Impossibility Theorems with Interpersonally Comparable Welfare Levels: The "Extended Sympathy Approach" Reconsidered

We re-examine a type of interpersonal welfare comparison, called the "extended sympathy" approach, which Arrow (1977), Hammond (1976) and Roberts (1980a) introduced in order to escape from Arrovian impossibility theorems. In particular, we extend the positional dictatorship theorem due to Roberts to the case where the domain of social choice rules satisfies the axiom of identity. We show that there is a positional dictator if the rule with the domain satisfies independence, Suppes unanimity and monotonicity
JEL Classification Numbers: 022, 025, 026     

Strategyproof and Nonbossy Multiple Assignments

We consider the allocation of heterogeneous indivisible objects without using monetary transfers. Each agent may be assigned more than one object. We show that an allocation rule is strategyproof, nonbossy, and satisfies citizen sovereignty if and only if it is a sequential dictatorship . In a sequential dictatorship agents are assigned their favorite objects that are still available, according to a sequentially endogenously determined hierarchy of the agents. We also establish that replacing nonbossiness by a stronger criterion restricts the characterized class of allocation rules to serial dictatorships , in which the hierarchy of the agents is fixed a priori.     

Strategy-proofness of the plurality rule over restricted domains

We give a complete characterization of preference domains over which the plurality rule is strategy-proof. In case strategy-proofness is required to hold under all tie-breaking rules, strategy-proof domains coincide with top-trivial ones where the range of the plurality rule admits at most two alternatives. This impossibility virtually prevails when strategy-proofness is weakened so as to hold under at least one tie-breaking rule: unless there are less than five voters, the top-triviality of a domain is equivalent to the (weak) non-manipulability of the plurality rule. We also characterize the cases with two, three or four voters. I am grateful to Attila Tasnadi for his thorough reading of the paper and pointing to an error in an earlier version. I thank Levent Kutlu, Clemens Puppe, Arunava Sen, an anonymous referee and an anonymous AE for their comments. This research is part of the project “Social Perception—A Social Choice Perspective” supported by Istanbul Bilgi University Research Fund. I also acknowledge the support of the Turkish Academy of Sciences Distinguished Young Scientist Award Program (TUBA-GEBIP).     

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate one of its subgroups to misrepresent their preferences and, after an appropriate redistribution of their shares, each obtains a weakly preferred share and all agents in the misrepresenting subgroup obtain a strictly preferred share. We characterize all bribe-proof rules as the class of Pareto efficient, strategy-proof, and weakly replacement monotonic rules. This class is larger than the set of sequential allotment rules identified in Barberà et al. [Barberà, S., Jackson, M., Neme, A., 1997. Strategy-proof allotment rules. Games Econ. Behav. 18, 1–21].     

Sraffa,interdependence and demand: the Gramscian influence

The influence of Sraffa' early commitments to Gramscian Marxism on his subsequent economic analysis have been little investigated by Sraffa scholars. The discussion here argues for a philosophical connection. Specifically, it is argued that organicist ideas found their way into Sraffa's thinking about interdependence in his 1926 critique of Marshall, in his reported critique of Wittgenstein's early philosophy, and in his 1960 Production of commodities. In each instance, atomist views were challenged in an understanding of agent or sectoral interdependence that made use a single criterion for agent or sectoral autonomy: that such autonomy depends upon the fulfilment of identify conditions for the individuation of autonomous agents or sectors. It is suggested that Sraffa's thinking in this regard ses the attempted fulfilment of these conditions in neoclassical theory as self-contradictory, thus allowing the characterization of his thinking as a form of impossibility logic. This impossibility logic is contrasted to that of Arrow, in order to advance general propositions about Sraffa's understanding of demand.     

The possibility of judgment aggregation on agendas with subjunctive implications

The new field of judgment aggregation aims to find collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic.     

Population-monotonicity and separability for economies with single-dipped preferences and the assignment of an indivisible object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. We consider rules that satisfy Pareto efficiency, strategy-proofness, and in addition either the consistency property separability or the solidarity property population-monotonicity. We show that the class of rules that satisfy Pareto efficiency, strategy-proofness, and separability equals the class of rules that satisfy Pareto efficiency, strategy-proofness, and non-bossiness. We also provide characterizations of all rules satisfying Pareto efficiency, strategy-proofness, and either separability or population-monotonicity. Since any such rule consists for the largest part of serial-dictatorship components, we can interpret the characterizations as impossibility results. Received: September 29, 1999; revised version: March 22, 2000     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.     

Group strategyproof cost sharing: The role of indifferences

Every agent reports his willingness to pay for one unit of a good. A mechanism allocates goods and cost shares to some agents. We characterize the group strategyproof (GSP) mechanisms under two alternative continuity conditions interpreted as tie-breaking rules. With the maximalist rule (MAX) an indifferent agent is always served. With the minimalist rule (MIN) an indifferent agent does not get a unit of the good.GSP and MAX characterize the cross-monotonic mechanisms. These mechanisms are appropriate whenever symmetry is required. On the other hand, GSP and MIN characterize the sequential mechanisms. These mechanisms are appropriate whenever there is scarcity of the good.Our results are independent of an underlying cost function; they unify and strengthen earlier results for particular classes of cost functions.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Between liberalism and democracy

We study and characterize axiomatically a class of voting rules, called consent rules, that incorporate aspects of majoritarianism and liberalism. An outcome of the vote specifies who among the voters are eligible to a certain right or qualification. Each outcome serves also as a permissible ballot. Consent rules are parameterized by the weights given to individuals in determining their own qualification. In one of these rules, the liberal rule, each individual's qualification is determined by her. In other rules, an individual's qualification requires social consent in various degrees. We also show the relation between self-determination and the liberal rule.     

Fair imposition

We introduce a new mechanism-design problem called fair imposition. In this setting a center wishes to fairly allocate tasks among a set of agents whose cost structures are known only to them, and thus will not reveal their true costs without appropriate incentives. The center, with the power to impose arbitrary tasks and payments on the agents, has the additional goal that his net payment to these agents is never positive (or, that it is tightly bounded if a loss is unavoidable). We consider two different notions of fairness that the center may wish to achieve. The central notion, which we call k-fairness, is in the spirit of max-min fairness. We present both positive results (in the form of concrete mechanisms) and negative results (in the form of impossibility theorems) concerning these criteria. We also briefly discuss an alternative, more traditional interpretation of our setting and results, in the context of auctions.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

A characterization of consistent collective choice rules

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference, which excludes the possibility of a “money pump.” The properties of collective choice rules used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available.     

Priorities in the location of multiple public facilities

A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We characterize the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among “interest groups”. We characterize the subclasses of priority rules that respectively satisfy anonymity, avoid the no-show paradox, strategy-proofness and population-monotonicity. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Any such rule can also be viewed as a collection of generalized peak-selection median rules, that are linked across populations, in a way that we describe.     

EFFICIENCY OF LIABILITY RULES WITH INTERDEPENDENT COSTS OF CARE

Abstract.  Most of the results of the law and economics literature relating to the question of efficiency of liability rules have been obtained in the context of two-party interactions in which the cost of care of each party is independent of the care level of the other. In this paper we analyse the question of efficiency of liability rules in the context of interactions in which the cost of care of at least one of the parties is not independent of the care level of the other and characterize efficient liability rules whenever possible and in all other instances we obtain impossibility results.     

Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities

We study strategy-proof allocation rules in economies with perfectly divisible multiple commodities and single-peaked preferences. In this setup, it is known that the incompatibility among strategy-proofness, Pareto efficiency and non-dictatorship arises in contrast with the Sprumont (Econometrica 59:509–519, 1991) one commodity model. We first investigate the existence problem of strategy-proof and second-best efficient rules, where a strategy-proof rule is second-best efficient if it is not Pareto-dominated by any other strategy-proof rules. We show that there exists an egalitarian rational (consequently, non-dictatorial) strategy-proof rule satisfying second-best efficiency. Second, we give a new characterization of the generalized uniform rule with the second-best efficiency in two-agent case.     

Asymmetric rules for claims problems without homogeneity

We introduce a general class of rules for claims problems, called the difference rules, and demonstrate that a rule satisfies composition down and composition up if and only if it is a difference rule. We show that these rules are very simple to describe when there are two agents. In a variable population framework, we introduce a family of rules satisfying consistency, composition down, and composition up, which we term the logarithmic-proportional rules. These rules satisfy neither symmetry nor homogeneity.     

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate one of its subgroups to misrepresent their preferences and, after an appropriate redistribution of their shares, each obtains a weakly preferred share and all agents in the misrepresenting subgroup obtain a strictly preferred share. We characterize all bribe-proof rules as the class of Pareto efficient, strategy-proof, and weakly replacement monotonic rules. This class is larger than the set of sequential allotment rules identified in Barberà et al. [Barberà, S., Jackson, M., Neme, A., 1997. Strategy-proof allotment rules. Games Econ. Behav. 18, 1–21].     

Fiscal Constitutions

We study the impact of fiscal constitutions on intergenerational transfers in an overlapping generation model with linear technology. Transfers represent outcomes of a voting game among selfish agents. Policies are decided one period at a time. Majoritarian systems, which accord voters maximum fiscal discretion, sustain all individually rational allocations, including dynamically inefficient ones. Constitutional rules, which give minorities veto power over fiscal policy changes proposed by the majority, are equivalent to precommitment. These rules eliminate fluctuating and dynamically inefficient transfers and sustain weakly increasing transfer sequences that converge to the golden rule. The golden rule allocation is the unique outcome of Markov constitutional rules. Journal of Economic Literature Classification Numbers: D72, H55.