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.     

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.     

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.     

When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds

We study the problem of rationing a divisible good among a group of people. Each person?s preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: any amount less than this threshold is just as good as receiving nothing at all. Any amount beyond his ideal quantity has no effect on his welfare.We search for Pareto-efficient, strategy-proof, and envy-free rules. The definitions of these axioms carry through from the more commonly studied problem without disposability or acceptance thresholds. However, these are not compatible in the model that we study. We adapt the equal-division lower bound axiom and propose another fairness axiom called awardee-envy-freeness. Unfortunately, these are also incompatible with strategy-proofness. We characterize all of the Pareto-efficient rules that satisfy these two properties. We also characterize all Pareto-efficient, strategy-proof, and non-bossy rules.     

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.     

Majority Rule in a Stochastic Model of Bargaining

In this paper we consider multilateral stochastic bargaining models with general agreement rules. For n-player games where in each period a player is randomly selected to allocate a stochastic level of surplus and q?n players have to agree on a proposal to induce its acceptance, we characterize the set of stationary subgame perfect equilibrium payoffs and establish their existence. We show that for agreement rules other than the unanimity rule, the equilibrium payoffs need not be unique. Furthermore, even when the equilibrium is unique, it need not be efficient. Journal of Economic Literature Classification Numbers: C73, C78, D70.     

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.     

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     

Consistent representative democracy

We study axioms which define “representative democracy” in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly makes no difference. We call this property representative consistency. Representative consistency formalizes the idea that a voting rule should be immune to gerrymandering. We characterize the class of rules satisfying unanimity, anonymity, and representative consistency. We call these rules “partial priority rules.” A partial priority rule can be interpreted as a rule in which each agent can “veto” certain alternatives. We investigate the implications of imposing other axioms to the list specified above. We also study the partial priority rules in the context of specific economic models.     

Bayesian and consistent assessments

In a Bayesian assessment, beliefs are computed from the strategy profile applying Bayes rule at positive probability information sets. A consistent assessment is the limit point of a sequence of completely mixed Bayesian assessments. We characterize the set of extensive forms for which the sets of Bayesian and consistent assessments coincide. As an illustration of the results, we characterize consistency in some multi-period games with simultaneous actions.     

Separability and aggregation of equivalence relations

We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability and unanimity characterize the family of meet aggregators. We show another characterization of the family of meet aggregators using conjunctive separability and two Pareto axioms, Pareto⁺ and Pareto^?. If we drop Pareto^?, then conjunctive separability and Pareto⁺ characterize the family of meet aggregators along with a trivial aggregator.     

The rule approach in evolutionary economics: A methodological template for empirical research

Dopfer and Potts (2008) have proposed a new analytic foundation to evolutionary economics based on the unified rule approach. While they contend that their approach is ontologically and analytically coherent and useful, scholars sympathetic with it, e.g., Ostrom and Basurto (2011), have called for further methodological and empirical specification. In the same vein, this paper seeks to develop the Dopfer-Potts framework by proposing an analytic methodology to translate their rule-based approach into an operational method for identifying and testing hypotheses that relate to rules. It does so by defining a methodology connecting explanandum (response rule) and explanantia (factor rules) at the same level of rules. The concept of a ‘savings rule’ serves as a roving example that later is extended into a case study. The paper offers a methodological template for applied evolutionary analysis in economics.     

Joint misrepresentation with bribes

We study the problem of assigning objects to buyers. Monetary transfers are allowed. Each buyer’s preference space contains, but is not limited to, the linear additively separable preferences. A rule maps each preference profile to an allocation. We are concerned about the possibility that a group of buyers may engage in the following kind of manipulation: They make side payments internally and then carry out a joint misrepresentation. A rule is strongly group strategy-proof if no group can gain by engaging in such operations. We also consider several other appealing requirements. We find that the posted-price rules are the only one that satisfies non-triviality, non-imposition, envy-freeness, and strong group strategy-proofness.     

Coalitional Strategy-Proofness in 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. Our main result is the characterization of the class of Pareto optimal and coalitionally strategy-proof allocation rules. Alternatively, this class of rules, which largely consists of serially dictatorial components, can be characterized by Pareto optimality, strategy-proofness, and weak non-bossiness (in terms of welfare). Furthermore, we study properties of fairness such as anonymity and no-envy. Journal of Economic Literature Classification Numbers: D63, D71.     

The network of weighted majority rules and its geometric realizations

In a previous work the first author considered the network G(n,p) of weighted majority rules (WMR) for n decision makers whose competencies are given by their probabilities p=(p₁,…,p_n) of making a correct decision. On this paper we consider chains of decision profiles, which must occur in G(n,p) in a fixed order, and show that they can be mapped onto straight lines in a low-dimensional geometric realization. The minimal number of directions which must used to separate all edges is given as the chromatic number of a certain incidence graph. We also define degenerate networks in which several nodes coalesce.     

Efficient priority rules

We study the assignment of indivisible objects with quotas (universities, jobs, or offices) to a set of agents (students, job applicants, or professors). Each agent receives at most one object and monetary compensations are not possible. We characterize efficient priority rules by efficiency, strategy-proofness, and reallocation-consistency. Such a rule respects an acyclic priority structure and the allocations are determined using the deferred acceptance algorithm.     

Strategy-proof risk sharing

We consider risk sharing problems with a single good and a finite number of states. Agents have a common prior and their preferences are represented in the expected utility form and are risk averse. We study efficient and individually rational risk sharing rules satisfying strategy-proofness, the requirement that no one can ever benefit by misrepresenting his preference. When aggregate certainty holds, we show that “fixed price selections” from Walrasian correspondence are the only rules satisfying efficiency, individual rationality, and strategy-proofness. However, when aggregate uncertainty holds, we show that there exists no rule satisfying the three requirements. Moreover, in the two agents case, we show that dictatorial rules are the only efficient and strategy-proof rules. Dropping the common prior assumption in the model, we show that this assumption is necessary and sufficient for the existence of rules satisfying the three main requirements in the two agents and aggregate certainty case.     

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.     

Non-monotoniticies and the all-pay auction tie-breaking rule

Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The best results available ensure equilibrium existence only in mixed strategy with endogenously defined tie-breaking rules and communication of private information. We show that an all-pay auction tie-breaking rule is sufficient for the existence of pure strategy equilibrium in a class of auctions. The rule is explicitly defined and does not require communication of private information. We also characterize when special tie-breaking rules are really needed.      

PARETO EFFICIENCY AND WEIGHTED MAJORITY RULES

We consider the design of decision rules in an environment with two alternatives, independent private values and no monetary transfers. The utilitarian rule subject to incentive compatibility constraints is a weighted majority rule, where agents' weights correspond to expected gains given that their favorite alternative is chosen. It is shown that a rule is interim incentive efficient if and only if it is a weighted majority rule, and we characterize those weighted majority rules that are ex ante incentive efficient. We also discuss efficiency in the class of anonymous mechanisms and the stability of weighted majority rules.