I strongly disagree with this. The improvements in reasoning, applied bilaterally AND to the jury, work in favour of the side that is in fact correct, just as would increase in everyone's IQ (including that of the jury)
Consider a game of chess. There is one side, other side, and an arbiter. If neither player cares about chess rules, and arbiter is incompetent at enforcing rules, you fail to even play a game of chess at all. If you teach rules of chess to all 3 and provide chess training to the players, you set up situation where the best-reasoning opponent wins (and if one side lacks some pieces at start, that side will reliably lose).
Consider a game of chess. Giving access to chess training to both sides makes the smartest (best reasoning) side more likely to win.
Doesn't sound likely. I'd expect the advantage of superior reasoning to be reduced by equal amounts of training for both sides.
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 ).
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?