Voting by Committees under Constraints

We consider social choice problems where a society must choose a subset from a set of objects. Specifically, we characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters' preferences are separable or additively representable.Voting, strategy-proofness, additive and separable preferences

The Multiple-partners Assignment Game with Heterogeneous Sells and Multi-unit Demands: Competitive Equilibria

A multiple-partners assignment game with heterogeneous sells and multi-unit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by only using linear programming. We show that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all equilibrium assignments, and vice versa. We also show that the set of (restricted) equilibrium price vectors has a natural lattice structure and we study how this structure is translated into the set of agents' utilities that are attainable at equilibrium.Matching, Assignment Game, Indivisible Goods, Competitive Equilibrium, Lattice

Bribe-proof Rules in the Division Problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate another agent to misrepresent his preference and, after an appropriate redistribution of their shares, each obtain a strictly preferred share. We characterize all bribe-proof rules as the class of efficient, strategy-proof, and weak replacement monotonic rules. In addition, we identify the functional form of all bribe-proof and tops-only rules.Bribe-proofness, Strategy-proofness, Efficiency, Replacement Monotonicity, Single-peakedness

A Maximal Domain of Preferences for Tops-only Rules in the Division Problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.Strategy-proofness, single-plateaued preferences

On cooperative solutions of a generalized assignment game : limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We establish that the Set-wise stable set is contained in the Core and contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Second, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff

A Maximal Domain of Preferences for Tops-only Rules in the Division Problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.The work of Alejandro Neme is partially supported by Research Grant 319502 from the Universidad Nacional de San Luis. The work of Jordi Massó is partially supported by Research Grants PB98-0870 from the Spanish Ministerio de Educación y Cultura, and 2001SGR-00162 from the Generalitat de Catalunya

On the Invariance of the Set of Core Matchings with Respect to Preference Profiles

We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal.Matching, Core

Ordinal relative satisficing behavior : theory and experiments

Altres ajuts: partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through grant PIP 112-200801-00655.We propose a notion of r-rationality, a relative version of satisficing behavior based on the idea that, for any set of available alternatives, individuals choose one of their r-best according to a single preference. We fully characterize the choice functions satisfying the condition for any r, and provide an algorithm to compute the maximal degree of r-rationality associated with any given choice function. The notion is extended to individuals whose r may vary with the set of available alternatives. We provide experimental evidence that the predictive power of our theory, measured by Seltenís index, improves upon that of alternative ones

On two basic properties of equilibria of voting with exit

We consider the problem of a society whose members must choose from a finite set of alternatives. After knowing the chosen alternative, members may reconsider their membership. Thus, they must take into account, when voting, the effect of their votes not only on the chosen alternative but also on the final composition of the society. We show that, under plausible restrictions on preferences, equilibria of this two-stage game satisfy stability and voter's sovereignty.