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.     

Public information and social choice

We examine the value of public information when a society uses a social choice rule to decide among a set of outcomes. We require that a social choice function satisfies unrestricted domain, non-decisiveness and the Pareto principle. We show that there exist payoff structures for every social choice function, such that an arbitrary subset of voters is worse off by public information. We apply the proposition to collective information acquisition and to irreversible investments. Received: 2 June 1997/Accepted: 30 September 1998     

Multi-valued strategy-proof social choice rules

In this paper we introduce a new definition of strategy-proofness for multi-valued social choice correspondences. We prove two Gibbard-Satterthwaite type results for strategy-proof social choice correspondences. These results show that allowing multiple outcomes as social choices will not necessarily lead to an escape from the Gibbard-Satterthwaite impossibility theorem. Received: 24 January 2001/Accepted: 19 March 2001     

Moral sentiments and social choice

We examine the implications, for social choice, of individuals having an intrinsic sense of fairness. Taking the viewpoint that social justice reflects the moral attitudes of the constituent members, we analyze the effect of the intensity of the individual sense of fairness on the solution of Nash bargaining over random allocation procedures. We use a stylized model of university admission policies to illustrate our approach. We show that even if social policies are ultimately determined by the bargaining power of the different groups, a society whose members have a common notion of fairness tends to implement fairer admission policies when the intensity of the sense of fairness of individual members increases. While working on the research that is summarized in this paper the authors visited several institutions. Edi Karni visited the Berglas School of Economics, Tel Aviv University and GRID, at Ecole Normale Superieur de Cachan. Zvi Safra visited CERMCEM and EUREQua, at the University of Paris I and LIP6, at the University of Paris 6. The hospitality of these institutions is gratefully acknowledged. We are also grateful to the editor and two anonymous referees for their very useful comments and suggestions. Zvi Safra thanks The Israel Science Foudation (grant 1299/05) for its support.     

Strategy-proof resolute social choice correspondences

We qualify a social choice correspondence as resolute when its set valued outcomes are interpreted as mutually compatible alternatives which are altogether chosen. We refer to such sets as “committees” and analyze the manipulability of resolute social choice correspondences which pick fixed size committees. When the domain of preferences over committees is unrestricted, the Gibbard–Satterthwaite theorem—naturally—applies. We show that in case we wish to “reasonably” relate preferences over committees to preferences over committee members, there is no domain restriction which allows escaping Gibbard–Satterthwaite type of impossibilities. We also consider a more general model where the range of the social choice rule is determined by imposing a lower and an upper bound on the cardinalities of the committees. The results are again of the Gibbard–Satterthwaite taste, though under more restrictive extension axioms.     

Informational geometry of social choice

 Elementary geometry is used to understand, extend and resolve basic informational difficulties in choice theory. This includes axiomatic conclusions such as Arrow’s Theorem, Chichilnisky’s dictator, and the Gibbard–Satterthwaite result. In this manner new results about positional voting methods are outlined, and difficulties with axiomatic approach are discussed. A topological result about “dictatorial” behavior is offered. Received: 15 December 1993/Accepted: 22 April 1996     

On strategy-proof social choice correspondences

We introduce two new concepts of strategy-proofness for social choice correspondences based on the theory of preferences over sets of alternatives under complete uncertainty. One is based on Pattanaik and Peleg (Soc Choice Welf 1:113–122, 1984) and the other is based on Bossert et al. (Econ Theory 16:295–312, 2000). We prove that there is no social choice correspondence satisfying anonymity, neutrality, a range condition, and either of our concepts of strategy-proofness. An erratum to this article can be found at     

Veto in fixed agenda social choice correspondences

In this paper we analyze the relationship between social decision functions (SDF) and fixed agenda social choice correspondences (fixed agenda SCC), satisfying some rationality conditions (such as Pareto, Independence, Monotonicity, Neutrality or Anonimity), with the aim of translating known results on the existence of individuals with veto power into the fixed agenda framework (e.g., Blair and Pollak [2], Blau and Deb [3], …). In order to do this, a new independence condition (which we call Pseudo-Independence), as well as a notion of veto power, are introduced in the context of fixed agenda SCC. The conclusion is that, by fixing the agenda, under Independence and Pareto assumptions, the existence of individuals with veto power cannot be avoided. Received: 6 November 1995 / Accepted: 9 September 1997     

Acyclic social choice from finite sets

This paper characterizes acyclic preference aggregation rules under various combinations of monotonicity, neutrality, decisiveness, and anonymity, in the spirit of Nakamura's (1979) Theorem on the core of simple games. Each of these characterizations can be seen to follow from Ferejohn and Fishburn's (1979) result on acyclic aggregation rules assuming only independence of irrelevant alternatives. We then state as corollaries to these characterizations extant results such as Sen's (1970) liberal paradox, Blau and Deb's (1977) theorem on the existence of vetoers, and Brown's (1975) theorem on the non-emptiness of the collegium.I thank David Austen-Smith, Michel Le Breton, Maurice Salles, and two anonymous referees for numerous enlightening conversations and comments. I also thank the National Science Foundation and Sloan Foundation for generous financial assistance.     

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.     

Public goods and Arrovian social choice

A social welfare function satisfying Arrow's independence axiom is constant or authoritarian if it generates continuous and transitive social preferences over the space of allocations of public and private goods, and individual preferences have the classical economic properties. The social welfare function will be oligarchial if it generates continuous and quasitransitive social preferences and satisfies a weak version of the Pareto criterion in addition to the independence axiom.This work was supported by the National Sciences Foundation grant no. SES 9007953. I am grateful to anonymous referees whose suggestions led to several substantial improvements.     

Nonbinary social choice for economic environments

Assume a finite integer l2 and a social choice correspondence mapping each (p, Z) into a nonempty subset (p, Z) of Z, where p is a profile of individual preferences and Z is a set of outcomes of cardinality l or more. Suppose that satisfies Arrow's choice axiom, independence of infeasible alternatives, and the Pareto criterion. If the preference domain is the family of profiles of classical economic preferences over the space of allocations of public goods, then is dictatorial.I am grateful for some especially helpful comments by Jerry Kelly, John Weymark, and two anonymous referees. In fact, they uncovered so many errors that I must revive the traditional disclaimer: All remaining mistakes are my own responsibility. It is a pleasure to acknowledge the financial support of the National Science Foundation, grants no. SES 9007953 and SES 9209039.     

A power rule for social choice

Recognizing that all social choice takes place in the context of some status quo, the social choice process is modeled as a sequence of challenges to the status quo. In order to mount a successful challenge, the proponents of change must generate sufficient power to overcome the status quo. Power is viewed as an amalgam of economic, political and more general social power — such as the ability to communicate and shape public opinion. Individual power expresses both the ability and the desire to influence outcomes and, as such, varies from individual to individual as well as from social state to social state for each individual.Existence of equilibrium under a power rule is established, and stability of equilibrium is discussed.