Majority voting on restricted domains

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments sufficient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results support the robustness of majority rule.     

Judgment aggregation: (im)possibility theorems

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore suggest restricting independence to “premises”, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent.     

The premiss-based approach to judgment aggregation

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to dictatorship (resp. oligarchy), either just on the premisses or on the whole agenda. Our analysis is inspired by the doctrinal paradox of legal theory and is arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory.     

Representation and aggregation of preferences under uncertainty

We axiomatize in the Anscombe-Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.     

The possibility of judgment aggregation on agendas with subjunctive implications

The new field of judgment aggregation aims to find collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic.     

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

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.     

Judgment aggregation in search for the truth

We analyze the problem of aggregating judgments over multiple issues from the perspective of whether aggregate judgments manage to efficiently use all voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives where voters' disagreements stem from conflicts of information rather than of interest. Combining the two bodies of literature, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. Assuming that voters share a preference for true collective judgments, we analyze the resulting strategic incentives and determine which voting rules efficiently use all private information. We find that in certain, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of ‘yes’ votes exceeds a particular quota.     

Towards a framework to understand purpose in Futures Studies: The role of Vickers' Appreciative System

There have been comments recently about the efficacy of Futures Studies (and scenario planning) projects, relating to confusion on knowledge aggregation and methodology, which can be summarised in the question: “how to determine the purpose of such projects”. The lack of a purpose framework makes it difficult for ‘clients’ initiating such projects to determine if outcomes meet their original expectations. This paper proposes a framework to help understand the nature, objective and purpose of Futures Studies (and scenario planning) projects, which we will argue helps to overcome these concerns. The proposed framework is based on Vickers' definition of an Appreciative System, highlighting how decision making involves three areas of judgment — reality judgment, value judgment, and instrumental judgment. It will be argued that decision-makers and policymakers call for Futures Studies projects when they become aware of an organizational deficiency in one or more of these areas.Each element, alone or in combination, could form the basis of a purpose definition for a Futures Studies project, and, therefore, needs to be considered to ensure that the project meets client expectations and is experienced as purposeful and rewarding. The paper elaborates on each of the three elements, and then discusses their integrated nature. This is followed by a discussion of the implications of Appreciative System theory for three key players in the decision making process, the organizational leadership, the professionals and the organization at large involved in the practice of Futures Studies (and scenario planning) projects.     

Priorities in the location of multiple public facilities

A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We characterize the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among “interest groups”. We characterize the subclasses of priority rules that respectively satisfy anonymity, avoid the no-show paradox, strategy-proofness and population-monotonicity. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Any such rule can also be viewed as a collection of generalized peak-selection median rules, that are linked across populations, in a way that we describe.     

Aggregation of binary evaluations

We study a general aggregation problem in which a society has to determine its position (yes/no) on each of several issues, based on the positions of the members of the society on those issues. There is a prescribed set of feasible evaluations, i.e., permissible combinations of positions on the issues. This framework for the theory of aggregation was introduced by Wilson and further developed by Rubinstein and Fishburn. Among other things, it admits the modeling of preference aggregation (where the issues are pairwise comparisons and feasibility reflects rationality), and of judgment aggregation (where the issues are propositions and feasibility reflects logical consistency). We characterize those sets of feasible evaluations for which the natural analogue of Arrow's impossibility theorem holds true in this framework.     

A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information

This paper deals with the existence of a nonconcavity in the value of information, as was first explained by Radner and Stiglitz [A nonconcavity in the value of information, in: M. Boyer, R.E. Kihlstrom (Eds.), Bayesian Models in Economic Theory, Elsevier Science Publishers, Amsterdam, 1984, pp. 33-52 (Chapter 3)]. After defining infinitesimal information distance variationIIDV, we find that IIDV=0 is sufficient for a zero marginal value of information at the null. This is a condition only on the information structure and in particular is independent of the decision maker's preferences. This condition is tight: when IIDV>0, there exists a payoff function for which the marginal value of information at the null is positive under general assumptions.     

Introduction to judgment aggregation

This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individuals' judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impossibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium.     

Adverse selection problems without the Spence-Mirrlees condition

This paper studies a class of one-dimensional screening problems where the agent's utility function does not satisfy the Spence-Mirrlees condition (SMC). The strength of the SMC for hidden information problems is to provide a full characterization of implementable contracts using only the local incentive compatibility (IC) constraints. These constraints are equivalent to the monotonicity of the decision variable with respect to the agent's unobservable one-dimensional parameter. When the SMC is violated the local IC constraints are no longer sufficient for implementability and additional (global) IC constraints have to be taken into account. In particular, implementable decisions may not be monotonic and discretely pooled types must have the same marginal utility of the decision (or equivalently, get the same marginal tariff). Moreover, at the optimal decision, the principal must preserve the same trade-off between rent extraction and allocative distortion measured in the agent's marginal rent unit. In a specific setting where non-monotone contracts may be optimal we fully characterize the solution.     

Monetary policy committees and interest rate setting

This paper shows that it is preferable for monetary policy to be conducted by a committee instead of a single policy maker if there is uncertainty about potential output. We examine three decision procedures - an optimal procedure, averaging and voting - and find that the latter is the appropriate way to reach decisions if policy makers are not equally skilled. Finally, we demonstrate that efficient decision procedures reduce the persistence of shocks.     

Is Transparency To No Avail?*

Transparent decision‐making processes are widely regarded as a prerequisite for the working of a representative democracy. It facilitates accountability, and citizens might suspect that decisions, if taken behind closed doors, do not promote their interests. Why else would there be the secrecy? We provide a model of committee decision‐making that explains the public's demand for transparency, and committee members' aversion to it. In line with case study evidence, we show how pressures to become transparent induce committee members to organize pre‐meetings away from the public eye. Transparency does not improve accountability, but it might improve the decision.     

A note on redistributive fairness and economic reform

To understand reasons for possible failures of ‘good’ economic reforms, we consider an institution which is always successful in making the best public decision from the utilitarian perspective. We show it is bound to introduce inequality if costs of a reform are privately known: the losers can not be always compensated. Thus, if equity is a primary concern, then some reforms with positive aggregate net gain might not be undertaken. If the utilitarian welfare is the only guide for making public decisions, implementing a reform might require the ability to ignore the associated social costs of inequality.     

Greater prudence and greater downside risk aversion

Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=−u^?/u^″, is related to downside risk aversion, which is indicated by a positive value for u^?. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.     

Selectivity in hierarchical social systems

We consider a selection process and a hierarchical institution in a dynamic model as in Harrington (1998) [4], where agents are “climbing the pyramid” in a rank-order contest based on the “up or out” policy. Agents are matched in pairs to compete, and each pair faces a particular environment. They are ranked according to the quality of their performances in this particular environment, and a fraction of the highest ranked agents are promoted. The size of this fraction characterizes the selectivity of the process, and we distinguish between local and global selectivity. We study the role of the degree of selectivity in the dynamic process where types of agent differ in their expected performances. Surprisingly, we find that an increase in the selectivity of the process can be detrimental to the agents with the highest expected performances and can increase the survivability of the lesser performing. However, if the selectivity decreases, the only survivor is the agent with the highest expected performance.     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

The art of long-term thinking: A bridge between sustainability science and politics

Policy makers are dependent upon scientific knowledge. However, scientific results cannot be applied straightforwardly in practical decision making. We deploy Kant's term “power of judgment” – the human capacity to apply general insights to specific, contingent situations – to show that this problem is systematic rather than coincidental: decision making requires the power of judgment to make use of scientific knowledge. Power of judgment, in turns, can be supported by heuristics. Against this background, we focus on sustainability politics and outline a heuristic for framing and analyzing sustainability problems. Because time is a key factor in relation to sustainability we distinguish three distinct concepts of time and argue that the economic concepts of “stocks” and “institutions” can be used to foster power of judgment with respect to these time concepts. Based on these concepts, the heuristic serves to bridge the gap between scientific knowledge and practical decision making in sustainability politics.