I'm going to attempt to hijack this thread with something closer to the supposed topic of "rational justice" than merely using bayesian evidence to determine guilt or innocence.
I have a wild idea that the ideas behind TDT could be used to place Rawls' theory of justice on a less irritating foundation. For the uninitiated, Rawls argues that society should determine rules as if they were mediated in an "original position" in which nobody knows their ultimate role or social class in life, and that it is rules determined in such a way that may truly be called "just". This "original position" and the "veil of ignorance" that separates it from the practical world is profoundly frustrating, because in my opinion the individuality that would be necessary for us to consent to the deliberation of rules is necessarily stripped in the "original position", preventing rules determined in such a way from being meaningful.
I don't know very much about TDT, though, and so this could all very well be nonsense. Any opinions?
...For the uninitiated, Rawls argues that society should determine rules as if they were mediated in an "original position" in which nobody knows their ultimate role or social class in life, and that it is rules determined in such a way that may truly be called "just". This "original position" and the "veil of ignorance" that separates it from the practical world is profoundly frustrating, because in my opinion the individuality that would be necessary for us to consent to the deliberation of rules is necessarily strip
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?