Assuming a jury is like a sample of a population.
Assume the following:
The population is a million people. There are X percent who think the defendant is guilty. Choose N random people to be a jury.
Given X, how many jurors (what sample size) would you need to give 95% accuracy of the juror decision being the same majority decision as the entire population.
I would guess that if X is closer to 50% like 50.1% then you would need a very large jury to make sure you got the accurate result. Whereas if X is closer to 0% or 100% you might need just one juror.
So assume the everyone in the population chooses guilty or innocent at random 50/50. (So they might do this and 60% have randomly chosen guilty.) On average how many jurors would you need for them to give the same result as a census 95% of the time? [I added this assumption because we need to know how often the population is split and how often the population is in agreement which will affect the results. But thinking about it this condition would mean the jury would only agree with the population 50% of the time! Right??? So perhaps the condition should be "Provided above 60% of the population is in agreement the jury should agree with the population 95% of the time. How many jurors are needed in the worst case scenario?" ].
i.e. is there some way to calculate the best number of people for a jury such that the population as a whole will be happy most (95%) of the time? And justice is "seen" to be done?