Racetrack Betting and Consensus of Subjective Probabilities

In this paper we consider the dynamic process of race track betting. We show that there is a close connection between the dynamic race track betting process and the pari-mutuel method for constructing consensus of subjective probabilities considered in Eisenberg and Gale. This enables us to show that there exists a unique equilibrium point for the betting process. We further show that the dynamic betting process converges to this equilibrium point almost surely. Therefore the sequential race track betting gives a natural approach to inducing the consensus probabilities in Eisenberg and Gale. These consensus probabilities are different from the average of the subjective probabilities which is used in the conventional way of combining individually held opinions into a collective group statement. We compare these probabilities and this leads to a potential explanation of the favorite-longshot bias consistently observed in the studies of race track betting.