Many inspections are manipulable
一个自称专家的人根据随机过程的历史观测做概率预测,检查者用测试函数检验其可靠性。本文证明,如果测试函数是Borel的且真专家总能通过,那么无知专家也能操纵通过。
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.