102,625 research outputs found
Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship
This paper offers a comprehensive treatment of the question as to whether a
binary relation can be consistent (transitive) without being decisive
(complete), or decisive without being consistent, or simultaneously
inconsistent or indecisive, in the presence of a continuity hypothesis that is,
in principle, non-testable. It identifies topological connectedness of the
(choice) set over which the continuous binary relation is defined as being
crucial to this question. Referring to the two-way relationship as the
Eilenberg-Sonnenschein (ES) research program, it presents four synthetic, and
complete, characterizations of connectedness, and its natural extensions; and
two consequences that only stem from it. The six theorems are novel to both the
economic and the mathematical literature: they generalize pioneering results of
Eilenberg (1941), Sonnenschein (1965), Schmeidler (1971) and Sen (1969), and
are relevant to several applied contexts, as well as to ongoing theoretical
work.Comment: 47 pages, 4 figure
Common Mathematical Foundations of Expected Utility and Dual Utility Theories
We show that the main results of the expected utility and dual utility
theories can be derived in a unified way from two fundamental mathematical
ideas: the separation principle of convex analysis, and integral
representations of continuous linear functionals from functional analysis. Our
analysis reveals the dual character of utility functions. We also derive new
integral representations of dual utility models
Some discrete approaches to continuum economies
Given the preferences of the agents of a continuum economy, we define the average and unanimous preference. This allow us to consider several sequences of economies, in which only a finite number of different agents' characteristics can be distinguished. We obtain approximation results for the core of these economies
Compromises Between Cardinality and Ordinality in Preference Theory and Social Choice
By taking sets of utility functions as a primitive description of agents, we define an ordering over assumptions on utility functions that gauges their implicit measurement requirements. Cardinal and ordinal assumptions constitute two types of measurement requirements, but several standard assumptions in economics lie between these extremes. We first apply the ordering to different theories for why consumer preferences should be convex and show that diminishing marginal utility, which for complete preferences implies convexity, is an example of a compromise between cardinality and ordinality. In contrast, the Arrow-Koopmans theory of convexity, although proposed as an ordinal theory, relies on utility functions that lie in the cardinal measurement class. In a second application, we show that diminishing marginal utility, rather than the standard stronger assumption of cardinality, also justifies utilitarian recommendations on redistribution and axiomatizes the Pigou-Dalton principle. We also show that transitivity and order-density (but not completeness) characterize the ordinal preferences that can be induced from sets of utility functions, present a general cardinality theorem for additively separable preferences, and provide sufficient conditions for orderings of assumptions on utility functions to be acyclic and transitive.Cardinal utility, ordinal utility, measurement theory, utilitarianism
Social choice of convex risk measures through Arrovian aggregation of variational preferences
It is known that a combination of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preferences with the Föllmer-Schied (2002,2004) representation theorem for concave monetary utility functionals provides an (individual) decision-theoretic foundation for convex risk measures. The present paper is devoted to collective decision making with regard to convex risk measures and addresses the existence problem for non-dictatorial aggregation functions of convex risk measures - in the guise of variational preferences - satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). We prove an impossibility result for finite electorates, viz. a variational analogue of Arrow's impossibility theorem. For infinite electorates, the possibility of rational aggregation of variational preferences (i.e. convex risk measures) depends on a uniform continuity condition for the variational preference profiles: We shall prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. Methodologically, we adopt the model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). In an appendix, we apply the Dietrich-List (2010) analysis of logical aggregation based on majority voting to the problem of variational preference aggregation. The fruit is a possibility theorem, but at the cost of considerable and - at least at first sight - rather unnatural restrictions on the domain of the variational preference aggregator.variational preference representation, convex risk measure, multiple priors preferences, Arrow-type preference aggregation, judgment aggregation, abstract aggregation theory, model theory, first-order predicate logic, ultrafilter, ultraproduct
Egalitarian-Equivalence and the Pareto Principle for Social Preferences
When we construct social preferences, the Pareto principle is often in conflict with the equity criteria: there exist two allocations x and y such that x Pareto dominates y, but y is an equitable allocation whereas x is not. The efficiency-first principle requires to rank an allocation x higher than y if (i) x Pareto dominates y or (ii) x and y are Pareto-noncomparable and x is equitable whereas y is not. The equity-first principle reverses the order of application of the two criteria. Adopting egalitarian-equivalence as the notion of equity, we examine rationality of the social preference functions based on the efficiency-first or the equity-first principle. The degrees of rationality vary widely depending on which principle is adopted, and depending on the range of egalitarian-reference bundles. We show several impossibility and possibility results as well as a characterization of the social preference function introduced by Pazner and Schmeidler (1978). We also identify the sets of maximal allocations of the social preference relations in an Edgeworth box. The results are contrasted with those in the case where no-envy is the notion of equity.
Walrasian Solutions Without Utility Functions
SUMMARY: This note reviews consumersâ preference orderings in economics and shows that irrationality is a poor explanation for apparent violations of some axioms of order. Apparent violations seem to be better explained by the fact that consumersâ utility functions, if they exist at all, might not even belong to the class of quasi-concave functions. However, the main task of markets is the determination of equilibrium price vectors. The note shows in addition that, in Walrasian structures, quasi-concave utility functions are unnecessary for the determination of equilibrium price vectors.Walrasian structures, preference orderings, irrationality, utility functions, and equilibrium price vectors
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