On strategy-proofness and symmetric single-peakedness

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin, 1980) since, under the domain of symmetric single-peaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategy-proof on the smaller domain. Our result identifies the specific nature of these discontinuities which allow to design non-onto social choice functions to deal with feasibility constraints.     

Condorcet cycles in bipartite populations

Summary. Simple majority voting between pairs of alternatives is used to aggregate individual preferences. The occurence of Condorcet cycles is limited thanks to a principle of homogeneity on individual preferences. The restrictions induced on the domain of the latters are weak: among the n! possible orderings of n alternatives, more than one half are admissible within a domain. The resulting aggregated preference has then a neglectable probability of showing up cycles. We show moreover that the set of individual preferences can be `naturally' partitioned into two such domains. Received: June 17, 1996; revised version: April 15, 1997     

Euclidean individual preference and continuous social preference

Assume a finite society, a standard space of allocations of public goods, and an open and connected domain of profiles of Euclidean individual preferences. (There is an additional technical restriction on the domain.) If a social welfare function f satisfies Arrow's independence axiom and generates social preferences that are continuous and transitive, then f is constant or dictatorial or inversely dictatorial.     

Corrigendum to “Stable matchings and preferences of couples” [J. Econ. Theory 121 (1) (2005) 75–106]

We correct an omission in the definition of the domain of weakly responsive preferences introduced in [B. Klaus, F. Klijn, Stable matchings and preferences of couples, J. Econ. Theory 121 (2005) 75–106] or KK05 for short. The proof of the existence of stable matchings [KK05, Theorem 3.3] and a maximal domain result [KK05, Theorem 3.5] are adjusted accordingly.     

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.     

Strategy-proofness versus efficiency for small domains of preferences over public goods

Summary. It has long been known that when agents have von Neumann-Morgenstern preferences over lotteries, there is an incompatibility between strategy-proofness and efficiency (Gibbard, [9]; Hylland, [12]) – a solution satisfying those properties must be dictatorial. We strengthen this result by showing that it follows from the same incompatibility on a series of much smaller domains of preferences. Specifically, we first show the incompatibility to hold on our smallest domain, in which two agents are restricted to have linear preferences over one private good and one public good produced from the private good (Kolm triangle economies). This result then implies the same incompatibility on increasingly larger domains of preferences, ending finally with the class of von Neumann-Morgenstern preferences over lotteries. Received: February 6, 1997; revised version: January 29, 1998     

Risk aversion,prudence and temperance: An experiment in gain and loss

We characterize the individual's attitude towards risk, prudence and temperance in the gain and loss domains. We analyze the links between the three features of preferences for a given domain and between domains for each feature of preferences. Consequently, the reflection effect, the mixed risk aversion and the risk apportionment, are key concepts of our study. We also display some determinants for risk aversion, prudence and temperance in each domain. To do this, we conducted a lab experiment with students eliciting risk aversion, prudence and temperance in the two domains, and collected information about each subject's characteristics.     

Are incentives against economic justice?

We consider the problem of fairly allocating a social endowment of indivisible goods and money when the domain of admissible preferences contains, but is not restricted to, quasi-linear preferences. We analyze the manipulability of the Generalized Money Rawlsian Fair (GMRF) solutions. (i) We show that the Nash and strong Nash equilibrium correspondences of the “preference revelation game form” associated with each GMRF solution coincide with the no-envy solution (in equilibrium, efficiency is preserved according to agents' true preferences). (ii) A corollary is that the GMRF solutions “naturally implement” the no-envy solution in Nash and strong Nash equilibria.     

Voting over income tax schedules

In many voting situations, preferences over options may fail to be single-peaked. This is especially true when options consist of different amounts of a good which is provided through distortionary taxation. In this paper, voting over linear income tax schedules is considered. Although preferences may fail to be single-peaked, a choice set is shown to exist when only mild restrictions are imposed. For many choices in the public domain, the conditions required for this result are likely to be satisfied.     

Paths to stability for matching markets with couples

We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from ‘satisfying’ blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's [Roth, A.E., Vande Vate, J.H., 1990. Random paths to stability in two-sided matching. Econometrica 58, 1475–1480] result on path convergence to stability for decentralized singles markets.Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from ‘satisfying’ blocking coalitions that yields a stable matching.     

Decomposable Strategy-Proof Social Choice Functions

This article shows that a social choice function defined on a domain of separable preferences which satisfies a relatively weak domain-richness condition on a product set of alternatives is (i) strategy-proof and only depends on the tops of the individual preferences if and only if (ii) the range of the social choice function is a product set and the social choice function can be decomposed into the product of one-dimensional, strategy-proof, nontop-insensitive social choice functions.
JEL Classification Number: D71.     

Generous actors,selfish actions: markets with other-regarding preferences

This paper points out that classical competitive outcomes arise in two different market environments even if agents have non-classical preferences. Consumers with separable, other-regarding preferences behave as if they have classical preferences in competitive equilibrium. These outcomes need not be efficient, but under plausible conditions will be efficient following a redistribution of income. In simple double-auction environments competitive outcomes arise under a wide range of assumptions on preferences even without assuming separability. I discuss the importance of the domain of definition of preferences and how the preferences present in the economy influence the performance of the trading institution.

Necessary and sufficient conditions for a resolution of the social choice paradox

We present a restriction on the domain of individual preferences that is both necessary and sufficient for the existence of a social choice rule that is continuous, anonymous, and respects unanimity. The restriction is that the space of preferences be contractible. Contractibility admits a straightforward intuitive explanation, and is a generalisation of conditions such as single peakedness, value restrictedness and limited agreement, which were earlier shown to be sufficient for majority voting to be an acceptable rule. The only restriction on the number of individuals, is that it be finite and at least 2.     

A Measure Of The Trade‐Off Between Responsiveness and Nondictatorship for Arrovian Social Welfare Functions

If individuals are never indifferent between distinct alternatives then for any transitive‐valued social welfare function satisfying IIA, and any fraction t, either the set of pairs of alternatives that are socially ordered without consulting more than one individual's preferences comprises at least the fraction t of all pairs, or else the fraction of pairs that have their social ordering determined independently of everyone's s preferences exceeds, or is very close to, 1 ?t. The Pareto criterion is not imposed. (There is also a version of this result for the domain of preferences that admit indifference.)     

Proper scoring rules for general decision models

If a decision maker whose behavior conforms to the max-min expected utility model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there is a scoring rule inducing the agent to announce that prior. We also show that on the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors).     

A solution to the random assignment problem on the full preference domain

We consider the problem of allocating a set of indivisible objects to agents in a fair and efficient manner. In a recent paper, Bogomolnaia and Moulin consider the case in which all agents have strict preferences, and propose the probabilistic serial (PS) mechanism; they define a new notion of efficiency, called ordinal efficiency, and prove that the probabilistic serial mechanism finds an envy-free ordinally efficient assignment. However, the restrictive assumption of strict preferences is critical to their algorithm. Our main contribution is an analogous algorithm for the full preference domain in which agents are allowed to be indifferent between objects. Our algorithm is based on a reinterpretation of the PS mechanism as an iterative algorithm to compute a “flow” in an associated network. In addition we show that on the full preference domain it is impossible for even a weak strategyproof mechanism to find a random assignment that is both ordinally efficient and envy-free.     

A tangent cone analysis of smooth preferences on a topological vector space

Summary. A theory of smooth preferences on a locally convex, topological vector space is developed by characterizing the existence of a unique supporting hyperplane to a convex set at a given point. The results are expressed in terms of the tangent cone. A new concept of properness, called strict properness, is also proposed to characterize the existence of a strictly supporting hyperplane to a convex set at a given point. We say that strict preferences are properly smooth at a given point provided that they are smooth, strictly proper, and the secant cone has a non-empty interior. Proper smoothness is broadly consistent with Gâteaux-differentiable utility even when the preference domain has an empty interior. Yet proper smoothness also allows the possibility of incomplete or intransitive preferences. This concept has immediate applications to optimization and equilibrium theory. For example, we demonstrate a version of the Second Welfare Theorem for agents with properly smooth preferences.Received: 25 September 2002; revised version: February 5, 2003, Revised: 5 February 2003, JEL Classification Numbers: D46, D51.     

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.     

Stable matchings and preferences of couples

Couples looking for jobs in the same labor market may cause instabilities. We determine a natural preference domain, the domain of weakly responsive preferences, that guarantees stability. Under a restricted unemployment aversion condition we show that this domain is maximal for the existence of stable matchings. We illustrate how small deviations from (weak) responsiveness, that model the wish of couples to be closer together, cause instability, even when we use a weaker stability notion that excludes myopic blocking. Our remaining results deal with various properties of the set of stable matchings for “responsive couples markets”, viz., optimality, filled positions, and manipulation.     

Coalitional Strategy-Proof House Allocation

We consider house allocation without endowments. We show that there is a unique maximal domain including all strict preferences on which efficiency and coalitional strategy-proofness are compatible. A preference relation belongs to the unique maximal domain if it is a strict descending ranking of houses to a certain house and indifference holds over it and the remaining houses. We also show that on this domain mixed dictator-pairwise-exchange rules are the only rules satisfying efficiency and coalitional strategy-proofness. Journal of Economic Literature Classification Numbers: C78, D63, D71.