THE ECONOMIC MAN'S LOGIC,

The purely mathematical law of large numbers follows from the definition of a probability measure, combined with the assumption that each of an indefinitely long sequence of trials has the same probability distribution of outcomes. Such trials are called repeated and independent. Moreover, if the binary preference relation completely orders the set of decisions and obeys a few other axioms, the consistent decision maker will be indifferent between betting on a specified outcome of any one of such trials, and on any event whose probability is equal to the relative frequency of such outcomes in a large number of observed trials. In his Foundations of Inductive Logic, Sir Roy Harrod declares, on the other hand, that our experience justifies the assumption that a physical phenomenon always observed in the past will be frequently observed in the future. In the present paper, a contribution to a Volume in Honor of Harrod, the possible relation is discussed between this continuity principle of his and the properties of those sequences of physical events which the consistent decision-maker might regard as being, approximately, repeated and independent. Author