Biased coins a model for higher-order probabilities

Jeanne Peijnenburg

David Atkinson

pp. 241-248

in: Maria C. Galavotti, Elisabeth Nemeth, Friedrich Stadler (eds), European philosophy of science, Berlin, Springer, 2014

Abstract

Is it coherent to speak of the probability of a probability, and the probability of a probability of a probability, and so on? We show that it is, in the sense that a regress of higher-order probabilities can lead to convergent sequences that determine all these probabilities. By constructing an implementable model which is based on coin-making machines, we demonstrate the consistency of our regress.