Manipulable Tests and the Axioms of Probability.
Luciano Pomatto*, Alvaro Sandroni, Nabil Al-Najjar
Date: 2012-05-04 11:30 am – 12:00 pm
Last modified: 2012-04-17
Abstract
We study the problem of testing an expert's forecast. We show that it is intimately related to the axiomatization of probability. Every test that admits low Type-I error can be manipulated by a strategic expert, who can pass the test with arbitrarly high probability independently of the realized outcome. If the test excludes forecasts that violate countable additivity, then there exist non-manipulable tests. We study a class of
finitely additive probability measures satisfying a natural inductive property, and we conclude that it is a sufficient assumption for restricting the effect of manipulation.