Stochastic demand correspondences and their aggregation properties

Bandyopadhyay, Dasgupta and Pattanaik [JET, 2002] have presented a construction that aggregates standard demand functions by a stochastic demand function, in such way that the latter satisfies the weak axiom of stochastic revealed preference when the former fulfil Samuelson's weak axiom of revealed preference. We introduce a concept of stochastic demand correspondences and generalize WASRP to this new setting. Also, we propose a procedure to aggregate stochastic demand correspondences that (a) includes the previous one by those authors, (b) aggregates the weak axiom of stochastic revealed preference (and thus stochastic substitutability when we started with tight stochastic demand functions), and (c) produces a stochastically rational stochastic demand correspondence when the primitive ones are stochastically rational. Interpretations of the model are provided too. An analogous to the result that rationalizability of stochastic demand functions by stochastic orderings implies WASRP holds for the correspondence setting. We also discuss the convenience of adopting a formal variation of the notion of being stochastically rational that was proposed in the literature.Weak Axiom of Stochastic Revealed Preference; Weak Axiom of Revealed Preference; representative consumer; stochastic demand aggregation.

Maximality with or without binariness: transfer-type characterizations

We provide the first necessary and su±cient conditions in the literature for the existence of maximal elements in a non-binary choice framework. As an application, the characterization of the existence of maximal elements for acyclic binary relations obtained in Rodriguez-Palmero and Garcia-Lapresta, 2002, Mathematical Social Sciences 43, 55-60, is deduced as a Corollary. Further characterizations in di®erent settings given by Tian and Zhou, 1995, Journal of Mathematical Economics 24, 281- 303, follow as well. Analogous characterization problems in the k- acyclic binary cases are solved too.maximization; non-binary choice function; transfer-continuity; k-acyclicity

Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto

This paper investigates ethical aggregation of infinite utility streams by representable social welfare relations. We prove that the Hammond Equity postulate and other variations of it like the Pigou-Dalton transfer principle are incompatible with positive responsiveness to welfare improvements by every generation. The case of Hammond Equity for the Future is investigated too.Social welfare function; Equity; Inequality aversion; Pareto axiom; Intergenerational justice

Stochastic demand correspondences and their aggregation properties

Bandyopadhyay, Dasgupta and Pattanaik [JET, 2002] have presented a construction that aggregates standard demand functions by a stochastic demand function, in such way that the latter satisfies the weak axiom of stochastic revealed preference when the former full Samuelson's weak axiom of revealed preference. We introduce a concept of stochastic demand correspondences and generalize WASRP to this new setting. Also, we propose a procedure to aggregate stochastic demand correspondences that (a) includes the previous one by those authors, (b) aggregates the weak axiom of stochastic revealed preference (and thus stochastic substitutability when we started with tight stochastic demand func- tions), and (c) produces a stochastically rational stochastic demand correspondence when the primitive ones are stochastically rational. Interpretations of the model are provided too. An analogous to the result that rationalizability of stochastic demand functions by stochastic orderings implies WASRP holds for the correspondence setting. We also dis- cuss the convenience of adopting a formal variation of the notion of being stochastically rational that was proposed in the literature.

Liberal approaches to ranking infinite utility streams: When can we avoid interferences?

In this work we analyse social welfare relations on sets of infinite utility streams that verify various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that agree with axioms of that kind together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani prove that a fully liberal non-interfering view of a finite society leads to dictatorship if weak Pareto optimality is imposed. We first prove that extending the horizon to infinity produces a reversal of such impossibility result. Then we investigate a related problem: namely, the possibility of combining “standard” semicontinuity with efficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between continuity and non-interference principles, both under ordinal and cardinal views of the problem. Our analysis ends with some insights on the property of representability in the presence of non-interference assumptions. In particular we prove that all social welfare functions that verify a very mild efficiency property must exert some interference (penalising both adverse and favorable changes) on the affairs of particular generations.Pareto axiom; Intergenerational justice; Social welfare relation; Non-interference; Continuity

On integrability and aggregation of superior demand functions

When each of the members of a collective displays a demand behavior that is consistent with a homogeneous of degree one in income demand, it is well known that some properties carry over to the aggregate representative consumer. We investigate those issues when the components of the society are allowed to behave in agreement with less restrictive demand patterns, namely superior demand functions.

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

A selection of maximal elements under non-transitive indifferences

In this work we are concerned with maximality issues under intransitivity of the indifference. Our approach relies on the analysis of "undominated maximals" (cf., Peris and Subiza, J Math Psychology 2002). Provided that an agent's binary relation is acyclic, this is a selection of its maximal elements that can always be done when the set of alternatives is finite. In the case of semiorders, proceeding in this way is the same as using Luce's selected maximals. We put forward a sufficient condition for the existence of undominated maximals for interval orders without any cardinality restriction. Its application to certain type of continuous semiorders is very intuitive and accommodates the well-known "sugar example" by Luce

Choice-Nash Equilibria

We provide existence results for equilibria of games where players employ abstract (non binary) choice rules. Such results are shown to encompass as a relevant instance that of games where players have (non-transitive) SSB (Skew-Symmetric Bilinear) preferences, as will as other well-known transitive (e. g. Nash´s) and non-transitive (e. g. Shafer and Sonnenschein´s) models in the literature. Further, our general model contains games where players display procedural rationality.