Clemens Puppe

The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces

Abstract We define a general notion of single-peaked preferences based on abstract betweenness relations. Special cases are the classical example of single-peaked preferences on a line, the separable preferences on the hypercube, the “multi-dimensionally single-peaked” preferences on the product of lines, but also the unrestricted preference domain. Generalizing and unifying the existing literature, we show that a social choice function is strategy-proof on a sufficiently rich domain of generalized single-peaked preferences if and only if it takes the form of voting by issues (“voting by committees”) satisfying a simple condition called the “Intersection Property.” Based on the Intersection Property, we show that the class of preference domains associated with “median spaces” gives rise to the strongest possibility results; in particular, we show that the existence of strategy-proof social choice rules that are non-dictatorial and neutral requires an underlying median space. A space is a median space if, for every triple of elements, there is a fourth element that is between each pair of the triple; numerous examples are given (some well-known, some novel), and the structure of median spaces and the associated preference domains is analysed.

DO WAGE CUTS DAMAGE WORK MORALE? EVIDENCE FROM A NATURAL FIELD EXPERIMENT

Employment contracts are often incomplete, leaving many responsibilities subject to workers’ discretion. High work morale is therefore essential for sustaining voluntary cooperation and high productivity in firms. We conducted a field experiment to test whether workers reciprocate wage cuts and raises with low or high work productivity. Wage cuts had a detrimental and persistent impact on productivity, reducing average output by more than 20 percent. An equivalent wage increase, however, did not result in any productivity gains. The results from an additional control experiment with high monetary performance incentives demonstrate that workers could still produce substantially more output, leaving enough room for positive reactions. Altogether, these results provide evidence consistent with a model of reciprocity, as opposed to inequality aversion.

Freedom of choice and rational decisions

The paper formalizes a notion of preference-based freedom and examines to which extent such a notion is consistent with otherwise standard conditions of rational decision making. The central result is as follows. Suppose that a preference-based ranking of opportunity sets satisfies a very mild condition of “preference for freedom of choice”. Then, either the ranking is degenerate in being discontinuous, or the underlying preference relation among the basic alternatives is incomplete. Hence, in any case preference-based rankings of freedom will violate at least some of the basic assumptions of traditional choice modelling. This conclusion is enhanced if the conditions on preference-based freedom are slightly strengthened.

Putting Reciprocity to Work - Positive Versus Negative Responses in the Field

We study the role of reciprocity in a labor market field experiment. In a recent paper, Gneezy and List (2006) investigate the impact of gift exchange in this context and find that it has only a transient effect on long run outcomes. Extending their work to examine both positive and negative reciprocity, we find consonant evidence in the positive reciprocity condition: the gift does not work well in the long run (if at all). Yet, in the negative reciprocity treatment we observe much stronger effects: a wage reduction has a significant and lasting negative impact on efforts. Together, these results highlight the asymmetry of positive and negative reciprocity that exists in the field, and provide an indication of the relative importance of each in the long run.

Consistent judgement aggregation: the truth-functional case

Generalizing the celebrated “discursive dilemma”, we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions (the “conclusions”) and on a set of “premises” by which the conclusions are truth-functionally determined. We show that for conclusion- and premise-based aggregation rules to be mutually consistent, the aggregation must always be “oligarchic”, that is: unanimous within a subset of agents, and typically even be dictatorial. We characterize exactly when consistent non-dictatorial (or anonymous) aggregation rules exist, allowing for arbitrary conclusions and arbitrary interdependencies among premises.

Distorted probabilities and choice under risk

1 Axiomatic Utility Theory under Risk.- 1.1 Historical Overview.- 1.2 The Axiomatic Basis of Expected Utility Theory.- 1.3 The Empirical Evidence against the Independence Axiom.- 1.4 Non-Linear Utility Theory under Risk.- 1.4.1 Weighted Linear Utility Theory.- 1.4.2 Theories with the Betweenness Property.- 1.4.3 Anticipated Utility Theory.- 1.4.4 The Dual Theory.- 1.4.5 The General Rank-Dependent Utility Model.- 1.4.6 Implicit Rank-Linear Utility Theory.- 2 A Rank-Dependent Utility Model with Prize-Dependent Distortion of Probabilities.- 2.1 Rank-Dependent Utility Theory Reconsidered.- 2.1.1 The Generalized Utility Function.- 2.1.2 Absolute Continuity.- 2.1.3 The Set of Elementary Lotteries.- 2.2 Homogeneity on Elementary Lotteries.- 2.2.1 The Common Ratio Effect.- 2.2.2 The Allais Paradox.- 2.3 Further Evidence for Prize-Dependent Distortions of Probabilities.- 2.4 A Characterization Theorem.- 2.5 Rank-Dependent Utility Theory and Relative Utility.- 2.6 A Generalized Model.- 3 Risk Aversion.- 3.1 Risk Aversion in the General Rank-Dependent Utility Model.- 3.2 Risk Aversion and Homogeneity.- 3.3 Decreasing Risk Aversion.- 3.4 The Friedman-Savage Hypothesis.- Conclusion.- References.

Efficient and strategy-proof voting rules: A characterization

Abstract The paper provides a characterization of all efficient and strategy-proof voting mechanisms on a large class of preference domains, the class of all generalized single-peaked domains. It is shown that a strategy-proof voting mechanism on such a domain is efficient if and only if it satisfies a weak neutrality condition and is either almost dictatorial, or defined on a median space of dimension less than or equal to two. In more than two dimensions, weakly neutral voting mechanisms are still “locally” efficient.

Decisions under risk and uncertainty: A survey of recent developments

SummaryThis paper reviews recently proposed axiomatic models of choice under uncertainty and risk. The presentation focuses on the various models of transitive preferences which abandon the expected utility hypothesis by weakening the strong separability assumption known as the sure thing principle in the case of uncertainty and as the independence axiom in the case of risk. Special emphasis is on the remarkable similarities held in common by both the approaches to decisions under uncertainty and under risk.

The Condorcet set: Majority voting over interconnected propositions

Judgement aggregation is a model of social choice in which the space of social alternatives is the set of consistent evaluations (‘views’) on a family of logically interconnected propositions, or yes/no issues. However, simply complying with the majority opinion in each issue often yields a logically inconsistent collective view. Thus, we consider the Condorcet set: the set of logically consistent views which agree with the majority on a maximal subset of issues. The elements of this set turn out to be exactly those that can be obtained through sequential majority voting, according to which issues are sequentially decided by simple majority unless earlier choices logically force the opposite decision. We investigate the size and structure of the Condorcet set for several important classes of judgement aggregation problems. While the Condorcet set verifies a version of McKelveys (1979) celebrated ‘chaos theorem’ in a number of contexts, in others it is shown to be very regular and well-behaved.

Diversity and dissimilarity in lines and hierarchies

Abstract Within the multi-attribute framework of Nehring and Puppe [Econometrica, 70 (2002) 1155], hierarchies and lines represent the simplest and most fundamental models of diversity. In both cases, the diversity of any set can be recursively determined from the pairwise dissimilarities between its elements. The present paper characterizes the restrictions on the dissimilarity metric entailed by the two models. In the hierarchical case, this generalizes a classical result on the representation of ultrametric distance functions.