The categorical approach to social choice theory

A number of different problems in social choice theory are given a common treatment in the framework of category theory. A social choice function is a map μ from a set Hom(A, PX) of profiles - in applications functions from a set A of agents to the set PX of linear orders on a set X of alternatives - to a set GPX the nature of which depends on the application. The main theorem established is applied to social welfare functions and strategy-proof voting schemes.     

Clusterwise aggregation of relations

In this paper we handle the general problem of finding q(> 1) central relations on a set of objects which best fit the information contained in a finite number of given relations on that set. The proposed CAR (clusterwise aggregation of relations) algorithm allows one to consider the well-known situation of determining a single central relation as a special case (q = 1) and takes into account the fact that the representation of appropriately selected subsets of relations by different central relations can provide additional insights into whether different clusters or segments of relations exist in the given set of relations. Two examples demonstrate the usefulness of the suggested approach.     

On non-binary social choice

In a recent paper Grether and Plott (1982) have extended Arrow's General Possibility Theorem to the case where choice over small (in particular ‘two-element’) sets may not be possible. This obviously raises the question whether the counterparts of other existing impossibility results will go through in the same framework. This note settles the question for the counterpart of the well-known impossibility theorem of Gibbard. By weakening the collective rationality condition of Arrow we show that all the social choice functions will be ‘oligarchical’ in Gibbard's sense, in the Grether and Plott (1982) framework.     

Social choice theory without Pareto: The pivotal voter approach

This paper extends the pivotal voter approach pioneered by Barberá [Barberá, S., 1980. Pivotal voters: A new proof of Arrow’s Theorem. Economics Letters 6, 13–6; Barberá, S., 1983. Strategy-proofness and pivotal voters: A direct proof of the Gibbard-Satterthwaite Theorem. International Economic Review 24, 413–7] to all social welfare functions satisfying independence of irrelevant alternatives. Arrow’s Theorem, Wilson’s Theorem, and the Muller–Satterthwaite Theorem are all immediate corollaries of the main result. It is further shown that a vanishingly small fraction of pairs of alternatives can be affected in the group preference ordering by multiple individuals, which generalizes each of the above theorems.     

Constitutional implementation of social choice correspondences

A game form constitutionally implements a social choice correspondence if it implements it in Nash equilibrium and, moreover, the associated effectivity functions coincide. This paper presents necessary and sufficient conditions for a unanimous social choice correspondence to be constitutionally implementable, and sufficient and almost necessary conditions for an arbitrary (but surjective) social choice correspondence to be constitutionally implementable. It is shown that the results apply to interesting classes of scoring and veto social choice correspondences.     

Social choice for bliss-point problems

This paper's concern is the axiomatic determination of social choice correspondences Ψ for a class of n-person problems that are characterized by some — generally — non-feasible bliss-point u(V)(?V∈τ . Meeting appropriate assumptions of ‘planner's rationality’ it is shown that Ψ is necessarily norm-induced, i.e. one can find some norm |·| in Rⁿ s.t. Ψ(V) = {u?V|6u-u(V)6=min{6v-u(V)6|v,V}}. The mathematical problem of recovering. from Ψ is one of integration which has its well-known parallel in the theory of revealed preference.     

Restricted domains,arrow-social welfare functions and noncorruptible and non-manipulable social choice correspondences: The case of private alternatives

An n-person social choice problem is considered in which the alternatives are n dimensional vectors, with the ith component of such a vector being the part of the alternatives affecting individual i alone. Assuming that individuals are selfish (individual i must be indifferent between any two alternatives with the same components), that they may be indifferent among alternatives and that each individual may choose his preferences out of a different set of permissible preferences, we prove that any set of restricted domains of preferences admits an n person non-dictatorial Arrow-type social welfare function if and only if it admits a two-person Arrow-type social welfare function: we characterize all the sets of restricted domains of preferences which admit two-person Arrow-type social welfare functions (and therefore also admit n-person Arrow-type social welfare functions) and then we prove that we also characterized all the sets of restricted domains of preferences which admit nondictatorial, nonmanipulable, noncorruptible and rational social choice correspondences.     

Modelling a social dilemma of mode choice based on commuters’ expectations and social learning

This study attempts to apply an agent-based approach to modelling a social dilemma of travel mode choice considering psychological and sociological aspects. A traveller is modelled to have expectations, which shows the traveller’s beliefs about the influence of other group members on his action, as decision-making rules. Social interaction using a group-based interaction is hypothesized to be important. We apply an imitation game based on social learning mechanisms to the model. Two kinds of mechanism are used: payoff-biased and conformist transmission. The model reveals the conditions that make cooperation as a possible outcome are optimistic bandwagon expectations, group-based interactions, and strong conformist transmissions.     

Multi-utilitarianism in two-agent quasilinear social choice

We introduce a new class of rules for resolving quasilinear social choice problems. These rules extend those of Green [9]. We call such rules multi-utilitarian rules. Each multi-utilitarian rule is associated with a probability measure over the set of weighted utilitarian rules, and is derived as the expectation of this probability. These rules are characterized by the axioms efficiency, translation invariance, transfer monotonicity, continuity, and additivity. By adding recursive invariance, we obtain a class of asymmetric rules generalizing those Green characterizes. A multi-utilitarian rule satisfying strict monotonicity has an associated probability measure with full support.I would like to thank Youngsub Chun, Federico Echenique, Jerry Green, Biung-Ghi Ju, William Thomson, and Walter Trockel for comments and discussions. Two anonymous referees also provided comments that proved very useful. All errors are my own.     

Optimal payoff under the generalized dual theory of choice

We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari’s dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The optimal portfolio yields an in-the-money payoff when the market is good and zero payoff otherwise. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff.     

The value of cognitive foundations for dynamic social theory

It is possible to develop models of social behavior that are predicated on detailed mechanical models of cognition. Cognitively based social models are potentially unified theoretical frameworks that can be used to explain a wide variety of social phenomena. Moreover, if a knowledge representation scheme and a knowledge acquisition scheme are specified in the underlying cognitive model then it is possible to produce a dynamic social model. The resulting social model can thus be used to predict and explain not only conditions for specific behaviors but changes in those behaviors over time.

Constructuralism is a theory of social behavior that rests on a cognitive model. The cognitive model specified has a knowledge representation scheme, knowledge acquisition procedures, and control procedures for shifting cognitive attention. The resulting social model is a dynamic model that can be used to explain both conditions for the occurrence of a behavior and social and individual changes that accrue do to a series of behaviors. The explanatory breadth of the model is illustrated by looking at predictions about a variety of social phenomena including: development of shared knowledge, identical behavior by members of the society, foreign language acquisition, clique formation, civil disobedience, and diffusion of innovative information.     

Equity,efficiency and rights in social choice

The impossibility of a Paretian liberal presented by Sen shows the incompatibility of the Pareto principle with a mild claim of libertarian rights when they are required of the collective choice rule with unrestricted domain. In view of the profound implications of this paradox, it is no wonder that there are many serious attempts in the literature to seek for a general resolution thereof. In this paper, we try to explore an avenue which has been left relatively less cultivated in the attempts to try to find a way out of this paradox, the essential idea thereof being to restrict the ‘legitimate’ exercise of the liberatarian rights by the claims of justice or equity. It will be shown that the gist of the successful resolution of the Pareto libertarian paradox along this line lies in the impartiality of the principle of justice held by the individuals and the prevalence of the sympathetic acceptance of each other's subjective preferences.     

Dynamic consumption and portfolio choice under prospect theory

This paper explicitly derives the optimal dynamic consumption and portfolio choice of an individual with prospect theory preferences. The individual is loss averse, endogenously updates his reference level over time, and distorts probabilities. We show that the optimal consumption strategy is rather insensitive to economic shocks. In particular, in case the individual sufficiently overweights unlikely unfavorable events, our model generates an endogenous floor on consumption. As a result, an individual with prospect theory preferences typically implements a (very) conservative portfolio strategy. We discuss implications of our results for the design of investment-linked annuity products.     

Multivalued social choice functions and strategic manipulation with counterthreats

In this paper, we examine the manipulability properties of social decision rules which select a non-empty subset of the set of alternatives. Assuming that if an individual prefers x to y, then he prefers the outcome set {x, y} to {y}, and also {x} to {x, y}, we show that a wide class of scf's which allow ties even in pairwise choice violates one of the weakest notions of strategyproofness — a single individual can profitably misrepresent his preferences, even when he takes into account the possibility of countercoalitions. This class of scf's also violates exact consistency — no equilibrium situation gives the same outcome set as the ‘true profile’.     

Research in decision theory: A personal perspective

This essay offers a personal view of developments in two main areas of decision theory — decision making under risk and uncertainty, and social choice theory — with emphasis on the past half century and on likely future directions. Remarks on helpful research practices are also included.     

Symmetric social choices and collective rationality

A social choice function C defined on the m-element subsets of a set X for n voters assigns a non-empty subset C(A,R) of A to each pair (A,R) in which ¦A¦ = m,A X, and R is an n-tuple of voter preference orders on X. When n > 2, 3 m < ¦X¦, and C satisfies natural conditions of independence, symmetry among voters and alternatives, and collective rationality, it is proved that C is completely indecisive in the sense that C(A,R) = A for all (A,R). This non-binary result complements a binary (m = 2) result proved by Hanson. It suggests that there is a fundamental incompatibility between collective rationality and conditions designed to assure equitable treatment of voters and of alternatives.     

A comparison between two distinct continuous models in projective cluster theory: The median and the tight-span construction

It is possible to consider two variants of cluster theory: Inaffine cluster theory, one considers collections ofsubsets of a given setX of objects or states, whereas inprojective cluster theory, one considers collections ofsplits (orbipartitions) of that set. In both contexts, it can be desirable to produce acontinuous model, that is, a spaceT encompassing the given setX which represents in a well-specified and more or less parsimonious way all possibleintermediate objects ortransition states compatible with certain restrictions derived from the given collection of subsets or splits. We investigate an interesting and intriguing relationship between two such constructions that appear in the context of projective cluster theory: TheBuneman construction and thetight-span (or justT)construction.