Aggregation of binary evaluations

We study a general aggregation problem in which a society has to determine its position (yes/no) on each of several issues, based on the positions of the members of the society on those issues. There is a prescribed set of feasible evaluations, i.e., permissible combinations of positions on the issues. This framework for the theory of aggregation was introduced by Wilson and further developed by Rubinstein and Fishburn. Among other things, it admits the modeling of preference aggregation (where the issues are pairwise comparisons and feasibility reflects rationality), and of judgment aggregation (where the issues are propositions and feasibility reflects logical consistency). We characterize those sets of feasible evaluations for which the natural analogue of Arrow's impossibility theorem holds true in this framework.     

Continuous linear representability of binary relations

Summary A very general result on continuous linear representability of binary relations on topological vector spaces is presented. Applications of this result include individual decision making under uncertainty, i.e. expected utility theory and collective decision making, in particular, utilitaristic social welfare functions.Thanks are due for helpful comments to Manfred Nermuth, David Schmeidler, Antonio Villar, and anonymous referees. Financial support from the DFG under Tr 120/4-2 is gratefully acknowledged.     

Nash implementation with partially honest individuals

We investigate the problem of Nash implementation in the presence of “partially honest” individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome than that which obtains when lying. We show that when there are at least three individuals, all social choice correspondences satisfying No Veto Power can be implemented. If all individuals are partially honest and if the domain is separable, then all social choice functions can be implemented in strictly dominant strategies by a mechanism which does not use “integer/modulo games”. We also provide necessary and sufficient conditions for implementation in the two-person case, and describe some implications of these characterization conditions.     

Characterizations of bargaining solutions in production economies with unequal skills

In production economies with unequal skills, this paper characterizes bargaining solutions by using axioms on allocation rules rather than axioms on classical bargaining solutions. We introduce a new axiom, consistency w.r.t. technological innovations, so that the non-welfaristic characterizations of bargaining solutions in the production economies are provided. By the characterizations, we can classify the three bargaining solutions (the Nash, the Kalai-Smorodinsky, and the Egalitarian solutions) from the viewpoint of responsibility and compensation discussed by Dworkin.     

Approximate cores of games and economies with clubs

We introduce the framework of parameterized collections of games with and without sidepayments and provide three nonemptiness of approximate core theorems. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. The results are applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results. A fundamental new mathematical result, the partition-balancing effect of large numbers, which promises to have further applications, is contained in Appendix A.     

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.     

Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare.We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium.We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small.     

A characterization of the Shapley value in queueing problems

A set of agents stand to receive a service. No two agents can be served simultaneously. A queue has to be organized, and agents having to wait should receive monetary compensations. We characterize the rule assigning positions in the queue and compensations corresponding to the payoffs recommended by the Shapley value of the associated cooperative game. We use a property of independence with respect to increase in some agents’ impatience, and an equal responsibility property.     

Non-existence of monotone equilibria in games with correlated signals

Participation in economic games such as auctions is typically costly, which means that players (potential bidders) must consider whether to participate. Such decisions may be no less crucial than how to bid, and yet the literature has been mostly concerned with bidding, assuming an exogenously given number of bidders; see Krishna [Auction Theory, Academic Press, New York, 2002]. Landsberger and Tsirelson [Correlated signals against monotone equilibria, preprint SSRN 222308, Social Science Research Network Electronic Library, May 2000. Available online: http://papers.ssrn.com/abstract=222308] have shown that fundamental results established in symmetric auction theory with correlated signals, such as the existence of a monotone equilibrium, may not hold if participation decisions are part of equilibrium. The major goal of this paper is to illustrate and explain this result that may be considered counter intuitive given the emphasis placed on monotone equilibria in the auction literature.     

Core equivalence theorem with production

In production economies, the extent to which non-equilibria are blocked depends on the allocation of control rights among shareholders, because a blocking coalition's resources are affected by the firms it jointly owns with outsiders. We formulate a notion of blocking that takes such interdependency problem into account, and we prove an analog of the Debreu-Scarf theorem for replica production economies. Our theorem differs from theirs in using an additional assumption, which we argue is indispensable and is driven by the interdependency problem.     

Parallel axiomatizations of majority and unanimity

The relative majority rule and the unanimity rule are characterized in the two alternatives case. The main axioms rely on the idea of determining the preference of a group by partitioning it into two subgroups and aggregating next their preferences.     

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.     

Market games with differential information and infinite dimensional commodity spaces: The core

Summary We provide an alternative proof of the existence of core allocations in exchange economies with differential information and infinite dimensional commodity spaces. We also identify a critical feature of information sharing rules that ensures nonemptiness of the core. In essence, the only condition we require on the sharing rules is that profitable insider trading be prohibited. In the absence of insider trading, balancedness is guaranteed and core nonemptiness follows.I thank Dan Arce, Erik Balder, Myrna Wooders, and Nicholas Yannelis for helpful comments. This paper is a greatly revised version of my paper entitled. A Variational Problem Arising in Market Games with Differential Information, written in August of 1991.     

Uniqueness of stationary equilibrium payoffs in coalitional bargaining

We study a model of sequential bargaining in which, in each period before an agreement is reached, the proposer?s identity is randomly determined, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. The theory of the fixed point index is used to show that stationary equilibrium expected payoffs of this coalitional bargaining game are unique. This generalizes Eraslan [34] insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected.     

The Possibility of Issue-Specific Decisions on Multiple Social Choice Issues

This paper considers an aggregation rule when each alternative consists of elements of multiple issues. I assume that each issue-specific aggregation rule can be applied to each issue and explore whether various different issue-specific aggregation rules are compatible. When the set of alternatives has some structure (which we call a set connected by loops), there exists a powerful individual whose preference always coincides with the social ordering in every issue. As a corollary, Arrow's General Possibility Theorem is obtained.     

Allocation rules for land division

This paper studies the classical land division problem formalized by Steinhaus (Econometrica 16 (1948) 101-104) in a multi-profile context. We propose a notion of an allocation rule for this setting.  We discuss several examples of rules and properties they may satisfy. Central among these properties is division independence: a parcel may be partitioned into smaller parcels, these smaller parcels allocated according to the rule, leaving a recommended allocation for the original parcel. In conjunction with two other normative properties, division independence is shown to imply the principle of utilitarianism.     

Implementation of individually rational social choice functions with guaranteed utilities

A simple mechanism is presented that allocates an indivisible object between two agents for almost any possible compensation rule. Furthermore, the equilibrium strategy guarantees a level of utility not less than −ε, where ε can be arbitrarily small.     

Sharing the surplus: An extension of the Shapley value for environments with externalities

Economic activities, both on the macro and micro level, often entail wide-spread externalities. This in turn leads to disputes regarding the compensation levels to the various parties affected. We propose a method of deciding upon the distribution of the gains (costs) of cooperation in the presence of externalities when forming the grand coalition is efficient. We show that any sharing rule satisfying efficiency, linearity, dummy player and a strong symmetry axioms can be obtained through an average game. Adding an additional axiom, we identify one unique rule satisfying these properties.     

A procedural condition necessary and sufficient for cyclic social preference

Several variations and generalizations of the Voting Paradox show that social-preference cycles are not peculiar to majority rule. I offer a new generalization that is demonstrably as general as possible: a relaxation of majority rule is necessary for a cycle of any sort and sufficient for a dominant one—given certain background assumptions, few and familiar. In its “Latin square” proof as well as its assumptions, the sufficiency theorem directly generalizes both the Voting Paradox and Sen's Liberal Paradox.     

Individual versus group strategy-proofness: When do they coincide?

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. There are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. We provide conditions on domains guaranteeing that for all rules defined on them, individual and group strategy-proofness become equivalent. We also provide a partial answer regarding the necessity of our conditions.