The structure of strategy-proof social choice — Part I: General characterization and possibility results on median spaces

We define a general notion of single-peaked preferences based on abstract betweenness relations. Special cases are the classical example of single-peaked preferences on a line, the separable preferences on the hypercube, the “multi-dimensionally single-peaked” preferences on the product of lines, but also the unrestricted preference domain. Generalizing and unifying the existing literature, we show that a social choice function is strategy-proof on a sufficiently rich domain of generalized single-peaked preferences if and only if it takes the form of voting by issues (“voting by committees”) satisfying a simple condition called the “Intersection Property.”Based on the Intersection Property, we show that the class of preference domains associated with “median spaces” gives rise to the strongest possibility results; in particular, we show that the existence of strategy-proof social choice rules that are non-dictatorial and neutral requires an underlying median space. A space is a median space if, for every triple of elements, there is a fourth element that is between each pair of the triple; numerous examples are given (some well-known, some novel), and the structure of median spaces and the associated preference domains is analysed.     

A fair rule in minimum cost spanning tree problems

We study minimum cost spanning tree problems and define a cost sharing rule that satisfies many more properties than other rules in the literature. Furthermore, we provide an axiomatic characterization based on monotonicity properties.     

Efficient spatial competition

Game-theoretic models of spatial competition usually assume that firms set prices after their choices of locations. Rather than make this assumption, this paper uses the core to model the competition between the firms. Two conditions are shown to be sufficient for efficient spatial competition. The first is that the firms' location choices satisfy a no-externalities condition. The second is that the second-stage game satisfy a separable-value condition, namely that the value (gains from trade) can be created on a buyer-by-buyer basis. This approach yields two further benefits. First, efficient location can be stable in situations with arbitrary distributions of buyers, arbitrary willingness-to-pay functions, and completely general location spaces. Second, efficiency in location games can be shown to be related to the Second Welfare Theorem.     

Consistent strategy-proof assignment by hierarchical exchange

We characterize the family of efficient, consistent, and strategy-proof rules in house allocation problems. These rules follow an endowment inheritance and trade procedure as in Pápai’s hierarchical exchange rules (Pápai in Econometrica 68, 1403–1433, 2000) and closely resemble Ergin’s priority rules (Ergin in Econometrica 70, 2489–2497, 2002). We prove that if there are at least four objects, these are the only rules that are efficient in two-agent problems, $2$ -consistent, and strategy-proof. A corollary is that these three basic properties together imply the full requirements of efficiency, consistency, group strategy-proofness, and reallocation-proofness.     

Self-enforcing exchange among generations: Implications for consumption and mobility

A three-generation OLG model with one-directional altruism and two-directional intra-family transfers is presented. Adults invest in their children's education and make transfers to their elderly parents. However, due to lack of altruism, adults with high earnings do not share consumption equally with their elderly parents but spend a larger share of their earnings on own consumption and on their children's education. This allows the model to be consistent with three empirical observations that are difficult to reconcile with traditional altruistic frameworks of intergenerational social interactions and mobility: (i) consumption is not perfectly shared between members of an extended family, (ii) consumption is not equally persistent over the lifecycle as across generations, and (iii) the intergenerational persistence of earnings is particularly high at the top end of the earnings distribution.     

The type-agent core for exchange economies with asymmetric information

The type-agent core is a new solution concept for exchange economies with asymmetric information. It coincides with the set of subgame-perfect equilibrium outcomes of a simple competitive screening game. Uninformed intermediaries help the agents to cooperate in an attempt to make some profit. The paper extends the work of Perez-Castrillo [Cooperative outcomes through non-cooperative games, Games Econ. Behav. 7 (1994) 428-440] to exchange economies with non-transferable utility and asymmetric information. The type-agent core is a subset of Wilson's coarse core [Wilson, Information, efficiency, and the core of an economy, Econometrica 46 (1978) 807-816]. It is never empty, even though it may be a strict subset of Wilson's fine core. In addition, it converges towards the set of constrained market equilibria as the economy is replicated.     

Kidney exchange: An egalitarian mechanism

Kidney exchange programs utilize both deceased-donor and live-donor kidneys. One of these programs, a two-way kidney paired donation (KPD), involves two patients exchanging their live donors? kidneys. Another possibility is a list exchange (LE): a living incompatible donor provides a kidney to a candidate on the deceased-donor waitlist and in return the intended recipient of this donor receives a priority on the waitlist. By taking into consideration the fact that transplants from live donors have a higher chance of success than those from cadavers, we characterize the set of efficient and egalitarian exchanges involving the KPD?s and LE?s.     

Efficient strategy-proof allocation functions in linear production economies

Summary. In a linear production model, we characterize the class of efficient and strategy-proof allocation functions, and the class of efficient and coalition strategy-proof allocation functions. In the former class, requiring equal treatment of equals allows us to identify a unique allocation function. This function is also the unique member of the latter class which satisfies uniform treatment of uniforms. Received: July 10, 1997 / Revised version: November 24, 1997     

A comparison between the core and the monopoly solutions in a mixed exchange economy

Summary. Using a mixed market model for analyzing imperfectly competitive economies, we maximize the oligopolists' Welfare Function, given individual rationality and feasibility constraints. We prove that solutions belong to the core for a large class of economies. This class includes, in particular, every monopoly having a single type of small traders. Note that all such solutions yield the large trader, utility-wise, strictly more than at any monopoly solution, where the monopolist plays strategically, and the ocean of small traders act as being as price-takers. Received: March 4, 1996; revised version July 7, 1996     

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 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.     

Some remarks on ranking opportunity sets and Arrow impossibility theorems: correspondence results

An earlier work by Dutta and Sen provides characterizations of a set of decision rules for the ranking of opportunity sets. This paper begins by demonstrating the redundancy of one of the axioms in the said characterizations and goes on to analyze in detail one of the theorems, the Generalized Utilitarian rules theorem, which is incorrect. Basically, we find that one of the axioms that the authors provide is not in all cases satisfied for the Utilitarian rules. In this paper, we discuss this issue before proposing an alternative characterization which preserves the spirit of the original authors.     

The strategy-proof provision of public goods under congestion and crowding preferences

We examine the strategy-proof provision of excludable public goods when agents care about the number of other consumers. We show that strategy-proof and efficient social choice functions satisfying an outsider independence condition must always assign a fixed number of consumers, regardless of individual desires to participate. A hierarchical rule selects participants and a generalized median rule selects the level of the public good. Under heterogeneity in agents’ views on the optimal number of consumers, strategy-proof, efficient, and outsider independent social choice functions are much more limited and in an important case must be dictatorial.     

An extreme point characterization of random strategy-proof social choice functions: The two alternative case

We show that every strategy-proof random social choice function is a convex combination of strategy-proof deterministic social choice functions in a two-alternative voting model. This completely characterizes all strategy-proof random social choice functions in this setting.     

Set-rationalizable choice and self-stability

Rationalizability and similar notions of consistency have proved to be highly problematic in the context of social choice, as witnessed by a range of impossibility results, among which Arrow?s is the most prominent. We propose to rationalize choice functions by preference relations over sets of alternatives (set-rationalizability) and introduce two consistency conditions, and , which are defined in analogy to Sen?s α and γ. We find that a choice function satisfies if and only if it is set-rationalizable and that it satisfies and if and only if it is self-stable, a new concept based on earlier work by Dutta. The class of self-stable social choice functions contains a number of appealing Condorcet extensions.     

Representation and aggregation of preferences under uncertainty

We axiomatize in the Anscombe-Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.     

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.     

The relationship between top trading cycles mechanism and top trading cycles and chains mechanism

In this paper, we show that there is a relationship between two important matching mechanisms: the Top Trading Cycles mechanism (TTC mechanism proposed by Abdulkadiroglu and Sonmez, 1999) and the Top Trading Cycles and Chains mechanism (TTCC mechanism proposed by Roth, Sonmez, and Unver, 2004). Our main result is that when a specific chain selection rule proposed by Roth et al. is used, these two mechanisms are equivalent. While the equivalence is relevant for one specific case of the TTCC mechanism, it is a particularly interesting case since it is the only version identified by Roth et al. to be both Pareto-efficient and strategy-proof.     

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.     

Weak Independence and Social Semi‐Orders

This paper provides variants of Arrow's impossibility theorem, which states that there exists no non‐dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi‐order properties of semi‐transitivity and the interval‐order property. We prove that there exists a vetoer when the number of alternatives is greater than or equal to six.