Many inspections are manipulable

Abstract

A self-proclaimed expert uses past observations of a stochastic process to make probabilistic predictions about the process. An inspector applies a test function to the infinite sequence of predictions provided by the expert and the observed realization of the process in order to check the expert’s reliability. If the test function is Borel and the inspection is such that a true expert always passes it, then it is also manipulable by an ignorant expert. The proof uses Martin’s theorem about the determinacy of Blackwell games. Under the axiom of choice, there exist non-Borel test functions that are not manipulable.