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Juries reach judgement by unanimity rule. There is a jury of q people and 1 defendant. There are two states: J (guilty), and L (innocent). One of 2 actions is chosen: d (acquit), or f (condemn). If is state J the optimal action is f; if the state is L, the optimal action is d. No jury member has prior information, and prior probability for either state is 1/2. Each member interprets through their personal experiences, and we think of the information they receive, conditional on the state, as an independent signal. Each signal is correct with probability p > 1/2. 1. If all q members vote according to their signal, what is the probability that an innocent defendant is condemned? And the probability that a guilty defendant is acquitted? (Ruling out mistrials). 2. Imagine instead that a simple majority of "guilty" votes were sufficient for conviction. If q = 3, what is the prob. that an innocent defendant is condemned if all vote according to their signal? And the probability that a guilty defendant is acquitted?

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