The paper characterizes the Shannon and Tsallis entropies in a standard framework of decision theory, mixture sets. Procedural mixture sets are introduced as a variant of mixture sets in which it is not necessarily true that a mixture of two identical elements yields the same element. This allows the process of mixing itself to have an intrinsic value. The paper proves the surprising result that simply imposing the standard axioms of von Neumann-Morgenstern on preferences on a procedural mixture set yields the entropy as a representation of procedural value. An application to the relation between choice probabilities and decision times in decision processes elucidates the difficulty of extending the drift-diffusion model to multi-alternative choice.
This paper was the Jaffray lecture at RUD 2023.
This paper axiomatizes an index of consumer freedom of choice and applies it to U.S. consumer data from 2004 to 2017. The Renyi entropy arises naturally as an index of the residual of welfare that remains after accounting for total consumption, the price level, and inequality. We
show that this index can be interpreted as the freedom of choice of a representative consumer allocating a dollar of expenditure to goods. When applied to data, we find that the freedom of choice index was stagnant between 2004 and 2009 but substantially increased thereafter. This
increase is driven by an increase in the total number of goods consumed as well as a more even distribution of expenditure across goods.
We analyze the problem of the choice of a central bank constitution. We model the decision problem as a choice behind a veil of ignorance in which the policy maker only receives information about predicted behavior under different policies. The policy maker is informed about (probability distributions of) consumers’ behavior and the distribution of productivity shocks but does not know consumers’ interpersonally comparable utility functions. Starting from a representation theorem for the policy maker’s preferences over policies, we compare price stabilization, output stabilization, and inflation targeting in a standard new Keynesian model with Calvo price staggering. Surprisingly, under our policy criterion, the policy maker perceives a tradeoff between output stabilization and price stabilization. The reason is that in the absence of knowledge about cardinal utility functions, stabilizing the natural level of output is not normatively desirable. We find that the policy maker puts a higher emphasis on price stability than output stability if price staggering is low, intertemporal discounting is high,
intertemporal substitutability is low, or substitutability between goods is high.
Behind the veil of ignorance, a policy maker ranks combinations of game forms and information about how players interact within the game forms. The paper presents axioms on the preferences of the policy maker that are necessary and sufficient for the policy maker’s preferences to be represented by the sum of an expected valuation and a freedom measure. The freedom measure is the mutual information between players’ strategies and the players’ outcomes of the game, capturing the degree to which players control their outcomes. The measure extends several measures from the opportunity set based freedom literature to situations where agents interact. This allows freedom to be measured in general economic models and thus derive policy recommendations based on the freedom instead of the welfare of agents. To illustrate the measure and axioms, applications to civil liberties and optimal taxation are provided.
We propose a behavioral theory of preference for decision rights, driven by preference for freedom, power, or non-interference, which can lead subjects to value decision rights intrinsically, i.e., beyond the expected utility associated with them. We conduct a novel laboratory experiment in which the effect of each preference is distinguished. We find that the intrinsic value of decision rights is driven more strongly by preference for non-interference than by preference for freedom or power. This result suggests that individuals value decision rights not because of the actual decision-making process but rather because they dislike others interfering in their outcomes.