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].     

Maximal Domain of Preferences in the Division Problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, then the uniform allocation rule is the unique strategy-proof, efficient, and anonymous rule. We identify the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry. In addition, we show that our characterization implies a slightly weaker version of Ching and Serizawa's (1998) result. Journal of Economic Literature Classification Numbers: D71, D78, D63.     

Group identification with (incomplete) preferences

We consider the problem of identifying members of a group based on individual opinions. Since agents do not have preferences in the model, properties of rules that concern preferences (e.g., strategy‐proofness and efficiency) have not been studied in the literature. We fill this gap by working with a class of incomplete preferences derived directly from opinions. Our main result characterizes a new family of group identification rules, called voting‐by‐equitable‐committees rules, using two well‐known properties: strategy‐proofness and equal treatment of equals. Our family contains as a special case the consent rules (Samet & Schmeidler. J. Econ. Theory, 110 (2003), pp. 213–233), which are symmetric and embody various degrees of liberalism and democracy; and it also includes dictatorial and oligarchic rules that value agents’ opinions differently. In the presence of strategy‐proofness, efficiency turns out to be equivalent to non‐degeneracy (i.e., any agent may potentially be included or excluded from the group). This implies that a rule satisfies strategy‐proofness, efficiency, and equal treatment of equals if, and only if, it is a non‐degenerate voting‐by‐equitable‐committees rule.     

On the stability of coalition structures

We resolve a seeming conflict between a non-existence result on solutions to coalition formation in hedonic games [Barberà, S., Gerber, A., 2007. A note on the impossibility of a satisfactory concept of stability for coalition formation games. Economics Letters 95, 85–90] and the universal existence of stable coalition structures in TU games under the χ-value [Casajus, A., 2008. Outside options, component efficiency, and stability, Games and Economic Behavior (forthcoming). doi: 10.1016/j.geb.2007.04.003].     

Public decisions: Solidarity and the status quo

A public decision model specifies a set of alternatives, a variable population, and a common set of admissible preferences. We study the implications of the principle of solidarity, for social choice functions in all such models. The principle says that when the environment changes, all agents not responsible for the change should either all weakly win, or all weakly lose. Under weak additional requirements, but regardless the domain of preferences, each of two formulations of this principle, population-monotonicity and replacement-domination, imply coalition-strategy-proofness; that the choice only depends on the set of preferences that are present in the society, but not on the number, nor on the labels of agents having particular preferences; and that there exists an alternative always weakly Pareto-dominated by the alternative selected by the rule. Replacement-domination is generally at least as strong as population-monotonicity.     

Allocation problems among sharing groups

We deal with allocation problems among sharing groups. There are n agents. The agents are divided into several sharing groups. A homogeneous good is allocated among sharing groups rather than among the agents. The good is a private good for sharing groups, and a public good for the members of each sharing group. That is, all of them in the same sharing group can consume it without rivalry. We introduce some allocation rules and axioms. The utilitarian allocation rule and the egalitarian allocation rule are characterized by some axioms.     

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.     

Water allocation by social choice rules: The case of sequential rules

This paper considers the problem of allocating shares of irrigation water to different agricultural agents with single-peaked preferences with respect to their own shares. We define two different sequential allocation rules that respect the asymmetry between the agents and maintain the properties of Pareto efficiency and strategy-proofness, and we design a specific algorithm to apply these rules. The results of the empirical application of these rules for the case of an irrigated area located in the Ebro Basin (Spain) show that the designed sequential rules are able to substantially improve the efficiency of the currently applied proportional rule in context of severe scarcity of water and/or high administrative water prices.     

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     

Individually rational rules for the division problem when the number of units to be allotted is endogenous

We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and efficient families of rules, whenever agents' preferences are symmetric single-peaked on the set of possible allotments. Rules in the two families are in addition envy-free, but they differ on whether envy-freeness is considered on losses or on awards. Our main result states that (a) the family of constrained equal losses rules coincides with the class of all individually rational and efficient rules that satisfy justified envy-freeness on losses and (b) the family of constrained equal awards rules coincides with the class of all individually rational and efficient rules that satisfy envy-freeness on awards.     

Regular Distributive Efficiency and the Distributive Liberal Social Contract

We consider abstract social systems of private property, made of n individuals endowed with nonpaternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto‐improving lump‐sum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is both: (i) a distributive optimum (i.e., is Pareto‐efficient relative to individual interdependent preferences) and (ii) unanimously weakly preferred to the initial market equilibrium. We elicit minimal conditions for meaningful social contract redistribution in this setup, namely, the weighted sums of individual interdependent utility functions, built from arbitrary positive weights, have suitable properties of nonsatiation and inequality aversion; individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima; and the initial market equilibrium is not a distributive optimum. We show that the relative interior of the set of social contract allocations is then a simply connected smooth manifold of dimension n ? 1. We also show that the distributive liberal social contract rules out transfer paradoxes in Arrow–Debreu social systems. We show, finally, that the liberal social contract yields a norm of collective action for the optimal provision of any pure public good.     

STRATEGIC CANDIDACY AND SINGLE‐PEAKEDNESS*

In elections, the voting outcomes are affected by strategic entries of candidates. We study a class of voting rules immune to strategic candidacy. Dutta et al. (2001 ) show that such rules satisfying unanimity are dictatorial if all orderings of candidates are admissible for voters’ preferences. When voters’ preferences are single‐peaked over a political spectrum, there exist non‐dictatorial rules immune to strategic candidacy. An example is the rule selecting the m‐th peak from the left among the peaks of voters’ preferences, where m is any natural number no more than the number of voters. We show that immunity from strategic candidacy with basic axioms fully characterizes the family of the m‐th leftmost peak rules.     

General allocation problems with single-peaked preferences: path-independence and related topics

We face the problem of allocationg a fixed amount of a perfectly divisible good among a group of agents with single-peaked preferences. We survey the three different cases studied in the literature: the pure distribution case, the redistribution case, and the gerneral case. The so called general case provide with a natural framework to analyze the idea of path-independence. In this framework, we explore the existence of rules fulfilling this property. Our first result is negative: a strong version of this property cannot be fulfilled together with efficiency. Nonetheless, some restricted versions of the path-independence property are compatible with interesting properties, in particular no manipulability, and no envy. We then identify two solutions satisfying this sort of property: the equal distance rule, and a new extension of the uniform rule.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

The most ordinally egalitarian of random voting rules

Aziz and Stursberg propose an “Egalitarian Simultaneous Reservation” rule (ESR), a generalization of Serial rule, one of the most discussed mechanisms in the random assignment problem, to the more general random social choice domain. This article provides an alternative definition, or characterization, of ESR as the unique most ordinally egalitarian one. Specifically, given a lottery p over alternatives, for each agent i the author considers the total probability share in p of objects from her first k indifference classes. ESR is shown to be the unique one which leximin maximizes the vector of all such shares (calculated for all i, k). Serial rule is known to be characterized by the same property. Thus, the author provides an alternative way to show that ESR, indeed, coincides with Serial rule on the assignment domain. Moreover, since both rules are defined as the unique most ordinally egalitarian ones, the result shows that ESR is “the right way” to think about generalizing Serial rule.     

On the informational efficiency of simple scoring rules

We study information aggregation in large elections. With two candidates, efficient information aggregation is possible (e.g., Feddersen and Pesendorfer [5], [6] and [7]). We show that this result does not extend to elections with more than two candidates. We study a class of simple scoring rules in voting games with Poisson population uncertainty and three candidates. No simple scoring rule aggregates information efficiently, even if preferences are dichotomous and a Condorcet winner always exists. We introduce a weaker criterion of informational efficiency that requires a voting rule to have at least one efficient equilibrium. Only approval voting satisfies this criterion.     

Strategy-Proof Voting on Compact Ranges

Strategy-proof social choice functions are characterized for societies where the space of alternatives is any full dimensional compact subset of a Euclidean space and all voters have generalized single-peaked preferences. Our results build upon and extend those obtained for cartesian product ranges by Border and Jordan (1983). By admitting a large set of non-Cartesian ranges, we give a partial answer to the major open question left unresolved in this pioneering article. We prove that our class is composed by generalized median voter schemes which satisfy an additional condition, called the intersection property [Barberà, Massó, and Neme (1997)].Journal of Economic LiteratureClassification Number: D71.     

Profit sharing in unique Nash equilibrium: Characterization in the two-agent case

Two agents jointly operate a decreasing marginal returns technology to produce a private good. We characterize the class of output-sharing rules for which the labor-supply game has a unique Nash equilibrium. It consists of two families: rules of the serial type which protect a small user from the negative externality imposed by a large user, and rules of the reverse serial type, where one agent effectively employs the other agent's labor. Exactly two rules satisfy symmetry; a result in sharp contrast with Moulin and Shenker's characterization of their serial mechanism as the unique cost-sharing rule satisfying the same incentives property [Moulin, H., Shenker, S., 1992. Serial cost sharing. Econometrica 60 (5), 1009–1037]. We also show that the familiar stand-alone test characterizes the class of fixed-path methods under our incentives criterion [Friedman, E.J., 2004. Strong monotonicity in surplus sharing. Econ. Theory 23, 643–658].     

The evolution of portfolio rules and the capital asset pricing model

The aim of this paper is to test the performance of capital asset pricing model (CAPM) in an evolutionary framework. We model an economy where a heterogeneous population of long-lived agents invest their wealth according to different portfolio rules, and prove that traders who either “believe” in CAPM and use it as a rule of thumb, or are endowed with genuine mean-variance preferences, under some very weak conditions, vanish in the long run.We show that a sufficient condition to drive CAPM or mean-variance traders’ wealth shares to zero is that an investor endowed with a logarithmic utility function enters the market.     

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.