We generalize a set of axioms introduced by Rubin, A weak system of axioms for “rational” behavior and the nonseparability of utility from prior, Statistics & Decisions, to the case of partial preference. That is, we consider cases in which not all uncertain acts are comparable to each other. We demonstrate some relations between these axioms and a decision theory based on sets of probability/utility pairs. We illustrate by example how comparisons solely between pairs of acts is not sufficient to distinguish between decision makers who base their choices on distinct sets of probability/utility pairs.
Digital Object Identifier: 10.1214/lnms/1196285378