Towards a revised probabilistic basis for quantum mechanics

This paper describes a modification of the concept of probability associated with quantum mechanics by replacing the quantitative notion with a comparative one. The comparative concept is axiomatized and given a frequentist interpretation. It provides a more fundamental description of physical reality than does the quantitative concept. Of particular interest are the facts that comparative probability admits new models of random phenomena and that these new models intrinsically exhibit behaviour like that of complementarity as well as a new phenomenon of quantization of uncertainty. In particular this proposal leads to a comparative probability description of joint observations of complementary observables and an assertion that the usual application of the correspondence principle can be taken as rigorously correct rather than as an approximation based upon arbitrarily small h/2π or arbitrarily large quantum numbers. (Auth.)