Strategy-proof Cardinal Decision Schemes

This paper analyses strategy-proof mechanisms or decision schemes which map profiles of cardinal utility functions to lotteries over a finite set of outcomes. We provide a new proof of Hylland’s theorem which shows that the only strategy-proof cardinal decision scheme satisfying a weak unanimity property is the random dictatorship. Our proof technique assumes a framework where individuals can discern utility differences only if the difference is at least some fixed number which we call the grid size. We also prove a limit random dictatorship result which shows that any sequence of strategy-proof and unanimous decision schemes defined on a sequence of decreasing grid sizes approaching zero must converge to a random dictatorship. We are most grateful to an Associate Editor and two referees for very helpful comments on an earlier version of the paper. An erratum to this article can be found at     

Ethnomethodology and sociology: an introduction

Arising as a powerful challenge to programmatic views of sociology that sought to determine stable laws underpinning social order, ethnomethodology set out an alternative programme to reveal social order as a dynamic, contingent ‘ongoing accomplishment’. This programme was neither micro nor macro, but was concerned with different contexts of accountability in which both individuals and institutions are given identity and reproduced. Recognising everyday life as an achievement, collective sense making, and the central importance of talk as a social process, ethnomethodology had an impact on all those arenas of sociology where ordinary interaction is an element. This introduction to the special section discusses the contributions of each of the papers – which cover mundane reasoning, social learning, the early acquisition of social competence, and the application of membership categorization analysis to gender – in relation to the continuing relevance of Garfinkel's legacy to contemporary sociological theory and practice.     

Axiomatic foundations for fairness-motivated preferences

Much work in social choice theory takes individual preferences as uninvestigated inputs into aggregation functions designed to reflect considerations of fairness. Advances in experimental and behavioural economics show that fairness can also be an important motivation in the preferences of individuals themselves. A proper characterisation of how fairness concerns enter such preferences can enrich the informational basis of many social choice exercises. This paper proposes axiomatic foundations for individual fairness-motivated preferences that cover most of the models developed to rationalise observed behaviour in experiments. These models fall into two classes: Outcome-based models, which see preferences as defined only over distributive outcomes, and context-dependent models, which allow rankings over distributive outcomes to change systematically with non-outcome factors. I accommodate outcome-based and context-sensitive fairness concerns by modelling fairness-motivated preferences as a reference-dependent preference structure. I first present a set of axioms and two theorems that generate commonly used outcome-based models as special cases. I then generalise the axiomatic basis to allow for reference-dependence, and derive a simple functional form in which the weight on each person’s payoff depends on a reference vector of how much each person deserves.     

Minimal manipulability: anonymity and unanimity

This paper is concerned with the minimal number of profiles at which a unanimous and anonymous social choice function for three alternatives is manipulable. The lower bound is derived and examples of social choice functions attaining the lower bound are given. It is conjectured that these social choice functions are in fact all minimally manipulable social choice functions. Since some of these social choice functions are Pareto optimal, it follows that the lower bound also holds for Pareto optimal and anonymous social choice functions. Some of the minimally manipulable Pareto optimal and anonymous social choice functions can be interpreted as status quo voting.     

Habitus,social elevation,and the channel of shame‐fear: The decision to expand Guinness advertising

This article explains the relationship between social habitus, social mobility and shame feelings using Elias's theoretical frame of figurational sociology. Much work to date has centred on Bourdieu's theoretical formulations and while there are clear parallels with Elias, significant differences exist. Elias identified how shame functions as a key channel for the transmission of social tensions generated by the structure of social relations into the social habitus of individuals. We explain how apparently rational decision‐making in organisations obscures the emotional dynamics of shame and fear connected with processes of social elevation, habitus change and shifting power relations between social classes. Our empirical case concerns the brewer Arthur Guinness & Sons Ltd and the decision in 1927 to sanction a direct advertising campaign in Britain for the first time.     

Harsanyi's Social Aggregation Theorem and the Weak Pareto Principle

Harsanyi's Social Aggregation Theorem is concerned with the aggregation of individual preferences defined on the set of lotteries generated from a finite set of basic prospects into a social preference. These preferences are assumed to satisfy the expected utility hypothesis and are represented by von Neumann-Morgenstern utility functions. Harsanyi's Theorem says that if Pareto Indifference is satisfied, then the social utility function must be an affine combination of the individual utility functions. This article considers the implications for Harsanyi's Theorem of replacing Pareto Indifference with Weak Pareto.I am grateful to Charles Blackorby, David Donaldson, Philippe Mongin, and an anonymous referee for their comments. The final version of this article was written while I was the Hinkley Visiting Professor at Johns Hopkins University. Research support was provided by the Social Sciences and Humanities Research Council of Canada.     

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.     

Flexibility of choice versus reduction of ambiguity

This paper explores the problem of a social planner willing to improve the welfare of individuals who are unable to compare all available alternatives. The optimal decision trades off the individuals’ desire for flexibility versus their aversion towards ambiguous choice situations. We introduce an axiom system that formalizes this idea. Our main result characterizes the preference maximizing opportunity set. It is a maximal set that consists of mutually comparable alternatives. It also has the property that it maximizes the sum of the distances between its ordered elements for some appropriate pseudometric imposed on the set of possible choices.     

Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities

This paper studies the existence of Pareto optimal, envy-free allocations of a heterogeneous, divisible commodity for a finite number of individuals. We model the commodity as a measurable space and make no convexity assumptions on the preferences of individuals. We show that if the utility function of each individual is uniformly continuous and strictly monotonic with respect to set inclusion, and if the partition matrix range of the utility functions is closed, a Pareto optimal envy-free partition exists. This result follows from the existence of Pareto optimal envy-free allocations in an extended version of the original allocation problem.     

How to reach legitimate decisions when the procedure is controversial

Imagine a group that faces a decision problem but does not agree on which decision procedure is appropriate. In that case, can a decision be reached that respects the procedural concerns of the group? There is a sense in which legitimate decisions are possible even if people disagree on which procedure to use. I propose to decide in favour of an option which maximizes the number of persons whose judged-right procedure happens to entail this decision given the profile. This decision rule is based not only on a profile in the standard sense, but in addition on a profile of judged-right procedures. To justify this decision rule, I present a set of simple axioms leading to it as the only solution.     

Bayesian utilitarianism and probability homogeneity

This paper investigates, within the axiomatic framework of Jeffrey-Bolker decision theory, two kinds of conditions and the relation between them: (1) The Utilitarian condition that social rankings of prospects be representable by an expected utility function that is a weighted sum of the expected utility functions representing individual rankings; and (2) Homogeneity conditions on the probabilities and preferences of individuals. In particular, we show that identity of individuals’ probabilities is necessary and sufficient for the Utilitarian condition to hold and that the homogeneity of individuals’ probabilities can be derived from a Pareto condition on the relation between individual and social rankings, provided that these rankings are separable in a particular sense.This paper has considerably benefited from comments by John Broome, Isaac Levi and an anonymous referee. Special thanks to Philippe Mongin who provided encouragement, help and careful criticism throughout the development of this paper.     

A pedagogical proof of Arrow's Impossibility Theorem

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 13³=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students.  This special case conveys the nature of Arrow's result. It is well known that the restriction to three options is not really limiting (any larger set of alternatives can be broken down into triplets, and any inconsistency within a triplet implies an inconsistency on the larger set). However, the general case of n≥3 individuals can be easily considered in this framework, by building on the proof of the simpler case. I hope that a motivated student, having mastered the simple case of three individuals, will find this extension approachable and rewarding.  This approach can be compared with the traditional simple proofs of Barberà (1980); Blau (1972); Denicolò (1996); Fishburn (1970); Kelly (1988); Mueller (1989); Riker and Ordeshook (1973); Sen (1979, 1986); Suzumura (1988), and Taylor (1995). Received: 5 January 1999/Accepted: 10 December 1999     

On strategy-proof social choice under categorization

I consider social choice problems such that (i) the set of alternatives can be partitioned into categories based on a prominent and objective feature and (ii) agents have strict preferences over the alternatives. Main results are characterizations of the structure of the strategy-proof social choice functions. I prove that each social choice function is strategy-proof if and only if it is decomposable into “small” strategy-proof social choice functions; one of them chooses one category and each of the others chooses one alternative from a category.     

Reliability of an Automated Decision Support System for Behavioral Treatment Planning

Abstract

Automated decision support systems can provide inexperienced individuals with expert advice. But while a computer will always arrive at the same conclusion from a given set of data, human users bring individual variability to decision making. This study, therefore, examined the reliability of the decision support component of an expert system, the Mental Retardation-Expert (MR-E), which assists clinicians who treat problem behaviors of individuals with mental retardation or developmental disabilities. Four clinicians independently used MR-E to obtain consultations on 31 separate cases abstracted from the published literature. They reached a high level of agreement on functional hypotheses regardless of clinical experience, familiarity with MR-E, use of MR-E's basic or advanced modes, or consecutive number of consultations obtained.     

Single-Crossing, Strategic Voting and the Median Choice Rule

This paper studies the strategic foundation of the Representative Voter Theorem (Rothstein in: Pub Choice 72:193–212, 1991), also called the “second version” of the Median Voter Theorem. As a by-product, it also considers the existence of strategy-proof social choice functions over the domain of single-crossing preferences. The main result shows that single-crossing constitutes a domain restriction over the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median rule, which is found to be group strategic-proof over the full set of alternatives and over every nonempty subset. In addition, the paper also examines the relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median rule to prove that the outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism. This mechanism is a two-stage voting procedure in which, first, individuals select a representative among themselves, and then the winner chooses a policy to be implemented by the planner.     

Libertarian collective decision-making: A new framework

A model of collective decision-making is presented which enables us to analyze the allocation of individual rights and liberties. The model broadens the traditional social choice framework. In social choice theory it is usually assumed that individuals have preferences over a set of feasible alternatives and that society reaches a decision on the basis of those preferences only. In the model presented in this paper, decision procedures do not only take information about individual preferences as input, but also information about individual freedom. The specific decision procedures we present and analyze can be characterized as libertarian.This paper was written while I was a visitor at the University of California, Riverside. The visit was made possible by financial support of the Netherlands Organization of Scientific Research (NWO). I am extremely grateful to Prasanta Pattanaik for many stimulating discussions on the subject. For helpful comments I also thank Ad van Deemen, Grahame Lock, Huib Pellikaan and Marcel Wissenburg. Finally, I express my thanks to Wulf Gaertner and two anonymous referees.     

Unlikelihood of Condorcet’s paradox in a large society

We provide intuitive, formal, and computational evidence that in a large society Condorcet’s paradox (the intransitivity of social preference obtained by pairwise vote) can hardly occur. For that purpose, we compare two models of social choice, one based on voting and another one based on summing individual cardinal utilities, expressed either in reals, or integers. We show that in a probabilistic model with a large number of independent individuals both models, almost surely, provide the same decision results. This implies that Condorcet’s and Borda’s methods tend to give the same decisions as the number of voters increases. Therefore, in the model with a large number of voters, the transitivity of the Borda preference is inherent in a majority preference as well. Received: 26 June 1998/Accepted: 16 April 1999     

NICHE THEORY AND SOCIAL MOVEMENTS: A POPULATION ECOLOGY APPROACH

The application of niche theory to current theories of social movements makes it possible to combine some seemingly disparate hypotheses under a more comprehensive framework. Several major issues are addressed, including: (1) the factors leading individuals to engage in social movements; (2) the relationship that social movements have to one another; (3) the effects of particular strategies on the success of movements; and (4) the potential limits to the number of social movements at any particular time. This article also makes some recommendations about the types of data that would be needed to test the propositions set forth.     

Social compromise and social metrics

In the context of constitutional design, a committee of citizens' representatives proposes (social choice) axioms. The outcome should not necessarily be the aggregation rule, or rules, satisfying each of the axioms. Alternative procedures are recommended for aggregating a set of axioms into a single summary axiom. The summary axiom generates a single social decision function when a social metric is applied.     

Aggregation of individuals' preference intensities into social preference intensity

A result of John Harsanyi concerns the aggregation of individuals' preferences into social preferences. The result states that if the individuals in a society and the society as a whole have preference relations that compare probability distributions on a set of outcomes, and the preference relations satisfy expected-utility conditions and Pareto conditions, then a utility function for the social preference relation is a positive affine function of utility functions for the individuals' preference relations. This paper presents an analogous result for preference relations that denote intensity of preference, i.e., preference relations that compare exchanges of outcomes. This approach avoids the difficulties of requiring that the individuals in the society have common beliefs regarding uncertainty. Received: 14 October 1996 / Accepted: 4 September 1997