Can randomization be informative?

Abstract

In this paper the Pair of Siblings Paradox introduced by Pereira [1] is extended by considering more than two children and more than one child observed for gender. We follow the same lines of Wechsler et al.[2] that generalizes the three prisoners' dilemma, introduced by Gardner [3]. This paper's conjecture is that the Pair of Siblings and the Three Prisoners dilemma are dual paradoxes. Looking at possible likelihoods, the sure (randomized) selection for the former is non informative (informative), the opposite that holds for the latter. This situation is maintained for generalizations. Non informative likelihood here means that prior and posterior are equal.