The axiomatic foundations of Bentham and Rawls solutions are discussed within the broader domain of cardinal preferences. It is unveiled that both solution concepts share all four of the following axioms: Nonemptiness, Anonymity, Unanimity, and Continuity. In order to fully characterize the Bentham and Rawls solutions, three variations of a consistency criterion are introduced and their compatibility with the other axioms is assessed. Each expression of consistency can be interpreted as a property of decision-making in uncertain environments.