yes" answers into "no". I wonder how much more accurate the latter makes the tests.

(It also puts me faintly in mind of the practice of loading one rifle with blanks when organising a firing squad.)

[cartesiandaemon.livejournal.com]

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...

[simont]

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.

[cartesiandaemon.livejournal.com]

Doh. I really can't believe I did that :(

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)

[steer.livejournal.com]

Damn -- got there before me. :-)

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.

[cartesiandaemon.livejournal.com]

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.

[simont]

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 :-)

[cartesiandaemon.livejournal.com]

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.

[nancylebov.livejournal.com]

I can see how this approach would break up a fixed strategy of saying "No, I've never killed any leopards" so that it requires more thought to maintain a lie.

I'd like to see a parallel program checking on whether people have abused "anonymous" answers.

I'd also like to see whether the 18% of ranchers having killed leopards has a good match with the apparent number of leopards killed.