Indifference, neutrality and informativeness: generalizing the three prisoners paradox

The well-known Three Prisoners Paradox has been solved by Bayesian conditioning over the choice made by the Warder when asked to name a(nother) prisoner who will be shot. This paper generalizes the paradox to situations of N prisoners, k executions and m announcements made by the Warder. We also extend the consequences of hierarchically placing uniform and symmetrical priors (for example in the classical N = 3, k = 2,m = 1 scenario) for the probability p of the Warder naming Prisoner B, say. We prove that breaks of indifference and neutrality caused by assignment of uniform and symmetrical priors in lieu of degenerate indifference probabilities hold in general. We speculate on the general impossibility of maintaining noninformativeness throughout hierarchization.