A puzzle: what happens in the blue-eyed islanders puzzle if we allow a small probability p for each each person to make a mistake each night? Assume that the probability of a mistake is the same for each and is common knowledge, the islanders are all ideal Bayesian reasoners, and let’s say that 80% is the confidence cutoff past which someone leaves.
[Question] Probabilistic Blue-Eyed Islanders
A puzzle: what happens in the blue-eyed islanders puzzle if we allow a small probability p for each each person to make a mistake each night? Assume that the probability of a mistake is the same for each and is common knowledge, the islanders are all ideal Bayesian reasoners, and let’s say that 80% is the confidence cutoff past which someone leaves.