Taradas Bandyopadhyay

Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference

Abstract We address the problem of aggregating demand across a group of consumers, who are identical in terms of wealth and face identical price vectors, but vary in their chosen consumption bundles. We show that, when a stochastic demand function is constructed to aggregate a number of deterministic demand functions, satisfaction of the weak axiom of stochastic revealed preference by this stochastic demand function is weaker than the restriction that every underlying deterministic demand function satisfy Samuelsons weak axiom of revealed preference. Journal of Economic Literature Classification Number: D11.

Revealed Preference Theory, Ordering and the Axiom of Sequential Path Independence

This paper is concerned with the axiomatic foundation of the theory of choice. Describing a choice procedure which one often observes in real life, this paper shows that the requirement of path independence of such a procedure is a necessary and sufficient condition for transitive or full rationalization of a choice function, i.e. the existence of a preference ordering. It is shown that our result holds when rationality is identified with different interpretations of the binary relations of preference revealed by a choice function, e.g. the revealed preference relation of Arrow, the wide revealed preference relation of Richter. It is also shown that a weaker version of our path independence condition is both necessary and sufficient for a rational choice.

Revealed Preference Axioms for Rational Choice

This paper provides a simple axiomatic foundation of rational choice when the indifference relation is not necessarily transitive. Utilizing a notion of revealed preference relation, which says that an alternative x is revealed preferred to an alternative y whenever x is chosen while y is available, this paper establishes that the requirement that a rejected alternative of a set A can never be revealed preferred to some chosen element of A (resp. some element of A) is equivalent to quasi-transitive (resp. acyclic) rationalization; i.e., is a necessary and sufficient condition for the existence of a strict partial order (resp. a suborder); while the requirement that at least one of the chosen elements of a set A is always strictly revealed preferred to every rejected alternative of A is equivalent to pseudotransitive rationalization i.e., is a necessary and sufficient condition for the existence of an interval order. Copyright 1991 by Royal Economic Society.

Characterization of Generalized Weak Orders and Revealed Preference

SummaryThis short paper provides an alternative framework to axiomatize various binary preference relations such as semiorder, weak semiorder etc. A set of simple axioms is presented in terms of revealed-preferred and revealed-inferior alternatives which makes the connection between various binary preference relations transparent; and every single axiom is necessary and sufficient for the existence of a binary preference relation of a specified type.

Extension of an order on a set to the power set: some further observations

Abstract Kannai and Peleg have shown that two appealing axioms for extending a linear order on a set of at least six elements to a weak order on the power set are mutually incompatible. This note shows that these two axioms are indeed compatible when the set contains five elements. Providing an alternative definition of one of these axioms we examine the crucial factor in dividing the possibility and impossibility results in this context.

On the frontier between possibility and impossibility theorems in social choice

Abstract This paper attemts to make precise the frontier between possibility and impossibility theorems in social choice. It is shown that some criterion of rejection of some alternative is the critical factor. In the absence of such a condition, it is possible to construct a fairly wide class of “democratic” decision rules which satisfies a class of consistency conditions. Any one of these, together with the criterion of rejection, generates a power structure similar to the ones discovered by Arrow, Gibbard, and others when the decision rule is required to satisfy the weak Pareto principle and the independence condition.

The structure of coalitional power under probabilistic group decision rules

Abstract The paper extends the work of S. Barbera and H. Sonnenschein on probabilistic social welfare functions by permitting quasi-transitive and/or acyclic probabilistic social preferences. Allowing for quasi-transitivity it is shown that the social decision rule is characterized by a subadditive veto power structure. Gibbards result on oligarchy is shown to be a special case. Similarly, Sens theorem on Paretian Liberals is shown to be implied by the power structure in the acyclic case.

Pareto optimality and the decisive power structure with expansion consistency conditions

Abstract This paper establishes the implication of Pareto optimality requirement in social choice. It is shown that a Paretian social choice function satisfying certain expansion-consistency conditions, which are based on the rationality of optimization, generates extremely asymmetric power structure, e.g., dictatorship or oligarchic.

Coalitional manipulation and the Pareto rule

Abstract This paper examines aggregation procedures that map profiles of individual preferences into choice sets. An aggregation procedure is said to be “manipulable by a coalition” if there is a group of individuals, and a preference profile, such that every member of the group prefers the choice set obtained when they are misrepresenting their preferences, to the one obtained when they are honest. We show that the Pareto rule, which is an aggregation procedure that maps profiles of individual preferences into corresponding sets of Pareto optima, is not manipulable by any coalition of individuals under various behavioural assumptions which relate preferences over choice sets to preferences over alternatives. The non-manipulability of the Pareto rule by a single individual follows as a special case under these behavioural assumptions.

Revealed preference and the axiomatic foundations of intransitive indifference: the case of asymmetric subrelations

Abstract This paper provides an axiomatic structure for various binary preference relations that are reflexive, connected, and transitive in their asymmetric subrelations known as quasi-transitive orderings. A choice function generates various (distinct) binary preference relations, such as the base relation, the revealed preference relation, and the wide revealed preference relation. For each interpretation of a binary preference relation, we present an axiom that ensures the existence of a quasi-transitive preference ordering. A description of a choice procedure is considered which one often observes in real life and it is shown that the path independence of such a procedure is a sufficient condition for a quasi-transitive ordering of various binary preference relations.