Rational Justice

geebee2

I'm interested in how courts and juries might use rational techniques to arrive at correct decisions on guilt.

In a complex case, it would seem to sensible to assess each component of the prosecution and defence case, and estimate the relative likelihood. If the prosecution case is (say) 100 times more likely than the defence case, then you can say the defendant is guilty beyond reasonable doubt.

I never heard of this being done though. I recently made an analysis of the Massei report into the Amanda Knox case. It looked like this ( see http://massei-report-analysis.wikispaces.com/ for the entire analysis and some insight into the numbers below ).

Event	Prosecution Probability	Defence Probability
Phone at cottage at 22:13	1%	99%
DNA evidence correct	50%	50%
Break in staged to look like Rudy did it vs unstaged break-in	10%	90%
Conspiracy among 3 near strangers with no apparent motive vs burglary gone wrong	5%	95%
Murder weapon was two knives rather than one	10%	90%
Time of death 23:30 vs 21:10 according to empty duodenum	10%	90%

This is perhaps a bit vague. It's not a great example, because in the end I didn't find any credible prosecution evidence. It's not entirely clear what the "probability" numbers here actually are, and whether two columns are needed. But hopefully it shows that the Massei's account of the murder is quite improbable, and there is considerable doubt.

I'm interested in possibly devising a more complete framework for how such an assessment should be done, the pitfalls that need to be guarded against (how uncertain are the probability estimates?), and even views as to how "reasonable doubt" should be quantified.

Perhaps readers would like to make an assessment of other interesting cases, to explore the issues.

Or how would you approach this problem?

I'm interested in how courts and juries might use rational techniques to arrive at correct decisions on guilt.

Event	Prosecution Probability	Defence Probability
Phone at cottage at 22:13	1%	99%
DNA evidence correct	50%	50%
Break in staged to look like Rudy did it vs unstaged break-in	10%	90%
Conspiracy among 3 near strangers with no apparent motive vs burglary gone wrong	5%	95%
Murder weapon was two knives rather than one	10%	90%
Time of death 23:30 vs 21:10 according to empty duodenum	10%	90%

Perhaps readers would like to make an assessment of other interesting cases, to explore the issues.

Or how would you approach this problem?

I would still place the difference the other way. I'd give naive Kasparov (even) better odds against naive you than I would give trained Kasparov against a you of equal training and experience.

Well the chess is prone to ties, so maybe I'd be able to reliably tie the Kasparov if we had equal training and if I am nearly as smart as him. I do think though that my chances at winning would be massively better if we both played chess for first time after reading the rules off a book. I think it'd be close enough to 50/50 at start with him gaining the lead with each next game, winning reliably after some dozen games.

But the point with the legal debate is that one side is right, and other side is wrong; things do not start off symmetrical. Say, we are to put random people to play chess, with one side missing a queen. I play chess; it seems totally self evident to me that among trained players the one lacking the queen will be guaranteed to lose, while for the untrained players the outcome will be much more random.

For the trials I think the original point was to educate the jury, paralleling the teaching of rules to the chess arbiter. The jury doesn't need to think very hard to verify an argument, it only needs to know the valid rules of reasoning. Suppose we were to have a debate on some fact of mathematics, one real well trained guy trying to prove Pythagorean theorem and other real well trained guy trying to prove something wrong (e.g. approximating the hypotenuse with staircase and proving c=a+b). In front of the jury which decides. With today's jury, chances are the jury would be unreliable in their decision. But it is a fact that trained mathematicians are not so easily misled.