An alternative proof of Fishburn’s axiomatization of lexicographic preferences

We present an alternative proof of Fishburn’s (1975) axiomatization of lexicographic preferences. The essence of our proof lies in identifying “an extremely pivotal factor”. Our proof reconfirms the strong interconnections between Arrow’s and Gibbard–Satterthwaite’s theorems with Fishburn’s axiomatization.     

Individual decisions and group decisions: The fundamental differences

The paper contains a unified development of Arrow's impossibility theorem for rational group decisions, Gibbard and Satterthwaite's impossibility theorem for strategy-proof group decisions, and the close reciprocal relationship that exists between these two theorems.     

The structure of coalitional power under probabilistic group decision rules

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. Gibbard's result on oligarchy is shown to be a special case. Similarly, Sen's theorem on Paretian Liberals is shown to be implied by the power structure in the acyclic case.     

Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions

Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategy-proof if it always induces every committee member to cast a ballot revealing his preference. I prove three theorems. First, every strategy-proof voting procedure is dictatorial. Second, this paper's strategy-proofness condition for voting procedures corresponds to Arrow's rationality, independence of irrelevant alternatives, non-negative response, and citizens' sovereignty conditions for social welfare functions. Third, Arrow's general possibility theorem is proven in a new manner.     

Pivotal voters: A new proof of arrow's theorem

This paper presents a new proof of Arrow's ‘General Possibility Theorem’, focusing on the way how ‘social’ preferences change in response to changes in the preferences of individuals, under given social welfare functions.     

Another direct proof of the Gibbard–Satterthwaite Theorem

This paper provides a new and direct proof of the Gibbard–Satterthwaite Theorem based on induction on the number of individuals.     

On the existence of lindahl equilibria in economies with a measure space of non-transitive consumers

We present a generalization of Roberts' theorem on the existence of Lindahl equilibria in economies with a measure space of agents. The principal contribution of this paper is methodological. We show that by formulating the problem in what we consider to be its natural infinite dimensional setting, the basic structure of Debreu's proof in the theory of value can be applied. Our proof makes use of functional analysis and relies, in particular, on Artstein's characterization of weak sequential convergence in L₁(μ).     

Managerial risks and rewards in public enterprises

This essay explores a twofold problem: from the standpoint of the community, what is the appropriate attitude for managers of a public enterprise to have toward decisions with uncertain outcomes; and what is implied for the managerial rewards or penalties that are required to induce managers to adopt that attitude. Taking a theorem of Arrow's as a point of departure, the essay argues that managers should be induced to maximize expected benefit. With the aid of “career” and “bonus” functions, implications for managerial rewards and penalties are explored under     

A simple proof of Nataf's theorem on consistent aggregation

In this paper we present a simple and short proof of Nataf's theorem on consistent aggregation for the case that all functions involved have non-zero first derivatives.     

On the theory of aggregation

Kenneth Arrow's famous General Possibility Theorem, which describes logical restrictions on the possible ways of aggregating individuals' preference orderings into a social preference ordering, is extended and proved in general for aggregation procedures on arbitrary domains.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

A note on locally constant income elasticities

A simple proof of Willig's theorem that all non-unitary income elasticitiesthat are constant must be equal to one another is given. It is also shown that multiplicatively separable demand implies locally constant income elasticity.     

The impossibility of IQ

Arrow's Impossibility Theorem is applied to the problem of measuring IQ. It is necessary to combine specific ability orderings into a general intelligence ranking, but this is impossible without infringing one desirable condition. IQ scores have no place in economics.     

Equilibrium points of non-atomic games: Asymptotic results

An elementary proof, as well as an asymptotic version of David Schmeidler's theorem on the equilibrium points of non-atomic games is presented.     

On the uniqueness of individual demand at almost every price system

A simple new proof, based on Fubini's theorem, is given for the uniqueness of individual demand at almost every price system, even if preferences are nonconvex.     

A simple proof of Blackwell's “comparison of experiments” theorem

This note presents a simple proof of Blackwell's well-known theorem on the equivalence of two orderings of experiments, one based on the statistical concept of sufficiency, and the other on the economic concept of the value to the decision makers.     

On the generic inefficiency of differentiable market games

It is shown that a differentiable market game remains generically inefficient when its strategic outcome function is perturbed smoothly. The proof is based on Thom's transversality theorem and removes any restriction regarding the dimension of the strategy spaces. A converse result is that almost all efficient market games that are competitive are characterized by Bertrand-like non-differentiabilities. Finally a synthesis between the Cournot-and-Bertrand-type approaches to Walrasian equilibrium, as recently developed in the literature, is suggested.     

A general impossibility result on strategy-proof social choice hyperfunctions

A social choice hyperfunction picks a non-empty set of alternatives at each admissible preference profile over sets of alternatives. We analyze the manipulability of social choice hyperfunctions. We identify a domain D^λ of lexicographic orderings which exhibits an impossibility of the Gibbard–Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of D^λ. As most of the standard extension axioms induce superdomains of D^λ while social choice correspondences are particular social choice hyperfunctions, we are able to generalize many impossibility results in the literature.     

SOCIAL CHOICE FROM AN n‐DIMENSIONAL EUCLIDEAN SPACE: A SHORT IMPOSSIBILITY PROOF

Most presentations of social choice theory are difficult for a non‐specialist to follow. This paper attempts to provide some feel for what is going on by providing a short proof of an impossibility theorem in terms of the techniques that are familiar to political‐economists. We illustrate the advantages of this approach with a short proof of an impossibility theorem.     

The so-called “transformation problem” revisited: A comment

This comment shows that Lipietz's Marxist transformation theorem represents but a simple, though useful reinterpretation of obvious mathematical consequences of a standard Sraffa model—by making appropriate use of its known degree of freedom. Labor values are not involved in this new interpretation of conventional prices of production. A proposal is therefore made how their role in Marx's transformation may be investigated further on the basis of Lipietz's theorem and its interpretation of the “value of labor power”.