Correlation Probabilistic Sophistication

Abstract

We study binary choice under uncertainty when the comparison between two acts can depend on the joint distribution of their realized outcomes. This motivates correlation probabilistic sophistication (CPS), a subjective reduction principle that extends both probabilistic sophistication and Fishburn's nontransitive subjective expected utility. We show how simultaneous event exchangeability elicits a unique solvable finitely additive subjective probability and reduces binary comparisons of acts to induced joint laws. Under convex range, the induced domain coincides with the full finite joint-law domain, allowing the transfer of correlation-utility representations from risk and, under completeness and Strong Independence, correlation expected utility with a skew-symmetric comparison kernel. Under completeness and transitivity, CPS collapses to ordinary probabilistic sophistication. We further extend the framework to multiple small worlds, allowing correlation sensitivity to vary with the source of uncertainty.