Consistent representations of preferences

Pareto optimal, core, Walrasian, or Nash equilibrium outcomes depend on the preferences of the agents involved. On the other hand, value allocations, the Shapley value, the Nash bargaining solution, and the expected utility are contingent on the payoffs selected from an infinite number of representations of each preference. It also holds for risk aversion issues or welfare functions that combine individual utility functions to evaluate economic policies. To avoid inconsistencies and overcome this problem, we follow Kannai (Econometrica 38:791–815, 1970) to construct a “canonical” utility representation for each continuous preference. Exploring unique preference representations can lead to a more precise understanding of decision-making processes. This approach can help study economic solutions and policies in scenarios where there is diversity in individuals’ preferences, as it facilitates the ranking of consumption bundles, the ordering of transitions between bundles, and interpersonal comparisons. Thus, we provide theoretical foundations to the implicit assumption of consistency in problems where the solutions depend on utility functions or payoffs.