Joint Orders in Comparative Probability

Abstract

Comparative probability (CP) is a theory of probability in which uncertainty is measured by a CP ordering of events, rather than by a probability measure. A CP order is additive iff it has an agreeing probability measure. This paper deals with the formation of joint CP orders from given marginals, both with and without a certain independence condition, and with emphasis on the nonadditive case. Among the results are these: a CP model for many independent and identically distributed trials of a single experiment must be additive, with an agreeing probability measure of product type; there are CP marginals that have no joint CP order at all; there is a class of CP models, strictly containing all the additive ones, which are well behaved with respect to the formation of joint orders. We present as well several sufficient conditions, and one necessary condition, under which given marginals have a joint CP order.