Any Inspection is Manipulable

A forecaster provides a probabilistic prediction regarding the following day’s state of nature. To examine the forecaster, an inspector employs calibration tests that compare the average prediction and the empirical frequency of pre-specified events. This paper shows that any mixed test can be manipulated in the sense that, independently of the state realizations, the difference between the average prediction and the past empirical frequency that corresponds to almost any test employed diminishes to zero. In other words, a forecaster has a prediction scheme that passes almost any test. In particular, a forecaster can pass all the tests in a countable set simultaneously. I am grateful to Rann Smorodinsky, Sylvain Sorin and two anonymous referees for their helpful