Asymptotic uniqueness in long-term prediction

Vladimir Vovk

Abstract: This paper establishes the asymptotic uniqueness of long-term probability forecasts in the following form. Consider two forecasters who repeatedly issue probability forecasts for the infinite future. The main result of the paper says that either at least one of the two forecasters will be discredited or their forecasts will converge in total variation. This can be regarded as a game-theoretic version of the classical Blackwell–Dubins result getting rid of some of its limitations. This result is further strengthened along the lines of Richard Jeffrey’s radical probabilism.