What are opportunities and why should they be equal?

In order to clarify the concept of equal opportunities we need an accurate definition of opportunity. Opportunities can be defined in terms of qualifying actions through which an agent can achieve an advantageous position. It is concluded that equal opportunities is often used as a catchword in cases when opportunities are not really equal, and no one tries seriously to make them so. In many of these cases it would have been more accurate to speak of open opportunities and procedural justice. These are important enough aspects of social justice, that should be appreciated for what they are, rather than being falsely represented as equal opportunities.Received: 13 April 2001     

The voter who wasn’t there: Referenda,representation and abstention

We analyze single binary-choice voting rules and identify the presence of the No-Show paradox in this simple setting, as a consequence of specific turnout or quorum conditions that are included in actual rules. Since these conditions are meant to ensure a representative outcome, we formalize this concern and reach our main result: no voting rule can ensure representation if abstention is possible, unless restrictive assumptions are made on the preference domain of abstainers. We then focus on the main referendum systems and show that appropriate restrictions do make them compatible with representation. The main purpose of our paper is, however, to provide a tool for referendum design: rather than imposing arbitrary restrictions on the preference domain of non-voters, we recommend instead that a conscious choice be made on how abstention is to be interpreted and that this choice be used to derive the corresponding referendum rule.The idea for this paper started with some jocose but insightful notes written by José João Marques da Silva at the time of the first referendum held in Portugal (1998). When José João passed away in August 2000, ISEG lost a bright, interested and friendly scholar. May we dedicate this paper to his memory. This paper was presented at the 2002 Annual Meeting of the Public Choice Society and Economic Science Association, San Diego, CA and a preliminary version was presented at the 2001 Annual Meeting of the European Public Choice Society, Paris. We would like to thank Mathew Braham, Moshé Machover, Eric Maskin, Vincent Merlin, Hannu Nurmi, Katri Sieberg, Frank Steffen, and two anonymous referees for helpful comments. The usual proviso applies.     

Majority vote following a debate

Voters determine their preferences over alternatives based on cases (or arguments) that are raised in the public debate. Each voter is characterized by a matrix, measuring how much support each case lends to each alternative, and her ranking is additive in cases. We show that the majority vote in such a society can be any function from sets of cases to binary relations over alternatives. A similar result holds for voting with quota in the case of two alternatives.We wish to thank Enriqueta Aragones, Jean-Francois Laslier, Andrew Postlewaite, and David Schmeidler for the comments and discussions. We thank Lada Burde for her help in proofreading.     

Redistribution under proportional representation

The purpose of this paper is to study the relationship between proportional representation voting system and the size of government via its effects on political equilibrium. The multiparty spatial competition on tax-transfer policy and the post-electoral coalition formation are examined. The implemented policy does not necessarily reflect the median voters preference, ranging from laissez-faire to a redistributive economy according to income distribution. It can even reflect the preference of the lower income class in spite of equal income distribution, leading to the large-scale redistribution. Our results can explain the heterogeneous sizes of government observed among European proportional representation democracies.The author is grateful for helpful comments to Masahiro Ashiya, Nobuaki Hori, Moriki Hosoe, Toshihiro Ihori, Tatsuro Kuroda, Yasuhiro Sato, and seminar participants at the University of Tokyo, Kyushu University, and Nagoya University.     

Freedom of choice and diversity of options: Some difficulties

This paper explores the possibility for a (non-preference-based) freedom ranking of opportunity sets that is sensitive to the diversity of the options. It turns out that how distances between sets and alternatives are measured is crucial to the derivation of such a ranking. Several proposals are examined, each of which is shown to lead to impossibility results. Earlier versions of this paper were presented at conferences in Kortrijk, Osnabrück, Oisterwijk, Caen and Pavia. I thank the participants at these conferences for their comments. I would also like to thank Steven Hartkamp, Theo Kuipers, Clemens Puppe and especially Kotaro Suzumura for their helpful comments. Furthermore, I am very grateful to Somdeb Lahiri for pointing out a mistake in a previous version of this paper.     

A note on “Banks winners in tournaments are difficult to recognize” by G. J. Woeginger

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T. While Woeginger shows that recognizing whether a given vertex of T is a Banks winner is NP-complete, the computation of a Banks winner of T is polynomial, and more precisely linear with respect to the size of T.The article of G.J. Woeginger appeared in Soc Choice Welfare 20: 523–528 (2003)     

Lattices of choice functions and consensus problems

In this paper we consider the three classes of choice functions satisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices. The lattice of choice functions satisfying (H) is distributive, whereas the lattice of choice functions verifying (C) is atomistic and lower bounded, and so has many properties. On the contrary, the lattice of choice functions satisfying (O) is not even ranked. Then using results of the axiomatic and metric latticial theories of consensus as well as the properties of our three lattices of choice functions, we get results to aggregate profiles of such choice functions into one (or several) collective choice function(s).The authors thank two anonymous referee for several useful remarks or corrections on the first version of the paper.     

A limit theorem on the dual core of a distributive social system

I consider abstract social systems where the distribution of wealth is an object of common concern. I study, in particular, the systems where liberal distributive social contracts consist of the Pareto-efficient distributions that are unanimously preferred to the initial distribution. I define a Dual Distributive Core from a process of decentralized auction on the budget shares of Lindahl associated with net transfers, operated by coalitions aiming at increasing the value of the public good for their members while maintaining their utility levels. I establish that the dual distributive core converges, as the number of distributive agents becomes large relative to the number of agent types, to a typically finite number of distributive liberal social contracts, which correspond to the Lindahl equilibria that are unanimously preferred to the initial distribution. This process of decentralized auction provides a theoretical foundation for contractual policies of redistribution. The comparison with the usual notion of core with public goods (Foley 1970) yields the following results in this context: the Foley-core is a subset, generally proper, of the set of liberal distributive social contracts; it does not contain, in general, distributive Lindahl equilibria.     

Room assignment-rent division: A market approach

A group of friends consider renting a house but they shall first agree on how to allocate its rooms and share the rent. We propose an auction mechanism for room assignment-rent division problems which mimics the market mechanism. Our auction mechanism is efficient, envy-free, individually-rational and it yields a non-negative price to each room whenever that is possible with envy-freeness.We would like to thank seminar participants at Barcelona, Boston College, Duke, Koç, Málaga, MIT, Michigan, NYU, conference participants at the First Brazilian Workshop of Game Theory Society (Sao Paulo 2002), SED 2002-Conference on Economic Design (New York City 2002), The Sixth International Meeting of the Society for Social Choice and Welfare (Pasadena 2002), an anonymous referee for their comments and Ahmet Alkan, Selçuk Karabati, Bari Tan, nsan Tunali for insightful discussions. Sönmez gratefully acknowledges the research support of KoçBank via the KoçBank scholar program and Turkish Academy of Sciences in the framework of the Young Scientist Award Program via grant TS/TÜBA-GEBP/2002-1-19. Any errors are our own responsibility.     

Factors Contributing to Parents’ Preparation For Special-Needs Adoption

Three hundred and sixty-eight parents shared their perceptions of special-needs adoption preparation. Utilizing both quantitative and qualitative data to determine and understand what factors contribute to preparation, this study found that 12 child, family, and agency variables were correlated with perceived preparation, and that parents perceived level of preparation was predicted by the childs ability to attach, by the parents relationship with the agency, by the duration of the adoption, and by the parents ages at the time of adoption. Implications of these findings are discussed, as they relate to supporting parents, children, and families in special-needs adoptive placements.