An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains

We show that every strategy-proof and unanimous probabilistic rule on a binary restricted domain has binary support, and is a probabilistic mixture of strategy-proof and unanimous deterministic rules. Examples of binary restricted domains are single-dipped domains, which are of interest when considering the location of public bads. We also provide an extension to infinitely many alternatives.     

Circular domains

I introduce the notion of circular domains and prove that on any circular domain there is no strategy-proof and nondictatorial social choice function. Moreover, I show that on any proper subset of a minimal circular domain, there exists a group strategy-proof and essential social choice function. These results together detect the minimal size of the domains over which the incompatibility arises with respect to pairs of democratic-incentive requirements (nondictatorial, strategy-proof) and (essential, group strategy-proof).     

The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).     

Centralized allocation in multiple markets

We provide a characterization result for the problem of centralized allocation of indivisible objects in multiple markets. Each market may be interpreted either as a different type of object or as a different period. We show that every allocation rule that is strategy-proof, Pareto-efficient and nonbossy is a sequential dictatorship. The result holds for an arbitrary number of agents and for any preference domain that contains the class of lexicographical preferences.     

Sprumont's characterization of the uniform rule when all single-peaked preferences are admissible

Sprumont (1991) has established that the only allocation rule for the division problem that is strategy-proof, efficient, and anonymous is the uniform rule when the domain is the set of all possible profiles of continuous single-peaked preferences. Sprumont's characterization of the uniform rule is shown to hold on any larger domain of single-peaked preferences. Received: 15 December 1998 / Accepted: 12 April 1999     

Strategy-proof fuzzy aggregation rules

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategy-proof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategy-proof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.     

Researching with whom? Stability and manipulation

This paper explores the existence of stable research teams, when the preferences of each agent depend on the set of researchers who are collaborating. We introduce a property over researchers’ preferences, called top responsiveness, guaranteeing the existence of stable research teams configurations. We also provide a stable mechanism, induced by the so-called top covering algorithm, which is strategy-proof when researchers preferences satisfy top responsiveness. Furthermore, we find that, in this framework, the top covering mechanism is the only strategy-proof mechanism that always selects stable allocations.     

Efficiency and truthfulness with Leontief preferences. A note on two-agent,two-good economies

In exchange economies where agents have private information about their preferences, strategy-proof and individually rational social choice functions are in general not efficient. We provide a restricted domain, namely the set of preferences representable by Leontief utility functions, where there exist mechanisms which are strategy-proof, efficient and individually rational. In two-agent, two-good economies we are able to provide an even stronger result. We characterize the class of efficient and individually rational social choice functions, which are fully implementable in truthful strategies.Received: 28 April 2003, Accepted: 23 June 2003, JEL Classification: D51, D71The author thanks Matthew Jackson, Jordi Massó and James Schummer for fruitful discussions, William Thomson for many valuable comments on an earlier version. A particular thank to Salvador Barberá for his fundamental help.     

A note on strategy-proofness from the doctor side in matching with contracts

In a general one-to-many matching model with contracts, Hatfield and Milgrom (Ame Econ Rev 95:913–935, 2005) show that the doctor optimal stable rule is strategy-proof from the doctor side. We strengthen their result by showing that this rule is in fact the unique stable rule that is strategy-proof from the doctor side.     

Are serial Condorcet rules strategy-proof?

Abstract. This paper explores the extent to which majority rule is invulnerable to manipulation by individuals and coalitions, even when majority rule is used to select more than one alternative. The resulting rule may or may not be strategy-proof, depending on the size of the coalitions that can form, and on the nature of the individual preferences over sets of alternatives. No individual can manipulate with respect to a wide family of preferences over sets. The only restriction on the domain of true and revealed individual preferences is that the selection rule is always well defined. Received: 1 November 1999 / Accepted: 7 May 2001 We thank two anonymous referees for suggestions that have significantly improved the paper. We are also grateful to l'Université de Caen for sponsoring a Workshop on Social Choice Theory, where a first draft of this paper was presented in May, 1999, and to the workshop participants for helpful observations. Work on the final version of the paper was done while one of the authors was a guest of the Project on Intergenerational Equity supported by the Ministry of Education, Science, and Technology of Japan. We are grateful to the Ministry and to the project leader, Professor Kotaro Suzumura, for their support.     

Differentiable strategy-proof mechanisms for private and public goods in domains that are not necessarily large or quasi-linear

In this paper, we develop a differentiable approach to deal with incentives in a, possibly small, subset of a general domain of preferences in economies with one public and one private good. We show that, for two agents, there is no mechanism which is efficient, strategy-proof and where consumption of both goods is positive for all agents. For the case of two or more agents the same result occurs when nondictatorship is replaced by Individual Rationality. We are very grateful to Atila Abdulkadiroglu, Carmen Beviá, Xavier Calsamiglia, Marco Celentani, Bernardo Moreno, Antonio Romero-Medina, William Thomson, Walter Trockel, an associate editor, three anonymous referees and participants at seminars at Universities of Alicante, Autónoma de Barcelona and Rochester and the Spanish Economic Association meeting in Sevilla for very helpful comments and suggestions.     

A one-sided many-to-many matching problem

This study discusses a one-sided many-to-many matching model wherein agents may not be divided into two disjoint sets. Moreover, each agent is allowed to have multiple partnerships in our model. We restrict our attention to the case where the preference of each agent is single-peaked over: (i) the total number of partnerships with all other agents, and (ii) the number of partnerships that the agent has with each of the other agents. We represent a matching as a multigraph, and characterize a matching that is stable and constrained efficient. Finally, we show that any direct mechanism for selecting a stable and constrained efficient matching is not strategy-proof.     

Weakly fair allocations and strategy-proofness

This paper investigates the problem of allocating two types of indivisible objects among a group of agents when a priority-order must be respected and only restricted monetary transfers are allowed. Since the existence of a fair (as in envy-free) allocation is not generally guaranteed, due to the restrictions on the money transfers, the concept of fairness is weakened, and a new concept of fairness is introduced. This concept is called weak fairness. This paper defines an allocation rule that implements weakly fair allocations and demonstrates that it is coalitionally strategy-proof. In fact, under a mild regulatory condition and quasi-linear utility functions, it is demonstrated that this is the only coalitionally strategy-proof allocation rule that implements a weakly fair allocation. We would like to thank two anonymous referees, the participants at the Society for the Advancement of Economic Theory Conference (Greece, 2007) and the participants at the Association for Public Economic Theory Meeting (Nashville, USA, 2007) for valuable comments. The authors would also like to acknowledge financial support from The Jan Wallander and Tom Hedelius Foundation.     

The Blocking Lemma for a many-to-one matching model

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.     

Strategy-proof club formation with indivisible club facilities

Review of Economic Design - We investigate the strategy-proof provision and financing of indivisible club good facilities when individuals are subject to congestion costs that are non-decreasing in...     

A modified deferred acceptance algorithm for conditionally lexicographic-substitutable preferences

We study a class of preferences that generalize substitutable ones and allows complementarities in a college admissions model. We show that a stable matching exists under this class of preferences by using an algorithm which we call the Conditional Deferred Acceptance Algorithm. Furthermore, we show that the algorithm is strategy-proof for the student side if we assume in addition a law of aggregate demand adapted to our setting.     

Groves mechanisms and communication externalities

We put forward a model of private goods with externalities. Agents derive benefit from communicating with each other. In order to communicate they need to operate on a common platform. Adopting new platforms is costly. We first provide an algorithm that determines the efficient outcome. Then we prove that no individually rational and feasible Groves mechanism exists. We provide sufficient conditions that determine when an individually rational Groves mechanism runs a deficit and we characterize the individually rational Groves mechanism that minimizes such deficit whenever it occurs. Moreover, for 2-agent economies, we single out the only feasible and symmetrical Groves mechanism that is not Pareto dominated by another strategy-proof, feasible and symmetrical mechanism.     

Minimal manipulability: Unanimity and nondictatorship

This paper is concerned with the number of profiles at which a nondictatorial social choice function is manipulable. For three or more alternatives the lower bound is found for unanimous social choice functions. In the case of three alternatives the lower bound is found for surjective social choice functions. In both cases all social choice functions reaching the lower bound are characterized for more than two agents. In the case of two agents the characterized social choice functions form a subset of the set of all social choice functions reaching the minimum.     

Fakers becoming believers: how opinion dynamics are shaped by preference falsification,impression management and coherence heuristics

In the vast and rich literature on opinion dynamics, the role of preference falsification has generally been dismissed. Following the lead of Timur Kuran, in this paper we present one of the first multi-agent models that explores how opinion dynamics can be affected by the possible divorce between private and public opinions. It is also the first attempt to explore the role of social hierarchies in opinion dynamics conditioned by preference falsification. Our model formalizes heterogeneous evolving agents guided by a cognitively feasible set of heuristics and embedded in a social-rank-dependent structure of interactions. In social-rank-heterophilic encounters where people experience a high pressure of face-to-face interactions, unanimous support for the high social-rank preferred option emerges, while in any other scenario this option gathers majority but not unanimous support. Preference falsification has a crucial role in the emergence of unanimity, but it also creates the conditions for further private opinion actualizations that end up generating a self-sustained and sincere unanimity. When social-rank-homophilic encounters are the rule, or when group dynamics are irrelevant for opinion expression, agents never find incentives to falsify their opinions, therefore generating a social situation that resembles the general idea behind the ethnographic work of James C. Scott: true opinion expression in daily social-rank-homophilic encounters and a persistent opinion falsification in dissimilar social-rank interactions.     

Strategy-proof allocation of fixed costs

An economy can produce and consume a fixed-cost excludable public good only if its members fully fund the cost of the good. In this paper, we characterize the entire class of mechanisms for the provision of the public good and its cost that are Pareto optimal among the set of strategy-proof, voluntarily-participatory, budget-balancing, non-bossy, and replacement-monotonic mechanisms. We demonstrate that this class of mechanisms is quite small and can be characterized as simple step-price mechanisms.Received: 10 July 2001, Accepted: 5 February 2003, JEL Classification: C72, D71This work was done while Dearden was visiting Center for Economic Research, Tilburg University, The Netherlands. He is thankful for their gracious hospitality. The authors thank the editors and reviewers for their thoughtful comments.