Memos after 2008 SSCW Meeting

The two-stage rules for multi-issue allocation situations

Silvia María Lorenzo Freire Universidade da Coruña, slorenzo@udc.es
Gustavo Bergantiños Universidade de Vigo, gbergant@uvigo.es
Leticia Lorenzo Universidade de Vigo, leticiap@uvigo.es

In a bankruptcy problem, there is an estate to be divided among a number of claimants, whose total claim exceeds the estate available. The multi-issue allocation situations are used to model bankruptcy-like problems in which the estate is divided not on the basis of a single claim for each agent, but several claims resulting from so-called issues. We consider extensions of well-known bankruptcy rules such as the proportional rule, the constrained equal awards rule, and the constrained equal losses rule. These extensions are obtained by means of a procedure in two stages where first the estate is divided among the issues and then the quantity obtained for each issue is divided among the agents. We study these rules from an axiomatic point of view. In this way, we introduce suitable properties in this context and characterize some of the two-stage rules with them. Although these extensions have been studied previously (see Lorenzo-Freire et al. (2005), for example), we pursue a more ambitious program, surveying it from most of the perspectives that have found to be fruitful in previous literature on standard bankruptcy problems.

• This paper related with my paper with Eiichi and Toyo. They may need our paper since they are not aware of it.

Limited rights and social choice rules

Maurice Salles Universite de Caen, maurice.salles@unicaen.fr

In 1970 Sen introduced within social choice theory the notion of minimal liberty and proved an impossibility result concerning social decision functions. In the present paper, Sen''s condition of (minimal) liberty is weakened within the framework of social choice rules. It is then shown that the same kind of impossibility obtains for social choice functions.

• With his weakening of Sen's minimal liberalism, extended Pareto rule satisfies all axioms imposed in Sen's theorem. But is there other rules? Isn't the Pareto rule the only rule satisfying them? I asked this question and the author seems does not know the answer.

Implementation via code of rights

Semih Koray Bilkent University, ksemih@bilkent.edu.tr
Kemal Yildiz Bilkent University, kemaly@bilkent.edu.tr

Implementation of a social choice rule can be thought of as a design of power(re)distribution in the society such that the society''s "equilibrium outcomes" coincide with the alternatives chosen by the social choice rule at any preference profile of the society. In this paper, we introduce a new societal framework for implementation which takes the power distribution in the society, represented by a code of rights, as its point of departure. We examine and identify how implementation via code of rights (referred to as gamma implementation) is related to classical Nash implementation via a mechanism. We characterize gamma implementability when the state space on which the rights structure is to be specified consists of the alternatives from which a social choice is to be made. We show that a social choice rule is gamma implementable if it satisfies pivotal oligarchic monotonicity - a notion introduced in this study. Moreover, pivotal oligarchic monotonicity conjoined with Pareto optimality turns out to be sufficient for a non-empty valued social choice rule to be gamma implementable. Finally we revisit "liberal''s paradox" of A.K. Sen, which turns out to fit very well into the gamma implementation framework.

• Seems related with my paper on individual powers and social consent.