There should be experiments on different ways of deciding guilt to see which are most accurate. My understanding is that most of the current system was created centuries ago, and wasn't the result of experimentation.

We should determine the optimal number of people on a jury, and whether juries get better results with various selections of jurors (paid professional jurors or drafted jurors, high-IQ jurors or low-IQ jurors, old or young, diverse along various dimensions or not, etc.).