Collective choice functions on non-convex problems

Collective choice problems on sets in _boxclose_boxclose^n{\frak R}_+^n arise naturally in economics. Such problems have been extensively studied both in the theory of revealed preferences (Peters and Wakker, 1991) and in axiomatic bargaining theory under the assumption of convexity. However, our knowledge of collective choice functions on non-convex problems is still patchy. In this paper I study the existence and characterisation of continuous choice functions on the domain G\Gamma of comprehensive problems. The main result completely characterises rational choice functions that are continuous and satisfy Weak Pareto Optimality: they form the class of Monotone Path Choice Functions on G\Gamma. I also show that any discontinuous rational and weakly Pareto optimal choice function must be non- anonymous.     

Choice, preference and rationalizability in pareto’s theory of economic behavior

Pareto initiated the shift of economic theory from utility/preference to choice in order to fill a gap between theoretical and empirical economics. His suggestions for an empirically-oriented theory of choice were to be developed decades later in the literature on revealed preference and on the conditions of equivalence between preference-based and choice-based axiomatic structures. In the process, however, substantial departures from Pareto’s implicit design of the situation of choice were introduced. In this paper, the conditions for the rationalizability of choice are re-defined so that they fit the type of situation that Pareto had in mind. The result is that the main consistency axioms of standard choice theory have to give way to a different combination of axioms that concern decisiveness as well as consistency. (JEL:B13, D01, D11).     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001     

REMARKS ON A PROCEDURAL CONDITION FOR THE VOTING PARADOX

Schwartz [A Procedural Condition Necessary and Sufficient for Cyclic Social Preference, J. Econ. Theory 137 (2007), 688–695] provides a generalization of the voting paradox by using the impotence‐partition condition. This paper aims to clarify his result by providing several remarks. We show that a main result of Schwartz can be strengthened by replacing strong Pareto by weak Pareto. We also discuss how the impotence partition is related to the standard concept of decisiveness, which is widely employed in the literature on social choice.     

Pareto optimality in coalition formation

A minimal requirement on allocative efficiency in the social sciences is Pareto optimality. In this paper, we identify a close structural connection between Pareto optimality and perfection that has various algorithmic consequences for coalition formation. Based on this insight, we formulate the Preference Refinement Algorithm (PRA) which computes an individually rational and Pareto optimal outcome in hedonic coalition formation games. Our approach also leads to various results for specific classes of hedonic games. In particular, we show that computing and verifying Pareto optimal partitions in general hedonic games, anonymous games, three-cyclic games, room-roommate games and B-hedonic games is intractable while both problems are tractable for roommate games, W-hedonic games, and house allocation with existing tenants.     

The impossibility of a weakly path independent Paretian liberal

This paper shows that the conflict between two well cherished values related to moral and political philosophy, namely the Pareto optimality and the libertarian principle, cannot be resolved as long as a social choice function is required to satisfy a rationality-consistency condition which ensures some kind of path independence, however, weak.     

Pareto optimality and the decisive power structure with expansion consistency conditions

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.     

Social welfare orderings for ratio-scale measurable utilities

Summary. This article characterizes all of the continuous social welfare orderings which satisfy the Weak (resp. Strong) Pareto principle when utilities are ratio-scale measurable. With Weak Pareto, on both the nonnegative and positive orthants the social welfare ordering must be representable by a weakly increasing Cobb-Douglas social welfare function while on the whole Euclidean space the social welfare ordering must be strongly dictatorial. With Strong Pareto, on the positive orthant the social welfare ordering must be representable by a strictly increasing Cobb-Douglas social welfare function but on the other two domains an impossibility theorem is obtained. Received: July 31, 1995; revised version August 7, 1996     

A strategic market game with seigniorage costs of Fiat money

Summary. A model that includes the cost of producing money is presented and the nature of the inefficient equilibria in the model are examined. It is suggested that if one acknowledges that transactions are a form of production, which requires the consumption of resources, then the concept of Pareto optimality is inappropriate for assessing efficiency. Instead it becomes necessary to provide an appropriate comparative analysis of alternative transactions mechanisms in the appropriate context. Received: September 5, 2000; revised version: May 3, 2001     

An analytical-epistemological reconstruction of the genesis of pareto’sManuale di economia politica

Due to our lack of sources, we only know the essential stages of the long and winding path that leads Pareto from the theory of the final degree of utility to the theory of choice, which is the foundation of hisManuale di Economia Politica. We can still put forward the interpretation that his passage from one theory to the other was guided by the need, always deeply felt by Pareto, to give his theoretical line of reasoning foundations that were consistent with reality. Actually Pareto sees in the (for him) factual indifference curves not only the realistic foundation for the new exposition of pure economic theory, but also the guide to renewed empirical researches directed at giving quantitative bases to that theory.     

On the second optimality theorem of welfare economics

To what extent does the second optimality theorem of welfare economics (every Pareto optimal allocation can be repesented as a Walras equilibrium allocation) remain valid when preferences are allowed to be locally satiated? It is always valid for an exchange economy, and is valid for a production economy if there is a consumer who is not locally satiated, but not in general for a production economy where all consumers are locally satiated. A generalized equilibrium is defined, which includes the Walras equilibrium as a special case. Every Pareto optimum can be represented as a generalized equilibrium allocation. Furthermore, every Pareto optimal utility distribution can be realized by a Walras equilibrium allocation.     

Purification of incentive compatible allocations

In implementation theory it is common to consider social choice functions that map to lotteries over outcomes. For example, virtual implementation has been used widely with social choice functions that involve randomization. This paper investigates (in incomplete information environments) the possibility of purification of such social choice functions, where purification means that the “replacement” social choice function maps to outcomes rather than distributions over outcomes, is incentive compatible and generates the same distribution over payoffs and outcomes as the original social choice function. Received: July 31, 2000; revised version: December 2, 2002 RID="*" ID="*" Thanks are due to Ole Nielsen, Terence Tao and Lin Zhou for helpful conversations. Thanks are also due to an anonymous referee for detailed comments.     

企业研发边界影响因素的国外研究综述

企业研发边界的本质是寻求企业研发资源的最优配置。近年来,国外学者将影响企业研发边界的因素分为企业特征因素和行业与技术特征因素两大类。其中,企业特征因素包括研发强度、企业规模、纵向一体化、多样化、现金流和组织结构等;行业与技术特征因素包括专有性、信息流、创新速度等。可见,研发边界影响因素的相关结论并不十分一致,仍有待进一步的研究。     

On the difficulty of combining actual and potential criteria for an increase in social welfare

Summary. This paper examines two problems associated with the use of potential Pareto criteria in welfare economics. The first problem is the well-known intransitivity of the compensation criteria à la Kaldor-Hicks-Scitovsky. The second problem is the possible incompatibility between the Chipman-Moore-Samuelson criterion and the Pareto principle. The main result of this paper is that, in order to avoid either of these problems, it is necessary and sufficient that the domain to which these criteria are used is such that the Chipman-Moore-Samuelson criterion encompasses completely the Pareto criterion. When interpreted in a standard economic environment, this result is shown to be equivalent to Gorman's requirement of non-crossing between utility possibility frontiers. Received: June 18, 1998; revised version: March 2, 2000     

Optimal nonlinear income taxation with productive government expenditure

This paper develops an endogenous growth model with a production externality and nonlinear income taxation, and uses it to examine how the fiscal authority devises its nonlinear tax structure from the viewpoint of welfare maximization. It is found that, in the Barro (1990) model, Pareto optimality can be achieved if both policy instruments for the tax scalar and the extent of the tax progressivity/regressivity are set optimally.     

Remarks on the first welfare theorem with nonordered preferences

A strong convexity assumption is used to establish the first fundamental theorem of welfare economics using the strong definition of Pareto optimality without assuming that the weak preference relations are complete or transitive. An example demonstrates that Debreu's (Proc. Nat. Acad. Sci., 40 (1954), 588–592) nonsatiation and convexity assumptions are insufficient to establish the result in the absence of transitivity.     

The Supporting Line Property and the Additive Choice Function for Two-Dimensional Choice Problems

The paper provides an axiomatic characterization of the additive choice function using the additivity property. It is seen that, along with Pareto optimality, symmetry, and a supporting line property, the additivity axiom uniquely characterizes the additive choice function. The additive choice function as defined in this paper does not satisfy Nash's assumption of the independence of irrelevant alternatives. This raises the question of when a choice function is representable, an issue addressed in an appendix.     

Nash implementing non-monotonic social choice rules by awards

Summary. By a slight generalization of the definition of implementation (called implementation by awards), Maskin monotonicity is no more needed for Nash implementation. In fact, a weaker condition, to which we refer as almost monotonicity is both necessary and sufficient for social choice correspondences to be Nash implementable by awards. Hence our framework paves the way to the Nash implementation of social choice rules which otherwise fail to be Nash implementable. In particular, the Pareto social choice rule, the majority rule and the strong core are almost monotonic (hence Nash implementable by awards) while they are not Maskin monotonic (hence fail to be Nash implementable in the standard framework).Received: 12 April 2004, Revised: 18 March 2005, JEL Classification Numbers: D 79.I thank François Maniquet, Efe Ok and Ipek Ozkal-Sanver for their valuable contributions. The paper is part of a project on Electoral System Design supported by Bilgi University Research Fund.     

A reformulation of the foundations of welfare economics

Neoclassical welfare economics takes an outcome-oriented approach that uses Pareto optimality as its benchmark for welfare maximization. When one looks at the remarkable improvements in economic welfare that have characterized market economies, most of those improvements in welfare have been due to economic progress that has introduced new and improved goods and services into the economy, and innovations in production methods that have brought costs down, leading to higher real incomes. Pareto optimality is only peripherally related to actual economic welfare, and no economist would argue that people are materially better off today than a century ago because the economy is closer to Pareto optimality. After analyzing the actual factors that lead to improvements in welfare, this paper suggests a reformulation of the foundations of welfare economics to replace the almost irrelevant outcome-oriented concept of Pareto optimality as the benchmark for evaluating welfare with a process-oriented benchmark based on factors that generate economic progress. The paper then explores some implications of this reformulation.

Recursive contracts,lotteries and weakly concave Pareto sets

Marcet and Marimon (1994, revised 1998, revised 2011) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a flat region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through – one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal?s choice set is not convex but where randomization is possible.