Subjective Probability Does Not Exist

Abstract

Probabilities of one-time events are unobservable and unmeasurable. According to empiricist and positivist principles, they must be meaningless. However, our cognitive limitations do not prevent entities and effects from existing. We show that the argument for existence of subjective probabilities relies crucially on the non-existence of objective probabilities. In this case however, the existence of subjective probabilities reduces to a triviality. When objective probabilities do not exist, we are free to believe whatever we like about these probabilities, without any consequences. The theorems which establish the existence of subjective probabilities are normally interpreted as establishing the existence of beliefs about probabilities. We show that this interpretation is not tenable when objective probabilities do not exist. We establish the validity of an alternative interpretation: in absence of objective probabilities, we are free to choose any arbitrary number as a subjective probability.

Keywords: Subjective Probability, Bayesian Probability, Foundations of Probability, Frequency Theory

JEL Classification: B40, C11