Rational choice theory

Having asked you to follow me through some difficult terrain, here I want only to emphasize three summary observations. First, sociologists reject rational choice theory but use it just the same; in all other fields that try to analyze organic processes, rational choice theory remains dominant, too; it may be hardwired into our thinking, and thus may be more powerful than we are inclined to believe; and for all these reasons we shall keep on doing it, whether or not we attack it.     

A social choice theory of legitimacy

We develop a formal theory of legitimate collective choice. In our theory a policy choice is legitimate if the process through which the final choice was determined is consistent with some principle that can be used to (perhaps partially) rank the potential policy choices. The set of principles in any choice situation is taken to be exogenous, but a decision-making process is defined so as to deal with any nontrivial set of principles. Such a process is itself referred to as legitimate if it is guaranteed to select a legitimate outcome for each possible exogenous set of principles. We characterize the class of procedures that are legitimate, prove that legitimate policy decisions consistent with principles always exist and characterize the set of policy decisions that are legitimate for a any given set of principles. As we do not require the principles to be weak orders of the alternatives, our theory provides a notion of legitimacy that can be satisfied even when the guiding principles are potentially cyclic or incomplete. Accordingly, our theory illustrates one nontautological means by which majoritarian principles can be reconciled with legitimacy.     

A note on social choice theory without the Pareto principle

This paper was originally submitted to Journal of Economic Theory and was accepted. After presenting it at the first meeting of the society for social choice and welfare in Caen, France, we were informed by Professor Bernard Monjardet that a weak version of our main result (Proposition 1) had been proved in Y. Murakami's book, Logic and Social Choice, Routledge and Kegan Paul, London, 1968. We later voluntarily withdrew the paper from JET even though the editor was still willing to publish it on the ground that it would do the profession a service by making more people aware of a simple yet fundamental result in social choice theory. Instead we decide to submit this paper to Social Choice and Welfare, hoping that it will reach the intended readers more effectively.     

Topological and discrete social choice: in a search of a theory

 In this note we discuss a possibility of introducing topological methods in the combinatorial paradigm of the social choice theory. Received: 30 October 1994/Accepted: 22 April 1996     

Invariance axioms for preferences: applications to social choice theory

I investigate the role played by the combination of two invariance axioms for preferences in utility theory; namely, those of zero-independence and scale-independence, respectively. I provide a characterization of the preference relations on ${\mathbb{R}^{n}}$ that satisfy these two axioms as those which are either trivial, or what I call a two-serial total preorder on ${\mathbb{R}^{n}}$ . This result is then applied in social choice theory to characterize those social welfare functions that satisfy IIA and PI. Other characterizations involving the usual Pareto concepts are also provided.     

A new approach to rights in social choice theory which incorporates utilitarianism

The paper axiomatises a generalised utilitarian aggregation rule, under which different weights are assigned to utilities depending on the different rights involved. The relationship between actions, rights and the evaluation of utilities is investigated. Application is made to a famous example, Edwin-Angelina-the Judge, which appears in the social choice literature.     

Assent-maximizing social choice

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population’s preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population’s preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality.     

Multi-profile intergenerational social choice

In an infinite-horizon setting, Ferejohn and Page showed that any social welfare function satisfying Arrow’s axioms and stationarity must be a dictatorship of the first generation. Packel strengthened this result by proving that no collective choice rule generating complete social preferences can satisfy unlimited domain, weak Pareto and stationarity. We prove that this impossibility survives under a domain restriction and without completeness. We propose an alternative stationarity axiom and show that a social welfare function on a specific domain satisfies this modified version and some standard social choice axioms if and only if it is a chronological dictatorship.     

Self-selective social choice functions

It is not uncommon that a society facing a choice problem has also to choose the choice rule itself. In such situations, when information about voters’ preferences is complete, the voters’ preferences on alternatives induce voters’ preferences over the set of available voting rules. Such a setting immediately gives rise to a natural question concerning consistency between these two levels of choice. If a choice rule employed to resolve the society’s original choice problem does not choose itself, when it is also used for choosing the choice rule, then this phenomenon can be regarded as inconsistency of this choice rule as it rejects itself according to its own rationale. Koray (Econometrica 68: 981–995, 2000) proved that the only neutral, unanimous universally self-selective social choice functions are the dictatorial ones. Here we introduce to our society a constitution, which rules out inefficient social choice rules. When inefficient social choice rules become unavailable for comparison, the property of self-selectivity becomes more interesting and we show that some non-trivial self-selective social choice functions do exist. Under certain assumptions on the constitution we describe all of them.     

On the manipulation of social choice correspondences

Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules. They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally, we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives.     

On the informational basis of social choice

The notion of informational basis in social choice can be broadened so as to cover not only the standard notions related to interpersonal utility comparisons, but also information about utilities or preferences at (ir)relevant alternatives, non-utility features of alternatives, personal responsibility, unconcerned subpopulations, and feasibility constraints. This paper proposes a unified conceptual framework for all these notions, and analyzes the kind of information retained in each case. This new framework yields a deeper understanding of the difficulties and possibilities of social choice. New welfarism theorems are also obtained.I am indebted to W. Bossert, W. Gaertner, F. Gaspart, L. Gevers, N. Gravel, S. Kolm, M. Le Breton, Ph. Mongin, P. Hammond, K. Suzumura, K. Tadenuma, A. Trannoy and J. Weymark for many conversations on topics related to this paper. I have benefited from reactions of the audience at the conference in honor of Louis Gevers, Namur 1999, and at a seminar at the LSE, and from comments by two referees and the editor, F. Maniquet. None of them is responsible for the shortcomings of the paper.