Social Choice: Recent Developments

In the past quarter century, there has been a dramatic shift of focus in social choice theory, with structured sets of alternatives and restricted domains of the sort encountered in economic problems coming to the fore. This article provides an overview of some of the recent contributions to four topics in normative social choice theory in which economic modelling has played a prominent role: Arrovian social choice theory on economic domains, variable-population social choice, strategy-proof social choice, and axiomatic models of resource allocation.

Social Norms and Rationality of Choice

Ever since Sen (1993) criticized the notion of internal consistency of choice, there exists a wide spread perception that the standard rationalizability approach to the theory of choice has difficulties coping with the existence of external social norms. This paper introduces a concept of norm-conditional rationalizability and shows that external social norms can be accommodated so as to be compatible with norm-conditional rationalizability by means of suitably modified revealed preference axioms in the theory of rational choice on general domains à la Richter (1966;1971) and Hansson (1968)

Infinite-Horizon Choice Functions

We analyze infinite-horizon choice functions within the setting of a simple linear technology. Time consistency and efficiency 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. Examples illustrate the characterization results.

A Characterization of Consistent Collective Choice Rules

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference. The properties used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available.

Non-Deteriorating Choice without Full Transitivity

Although the theory of greatest-element rationalizability and maximal-element rationalizability under general domains and without full transitivity of rationalizing relations is well-developed in the literature, these standard notions of rational choice are often considered to be too demanding. An alternative definition of rationality of choice is that of non-deteriorating choice, which requires that the chosen alternatives must be judged at least as good as a reference alternative. In game theory, this definition is well-known under the name of individual rationality when the reference alternative is construed to be the status quo. This alternative form of rationality of individual and social choice is characterized in this paper on general domains and without full transitivity of rationalizing relations.

Single-Peaked Choice

Single-peaked preferences have played an important role in the literature ever since they were used by Black (1948) to formulate a domain restriction that is sufficient for the exclusion of cycles according to the majority rule. In this paper, we approach single-peakedness from a choice-theoretic perspective. We show that the well-known axiom independence of irrelevant alternatives (a form of contraction consistency) and a weak continuity requirement characterize a class of single-peaked choice functions. Moreover, we examine the rationalizability and the rationalizability-representability of these choice functions.

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 situation voters’ preferences on alternatives induce preferences over the 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 in 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 (2000) proved that the only neutral, unanimous universally self-selective social choice functions are the dictatorial ones. Here we in troduce 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 weaker 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.

The Lack of Credibility on the Web and its Ramifications Under Quebec’s Consumer Protection Act

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Multi-Profile Intergenerational Social Choice

Ferejohn and Page transplanted a stationarity axiom from Koopmans’ theory of impatience into Arrow’s social choice theory with an infinite horizon and showed that the Arrow axioms and stationarity lead to a dictatorship by the first generation. We prove that the negative implications of their stationarity axiom are more far-reaching: there is no Arrow social welfare function satisfying their stationarity axiom. We propose a more suitable stationarity axiom, and show that an Arrow social welfare function satisfies this modified version if and only if it is a lexicographic dictatorship where the generations are taken into consideration in chronological order.