Yes, bounded-rationality and rational ignorance are consequnces of the limits of human computational power. But humans have more than enough computational power to do better than in-group bias, anchoring effects, deciding when to follow authority simply because it is authority, or believing something because we want it to be true.
We've had that capacity since the recorded history began, but ordinary people tend to not notice that they are not considering all the possibilities. By contrast, it's not uncommon for people to realize that they lack some relevant knowledge. Which isn't to say that realization is common or easy to get people to admit, but it seems possible to change, which is much less clear for cognitive bias.
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?