Published Papers



We prove that every system of binary probabilities satisfying the triangle inequalities is induced by a regular system of choice probabilities.



We propose a class of decisive collective choice rules that rely on a linear ordering to partition the majority relation into two acyclic relations. The first of these relations is used to pare down the set of the feasible alternatives into a shortlist while the second is used to make a final choice from the shortlist. Rules in this class are characterized by four properties: two classical rationality requirements (Sen's expansion consistency and Manzini and Mariotti's weak WARP); and adaptations of two classical collective choice requirements (Arrow's independence of irrelevant alternatives and Saari and Barney's no preference reversal bias). These rules also satisfy some other desirable properties, including an adaptation of May's positive responsiveness.



We study the social aggregation problem in the preference-approval model of Brams and Sanver (The mathematics of preference, choice and order: essays in honor of Peter C. Fishburn. Springer, Berlin, 2009). Each voter reports a linear ordering of the alternatives and an acceptability threshold. A rule transforms every profile of such “opinions” into a social ordering. The approval rule ranks the alternatives according to the number of voters who find them acceptable. The broken Borda rule ranks them according to the total score they receive; the scores assigned by a voter follow the standard Borda scale except that a large break is introduced between the score of her worst acceptable alternative and the score of her best unacceptable alternative. We offer an axiomatization of this rule and other lexicographic combinations of the approval rule and a fixed social welfare function.


We describe the class of strategy-proof mechanisms for choosing sets of objects when preferences are additive and monotonic.


We model uncertain social prospects as acts mapping states of nature to (social) outcomes. A social choice function (or SCF) assigns an act to each profile of subjective expected utility preferences over acts. A SCF is strategyproof if no agent ever has an incentive to misrepresent her beliefs about the states of nature or her valuation of the outcomes. It is unanimous if it picks the feasible act that all agents find best whenever such an act exists. We offer a characterization of the class of strategyproof and unanimous SCFs in two settings. In the setting where all acts are feasible, the chosen act must yield the favorite outcome of some (possibly different) agent in every state of nature. The set of states in which an agent's favorite outcome is selected may vary with the reported belief profile; it is the union of all states assigned to her by a collection of constant, bilaterally dictatorial, or bilaterally consensual assignment rules. In a setting where each state of nature defines a possibly different subset of available outcomes, bilaterally dictatorial or consensual rules can only be used to assign control rights over states characterized by identical sets of available outcomes.


In the context of uncertainty, belief-weighted relative utilitarianism consists in comparing acts according to a weighted sum of the (0, 1) -normalized subjective expected utilities they yield. The weights may change with the profile of beliefs but do not depend upon the profile of individual utilities for the outcomes. This class of social welfare functions is characterized by the Pareto principle, the sure-thing principle, a continuity condition, and an independence condition requiring that the social ranking of two acts is unaffected by the addition of an outcome that leaves everyone’s best and worst outcomes unchanged. The weights must be constant if the social ranking of constant acts is independent of individual beliefs. Anonymity then pins down plain relative utilitarianism: acts are compared according the sum of (0, 1)-normalized subjective expected utilities they generate.


We study two informational simplicity conditions for aggregating von Neumann–Morgenstern preferences. When the best relevant alternative for each individual cannot be ascertained with confidence (as when allocating an uncertain endowment of goods), Independence of Harmless Expansions requires that the social ranking of lotteries be unaffected by the addition of any alternative that every agent deems at least as good as the one she originally found worst. This axiom, along with the Weak Pareto Principle and Anonymity, characterizes bottom-calibrated Nash welfarism: utilities are calibrated so that the worst alternative is worth zero and lotteries are ranked according to the product of such bottom-calibrated utilities. When the worst relevant alternatives are difficult to identify, replacing Independence of Harmless Expansions by the dual axiom of Independence of Useless Expansions yields a characterization of top-calibrated Nash welfarism: lotteries are ranked according to the opposite of the product of the absolute values of top-calibrated utilities. The distributive implications of our two informational simplicity axioms are thus drastically different: while bottom-calibrated Nash welfarism recommends randomizing between two alternatives that it deems equally good, top-calibrated Nash welfarism is randomization-averse.

 

 The belief-weighted Nash social welfare functions are methods for aggregating Savage preferences defined over a set of acts. Each such method works as follows. Fix a 0-normalized subjective expected utility representation of every possible preference and assign a vector of individual weights to each profile of beliefs. To compute the social preference at a given preference profile, rank the acts according to the weighted product of the individual 0-normalized subjective expected utilities they yield, where the weights are those associated with the belief profile generated by the preference profile. We show that these social welfare functions are characterized by the weak Pareto principle, a continuity axiom, and the following informational robustness property: the social ranking of two acts is unaffected by the addition of any outcome that every individual deems at least as good as the one she originally found worst. This makes the belief-weighted Nash social welfare functions appealing in contexts where the best relevant outcome for an individual is difficult to identify.


Non-dictatorial Paretian aggregation of subjective expected utility preferences is possible under binary uncertainty when differences in tastes are small compared to differences in beliefs.


Each item in a given collection is characterized by a set of possible performances. A (ranking) method is a function that assigns an ordering of the items to every performance profile. Ranking by Rating consists in evaluating each item’s performance by using an exogenous rating function, and ranking items according to their performance ratings. Any such method is separable: the ordering of two items does not depend on the performances of the remaining items. Consistency requires that if a change in an item’s performance improves its relative ranking against some other item at a given profile, the same change never decreases its relative ranking against any item at any profile. When performances belong to a finite set, ranking by rating is characterized by Separability and Consistency; this characterization generalizes to the infinite case under a continuity axiom. Consistency follows from Separability and Symmetry, or from Monotonicity alone. When performances are vectors in R_+^m, a separable, symmetric, monotonic, continuous, and invariant method must rank items according to a weighted geometric mean of their performances along the m dimensions. 

 

We propose an axiomatic approach to the problem of deriving a (linear) welfare ordering from a choice function. Admissibility requires that the ordering assigned to a rational choice function is the one that rationalizes it. Neutrality states that the solution covaries with permutations of the alternatives. Persistence stipulates that the ordering assigned to two choice functions is also assigned to every choice function in between. We prove that these properties characterize the sequential solution: the best alternative is the alternative chosen from the universal set; the second best is the one chosen when the best alternative is removed; and so on. We also discuss some alternative axioms and solutions.

 

A set-ranking method assigns to each tournament on a given set an ordering of the subsets of that set. Such a method is consistent if (i) the items in the set are ranked in the same order as the sets of items they beat and (ii) the ordering of the items fully determines the ordering of the sets of items. We describe two consistent set-ranking methods.

 

A measure of association on cross-classification tables is row-size invariant if it is unaffected by the multiplication of all entries in a row by the same positive number. It is class-size invariant if it is unaffected by the multiplication of all entries in a class (i.e., a row or a column). We prove that every class-size invariant measure of association assigns to each cross-classification table a number which depends only on the cross-product ratios of its 2×2 subtables. We submit that the degree of association should increase when mass is shifted from cells containing a proportion of observations lower than what is expected under statistical independence to cells containing a proportion higher than expected–provided that total mass in each class remains unchanged. We prove that no continuous row-size invariant measure of association satisfies this monotonicity axiom if there are at least four rows.

 

An aggregation rule maps each profile of individual strict preference orderings over a set of alternatives into a social ordering over that set. We call such a rule strategy-proof if misreporting one's preference never produces a different social ordering that is between the original ordering and one's own preference. After describing two examples of manipulable rules, we study in some detail three classes of strategy-proof rules: (i) rules based on a monotonic alteration of the majority relation generated by the preference profile; (ii) rules improving upon a fixed status-quo; and (iii) rules generalizing the Condorcet–Kemeny aggregation method.

 

A choice function is backwards-induction rationalizable if there exists a finite perfect-information extensive-form game such that for each subset of alternatives, the backwards-induction outcome of the restriction of the game to that subset of alternatives coincides with the choice from that subset. We prove that every choice function is backwards-induction rationalizable.

 

A single valuable object must be allocated to at most one of n agents. Monetary transfers are possible and preferences are quasilinear. We offer an explicit description of the individually rational mechanisms which are Pareto-optimal in the class of feasible, strategy-proof, anonymous and envy-free mechanisms. These mechanisms form a one-parameter infinite family; the Vickrey mechanism is the only Groves mechanism in that family.

 

We reconsider the problem of aggregating individual preference orderings into a single social ordering when alternatives are lotteries and individual preferences are of the von Neumann–Morgenstern type. Relative egalitarianism ranks alternatives by applying the leximin ordering to the distributions of 0–1 normalized utilities they generate. We propose an axiomatic characterization of this aggregation rule.

 

We study the problem of defining inequality-averse social orderings over allocations of commodities when individuals have different preferences. We formulate a notion of egalitarianism based on the axiom that any dominance between consumption bundles should be reduced. This Dominance Aversion requirement is compatible with Consensus, a version of the Pareto principle saying that an allocation y is better than x whenever everybody finds that everyoneʼs bundle at y is better than at x. We characterize a family of multidimensional leximin orderings satisfying Dominance Aversion and Consensus.

 

We offer an axiomatization of the serial cost-sharing method of Friedman and Moulin (1999). The key property in our axiom system is Group Demand Monotonicity, asking that when a group of agents raise their demands, not all of them should pay less.

 

We analyze infinite-horizon choice functions within the setting of a simple technology. Efficiency and time consistency are characterized by stationary consumption and inheritance functions, as well as a transversality condition. In addition, we consider the equity axioms Suppes–Sen, Pigou–Dalton, and resource monotonicity. We show that Suppes–Sen and Pigou–Dalton imply that the consumption and inheritance functions are monotone with respect to time—thus justifying sustainability—while resource monotonicity implies that the consumption and inheritance functions are monotone with respect to the resource.

 

We study the problem of provision and cost-sharing of a public good in large economies where exclusion, complete or partial, is possible. We search for incentive-constrained efficient allocation rules that display fairness properties. Population monotonicity says that an increase in population should not be detrimental to anyone. Demand monotonicity states that an increase in the demand for the public good (in the sense of a first-order stochastic dominance shift in the distribution of preferences) should not be detrimental to any agent whose preferences remain unchanged. Under suitable domain restrictions, we give an explicit characterization of all incentive-constrained efficient allocation rules. We then show that there exists a unique incentive-constrained efficient and demand-monotonic allocation rule: the so-called serial rule. In the binary public good case, the serial rule is also the only incentive-constrained efficient and population-monotonic rule.

 

We study the construction of a social ordering function for the case of a public good financed by contributions from the population. We extend the analysis of Maniquet and Sprumont (2004) to the case when cost shares cannot be negative, i.e., agents cannot receive subsidies from others. We adapt the Maniquet–Sprumont defense of public good welfare egalitarianism to this context. Weakening their Free Lunch Aversion axiom and adding a continuity requirement allows us to characterize the public good welfare maximin social ordering function.

 

A reference-dependent choice function is a generalization of a standard choice function where chosen alternatives may depend on a reference alternative in addition to the set of feasible options. Such a function is non-deteriorating if there exists an ordering over the universal set of alternatives according to which the chosen alternatives are at least as good as the reference option. We characterize non-deteriorating reference-dependent choice functions in a general framework and in an economic environment.

 

A group of agents participate in a cooperative enterprise producing a single good. Each participant contributes a particular type of input; output is nondecreasing in the input profile. How should it be shared? We analyze the implications of the axiom of Group Monotonicity: if a group of agents simultaneously decrease their input, not all of them should receive a bigger share of output. We show that in combination with other more familiar axioms, this condition pins down a very small class of methods, which we dub nearly serial.

 

We propose the following weakened version of WARP: if the decision maker selects an alternative x and rejects another alternative y in some context, he cannot select y and reject x in another context. This axiom is consistent with cyclic choices. It is necessary and sufficient for the choice from every subset A of a (finite) universal set X to coincide with the weak upper-contour set of the transitive closure of some fixed complete relation at some alternative in A. Adding further simple axioms forces the choice from each subset to coincide with the top cycle (in that subset) of some fixed tournament over the universal set.

 

An important aspect of the complex notion of fairness in collective choices is that agents should bear responsibility only for their own actions. As a corollary, they should be treated ‘similarly’ when a change occurs for which no one is responsible. A minimal condition of ‘similar’ treatment is certainly that nobody benefits from such a change if someone else suffers from it.

 

We reconsider the problem of ordering infinite utility streams. As has been established in earlier contributions, if no representability condition is imposed, there exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams. We examine the possibility of adding suitably formulated versions of classical equity conditions. First, we provide a characterization of all ordering extensions of the generalized Lorenz criterion as the only strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. Second, we offer a characterization of an infinite-horizon extension of leximin obtained by adding an equity-preference axiom to strong Pareto and finite anonymity.

 

We survey recent axiomatic results in the theory of cost-sharing. A method assigns cost shares to the users of a facility for any profile of demands and any monotonic cost function. We discuss two radically different views of the asymmetries of the cost function. Under full responsibility, each agent is accountable for the part of the costs that can be unambiguously separated and attributed to her own demand. Under partial responsibility, the asymmetries of the cost function have no bearing on individual cost shares, only the differences in demand levels matter. We describe several invariance and monotonicity properties that reflect both normative and strategic concerns. We uncover a number of logical trade-offs between our axioms, and derive axiomatic characterizations: in the full responsibility approach, of the Shapley-Shubik, Aumann-Shapley, and subsidy-free serial methods; in the partial responsibility approach, of the cross-subsidizing serial method and of the family of quasi-proportional methods.

 

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. Such weakenings are particularly relevant in the context of social choice. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of the rationalizing relation. Furthermore, we discuss sufficient conditions and necessary conditions for rational choice on arbitrary domains. Transitive, quasi-transitive, and acyclical rationalizability are fully characterized for domains that contain all singletons and all two-element subsets of the universal set.

 

We propose two cost-sharing theories in which agents demand comparable commodities and are responsible for their own demand. Under partial responsibility, agents are not responsible for the asymmetries of the cost function: two agents consuming the same quantity pay the same price; this holds under full responsibility only if the cost function is symmetric. If the cost function is additively separable, each agent pays her stand-alone cost under full responsibility; this holds under partial responsibility only if the cost function is also symmetric. We generalize Moulin and Shenker's Distributivity axiom to cost-sharing methods for heterogeneous goods [Moulin, H., Shenker, S., 1999. Distributive and additive costsharing of an homogeneous good. Games Econ. Behav. 27, 299–330]. The subsidy-free serial method [Moulin, H., 1995. On additive methods to share joint costs. Japan. Econ. Rev. 46, 303–332] is essentially the only distributive method meeting Ranking and Dummy. The cross-subsidizing serial method [Sprumont, Y., 1998. Ordinal cost sharing. J. Econ. Theory 81, 126–162] is the only distributive method satisfying Separability and Strong Ranking. We propose an alternative characterization of the latter method based on a strengthening of Distributivity.

 

Each agent in a finite set requests an integer quantity of an idiosyncratic good; the resulting total cost must be shared among the participating agents. The Aumann–Shapley prices are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann–Shapley cost-sharing method charges to an agent the sum of the prices attached to the units she consumes. We show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or to merge their consumptions. We offer a variant of this result using the No Reshuffling condition: the total cost share paid by a group of agents who consume perfectly substitutable goods depends only on their aggregate consumption. We extend this characterization to the case where agents are allowed to consume bundles of goods.

 

Under partial responsibility, the ranking of cost shares should never contradict that of demands.The Solidarity axiom says that if agent i demands more, j should not pay more if k pays less. It characterizes the quasi-proportional methods, sharing cost in proportion to `rescaled' demands. Full responsibility rules out cross-subsidization for additively separable costs. Restricting solidarity to submodular cost characterizes the fixed-flow methods, containing the Shapley–Shubik and serial methods. The quasi-proportional methods meet—but most fixed-flow methods fail—Group Monotonicity: if a group of agents increase their demands, not all of them pay less. Serial cost sharing is an exception.

 

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity.

 

Consistency of a binary relation requires any preference cycle to involve indifference only. It has been shown that consistency is necessary and sufficient for the existence of an ordering extension of a binary relation. It is therefore of interest to examine the rationalizability of choice functions by means of consistent relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency. All but one such notion are characterized for general domains, and all are characterized for domains that contain all two-element subsets of the universal set.

 

We study equity in economies where a set of agents commonly own a technology producing a non-rival good from their private contributions. A social ordering function associates to each economy a complete ranking of the allocations. We build social ordering functions satisfying the properties that individual welfare levels below the stand-alone lower bound (respectively, above the unanimity upper bound) should be increased (respectively, reduced). Combining either property with efficiency and robustness properties with respect to changes in the set of agents, we obtain a kind of welfare egalitarianism based on a constructed numerical representation of individual preferences.

 

We study fairness in economies with one private good and one partially excludable nonrival good. A social ordering function determines for each profile of preferences an ordering of all conceivable allocations. We propose the following Free Lunch Aversion condition: if the private good contributions of two agents consuming the same quantity of the nonrival good have opposite signs, reducing that gap improves social welfare. This condition, combined with the more standard requirements of Unanimous Indifference and Responsiveness, delivers a form of welfare egalitarianism in which an agent's welfare is measured by the quantity of the nonrival good that, consumed at no cost, would leave her indifferent to the bundle she is assigned.

 

We identify conditions under which preferences over subsets of a consumption world can be reduced to preferences over bundles of "commodities". We distinguish ordinal bundles, whose coordinates are defined up to monotone transformations, from cardinal bundles, whose coordinates are defined up to positive linear transformations.

 

We analyze collective choice procedures with respect to their rationalizability by means of profiles of individual preference orderings. A generalized choice function is an extension of a choice function where selected alternatives may depend on a reference (or status quo) alternative in addition to the set of feasible options. Given the number of agents n, a generalized choice function satisfies efficient and non-deteriorating n-rationalizability if there exists a profile of n orderings on the universal set of alternatives such that the selected alternatives are (i) efficient for that profile, and (ii) at least as good as the reference option according to each individual preference. We analyze efficient and non-deteriorating collective choice in a general abstract framework and provide characterization results on a universal set domain.

 

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. The core lower bounds require that no coalition should get less than the welfare it could achieve by using the water it controls. The aspiration upper bounds demand that no coalition enjoy a welfare higher than what it could achieve in the absence of the remaining agents. Exactly one welfare distribution satisfies the core lower bounds and the aspiration upper bounds: it is the marginal contribution vector corresponding to the ordering of the agents along the river.

 

Suzumura [Economica 43 (1976) 381] has shown that a binary relation has a weak order extension if and only if it is consistent. However, consistency is demonstrably not sufficient to extend an upper semicontinuous binary relation to an upper semicontinuous weak order. Jaffray [Journal of Mathematical Economics 2 (1975) 395] proved that any asymmetric (resp. reflexive), transitive and upper semicontinuous binary relation has an upper semicontinuous strict (resp. weak) order extension. We provide sufficient conditions for the existence of upper semicontinuous extensions of consistent rather than transitive relations. For asymmetric relations, consistency and upper semicontinuity suffice. For more general relations, we prove two sufficiency theorems, each of which uses one additional axiom. The first employs a comparability property, and in the second, another continuity requirement is added.

 

We provide a characterization of selection correspondences in two person exchange economies that can be core rationalized in the sense that there exists a preference profile with some standard properties that generates the observed choices as the set of core elements of the economy for any given endowment vector. The approach followed in this paper deviates from the standard rational choice model in that a rationalization in terms of a profile of individual orderings rather than in terms of a single individual or social preference relation is analyzed.

 

This paper discusses the core of the game corresponding to the standard fixed tree problem. We consider the weighted adaptation of the constrained egalitarian solution of Dutta and Ray (1989). The core of the standard fixed tree game equals the set of all weighted constrained egalitarian solutions. Each weighted constrained egalitarian solution is determined (in polynomial time) as a home-down allocation, which creates further insight in the local behaviour of the weighted constrained egalitarian solution. The constrained egalitarian solution is characterized in terms of a cost sharing mechanism.

 

We characterize the “regular” two-agent Paretian quasi-orders.

 

We reconsider the discrete version of the axiomatic cost-sharing model. We propose a condition of (informational) coherence requiring that not all informational refinements of a given problem be solved differently from the original problem. We prove that strictly coherent linear cost-sharing rules must be simple random-order rules.

 

We analyze collective choices in game forms from a revealed preference viewpoint. We call the joint choice behavior of n agents Nash- (respectively, Pareto-) rationalizable if there exist n preferences over the conceivable joint actions such that the joint actions selected from each game form coincide with the Nash equilibria (respectively, the Pareto optima) of the corresponding game. In the two-agent case, we show that every deterministic joint behavior which is Nash-rationalizable is also Pareto-rationalizable. The converse is false. We further identify general necessary and sufficient conditions for Nash-rationalizability of an n-agent joint choice behavior. We also define and characterize partial versions of the Nash- and Pareto-rationalizability requirements.

 

In the context of the classical fair division problem, we show that Efficiency and Resource Monotonicity are incompatible with the following “Conditional Equal Split” condition: If equal split of the collective endowment is efficient, it should be among the recommended allocations.

 

Two (Pareto) surfaces are ordinally equivalent if they can be mapped onto each other through an ordinal transformation, i.e., a list of monotone transformations of the individuals' utility levels. Otherwise, they are ordinally distinct. Assuming at least three individuals and some regularity conditions, we construct a set of “standard” Pareto surfaces which is an “ordinal basis” of the set of all surfaces: every Pareto surface is ordinally equivalent to some standard surface and all standard surfaces are ordinally distinct. We also show that any two ordinally equivalent surfaces are related through a unique ordinal transformation. The existence of (efficient and strictly individually rational) ordinal bargaining solutions is a direct corollary.

 

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.

 

In this paper we consider the fair division problem for large societies where the bundle of goods to be divided is fixed but societies are allowed to change. We provide a characterization of Pazner–Schmeidler's egalitarian-equivalent rules [Pazner, E., Schmeidler, D., 1978. Egalitarian-equivalent allocations: A new concept of economic equity. Q. J. Econ. 92, 671–687.] by the axioms of efficiency, the equal split lower bound for utilities, and solidarity with respect to changes in society.

 

We reconsider the problem of provision and cost-sharing of multiple public goods. The efficient equal factor equivalent allocation rule makes every agent indifferent between what he receives and the opportunity of choosing the bundle of public goods subject to the constraint of paying r times its cost, where r is set as low as possible. We show that this rule is characterized in economies with a continuum of agents by efficiency, a natural upper bound on everyone's welfare, and a property of solidarity with respect to changes in population and preferences.

 

We ask how the best known mechanisms for solving cost sharing problems with homogeneous cost functions—the value, proportional, and serial mechanisms—should be extended to arbitrary problems. We propose the Ordinality axiom, which requires that cost shares should be invariant under (essentially) all increasing transformations of the measuring scales. Following the value approach first, we present an axiomatization of the Shapley–Shubik rule based on Ordinality. Next, we define and axiomatize two extensions of the serial mechanism which, contrary to the Friedman–Moulin rule, are ordinal. Finally, we note that the Aumann–Shapley extension of the proportional mechanism is not ordinal. We propose and defend an alternative proportional extension which does satisfy Ordinality.

 

This paper reconsiders the issue of how income should be redistributed when people endowed with different levels of talent exert different levels of effort. Two new schemes, called balanced egalitarian equivalence and balanced conditional egalitarianism, are proposed and characterized.

 

The paper characterizes the class of transferable-utility cooperative games arising from public-good economies. In the symmetric case and in the three-player case, this class is precisely that of convex games. In general, a highly structured pattern of differences between the worths of the various coalitions is characteristic of the public-good games. This pattern implies convexity but also many other restrictions. Some of these restrictions express in a formal way the intuition that full cooperation is the only stable form of collective behaviour in public-good economies.

 

This paper formulates the principle of ordinal welfare egalitarianism in a general model of collective choice where both the feasibility constraints and the preferences may vary. An axiomatization of all choice rules satisfying this principle is presented. The key axiom is a solidarity property with respect to changes that may occur, possibly jointly, in the feasibility constraints and the preferences. Solidarity with respect to changes in the feasibility constraints and solidarity with respect to changes in the preferences together imply only a weaker form of egalitarianism.

 

This paper considers the problem of dividing a bundle of two private goods between two agents whose preferences are continuous, convex and strictly increasing. It is shown that every strategyproof scheme that is continuous in the preferences must let one agent choose his best bundle from some exogenous set.

 

This paper surveys some recent results characterizing strategyproof collective choice rules when preferences satisfy conditions that are meaningful in economic or political environments.

 

Given the preferences of two agents over a finite set of alternatives, an arbitration rule selects some fair compromise. We study the idea that more consensus should not be harmful: the closer your preferences are to mine (in the sense of Grandmont's (1978) intermediate preferences), the better I like the selected alternative. We describe several Pareto optimal rules satisfying this principle. If, in addition, a condition akin to Suppes' (1966) grading principle is imposed, the rule must always choose an alternative maximizing the welfare of the worst-off agent, measured by the number of alternatives that he finds worse than the chosen one.

 

This paper explores the problem of dividing some fixed amount of a good for which individuals have single-peaked preferences. We show that the requirements of strategy-proofness, efficiency, and anonymity point to a unique rule, namely the uniform allocation rule: everyone gets what he wants within the limits of a lower bound and an upper bound that are common to all agents. This remains true if the anonymity axiom is replaced by envy-freeness.

 

An allocation scheme for a cooperative game specifies how to allocate the worth of every coalition. It is population monotonic if each player's payoff increases as the coalition to which he belongs grows larger. We show that, essentially, a game has a population monotonic allocation scheme (PMAS) if and only if it is a positive linear combination of monotonic simple games with veto control. A dual characterization is also provided. Sufficient conditions for the existence of a PMAS include convexity and “increasing average marginal contributions.” If the game is convex, its (extended) Shapley value is a PMAS.

 

Nous présentons deux modèles d‘équilibre général à prix fixes où le système productif est désagrégé en plusieurs secteurs interdépendants. Nous montrons que cette interdépendance diminue l'efficacité d'une politique non sélective de stimulation de la demande. Dans le cas où les demandes intermédiaires des secteurs de production peuvent être rationnées, l'impact d'une légère variation de la demande autonome sur le revenu agrégé peut même être négatif.