Chance

David Z. Albert, Hans Christian von Baeyer

Simon W. Saunders

Abstract The concept of objective probability — chance — has three distinctive features: chances are measured by statistics, but only with high chance, increasing with the number of trials involved; when the chances of the outcomes of a chance process are known, even in the context of a single trial, then one's subjective probabilities — credences — in those outcomes should be set equal to those chances; and finally, chance processes involve uncertainty as to the outcomes of those processes. The second of these features is established for ratios in the squared norms of branches by the Born-rule theorem, proved in Chapter 8. This chapter shows that the first and third hold for those same quantities. All three characteristics of chance thus apply to branching in the Everett interpretation. In consequence, branching processes should be identified with chance processes, and ratios in the squared norms with chances.

Federico Levi

Saunders, Simon

The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection of chance with statistics, but with degrees of belief, and more broadly the entire phenomenology of (seemingly) chance events and their measurement. Branching structure in the decoherence-based many worlds theory provides an account of what chance is that satisfies all these desiderata, including the requirement that chance involves uncertainty.

Norman Phillips Campbell

Summary It is maintained that the chance of an event happening is always a physical property of a system, measured by a process of derived measurement involving the two fundamental magaitudes—nuumber of events and number of trials. Chances are not measurable by a process of fundamental measurement. Bat the calculation of chances is analogous to fundamental measurement. It is usually theoretical, and is valuable only in so far as the calculated chances are confirmed by measurement. When a proposition concerns a system characterized by a chance, it may sometimes (but by no means always) be regarded as having a definite probability determined by that chance. The probability of propositions which do not concern systems characterized by chances has nothing to do with chance.

Donald E. Groom, F. James