An optimal algorithm for stopping on the element closest to the center of an interval

Abstract A decision maker observes a sequence of n independent realizations from the uniform distribution on the unit interval. However, he does not observe the precise values of these realizations, but only their ranks relative to those that have appeared previously. The goal of the decision maker is to select the realization whose value is closest to 1 2 . A realization can only be selected at the moment of its appearance. We derive a stopping rule which maximizes the probability of achieving this goal, together with the asymptotic probability of success.