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.     

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.     

Justifiable group choice

We study the judgment aggregation problem from the perspective of justifying a particular collective decision by a corresponding aggregation on the criteria. In particular, we characterize the logical relations between the decision and the criteria that enable justification of a majority decision through a proposition-wise aggregation rule with no veto power on the criteria. While the well-studied “doctrinal paradox” provides a negative example in which no such justification exists, we show that genuine possibility results emerge if there is a gap between the necessary and the sufficient conditions for the decision. This happens, for instance, if there is only a partial consensus about the appropriate criteria for the decision, if only a subset of these criteria can be elicited, or if the judgment on criteria is based on probabilistic acceptance thresholds.     

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.     

Optimal agenda-setter timing

Abstract .  We analyze the optimal timing problem of an agenda setter who can propose a project that is then voted on by a committee. The payoff consists of a common stochastic component and an idiosyncratic component that differs among committee members. The agenda setter may be biased for or against the project, relative to the median committee member, and chooses when to call the vote. We analyze how the timing decision depends on the political environment and the bias of the agenda setter. We show that both positively and negatively biased agenda setters can implement decisions that differ from those preferred by the median committee member.     

Factoring out the impossibility of logical aggregation

According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow's and arguably enhances its paradoxical value.     

On the possibility of reasonable consistent majoritarian choice: Some positive results

Strictly Majoritarian Social Choice Functions (SMSCFs) are such that the choice on an agenda can be defined with the knowledge of the simple majority relation on the agenda as the sole information. The possibility for SMSCFs to satisfy both the General Pareto condition and choice consistency conditions strong enough to be meaningful has been doubted. Here we exhibit three reasonable SMSCFs that do both. One of them can be interpreted as eliminating from the agenda all alternatives one can suspect of being Pareto dominated by some other. We compare some of their properties with those of the SMSCFs already known in the literature.     

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.     

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.     

Financial expectations and the ‘left-right’ political value scale: Testing for the POUM hypothesis

Using a uniquely defined indicator of political ideology we test whether expectations of future financial well-being have an effect on an individual’s position on the political ‘left-right’ spectrum. We find evidence of a significant “prospect of upward mobility” effect.     

A model of benefit and tax share discrimination by a monopoly bureau

This paper integrates the theory of demand for publicly provided goods in a democracy with the theory of bureaucratic supply in order to develop a model of benefit share and tax share discrimination by a monopoly bureau. The demand side of the political market is based on a utility maximizing model of voter behavior with voters' demands aggregated through a majority voting process. The supply side of the political market is based on a budget maximizing model of bureaucratic behavior. The bureau is assumed to possess monopoly power as a result of either its control over benefit shares or tax shares and, hence, implicit tax prices or its control over budget proposals placed on the agenda. Different degrees of discrimination are examined and in each case the equilibrium of the model yields a total budget for the bureau as well as distributions of benefit shares or tax shares across voters.     

Gaus,Hayek, and the place of civil religion in a free society

In The Order of Public Reason, Gerald Gaus uses Hayekian insights to give a contractarian justification for the specific social rules the rules that comprise the social order of a free people. But in doing so, Gaus inadvertently endorses a kind of skepticism about our ability to justify the institutions that comprise our social order as a whole. The disadvantage of a political theory so pervasively skeptical is that, while contractors can arrive at a series of specific solutions to their social problems, they have no way to assure themselves that their moral nature and their moral practices as a whole are sufficiently sound that the rules they endorse are genuinely morally binding. I argue that this problem can be solved in political practice through the adoption of a civil religion. Civil religions provide narratives and social practices that assure members of free orders that their regimes are good or justified on the whole. In this way, we can introduce the idea of civil religion into contractarian political theory as a social technology for sustaining a free social order.     

From Vienna to Virginia: Exchange,rules, and social cooperation an introduction to the symposium

Serving as an introduction to the essays in this volume, we put forward an intellectual hardcore for a shared research agenda between Austrian and Virginia political economy. This research agenda rests on three pillars: exchange, rules, and social cooperation. Each of these pillars forms the distinctive flavor of Austrian and Virginian political economy with respect to theoretical approach, types and applications of empirics, and even to normative questions. Our essay explores the meaning of these pillars with respect to the broader study of political economy, as well as the intellectual superstructure of each respective school.     

Oil and political survival

Political economy theories on the “natural resource curse” predict that natural resource wealth is a determining factor for the length of time political leaderships remain in office. Whether resource wealth leads to longer or shorter durations in political office depends on the political incentives created by the natural resources, which in turn depend on the types of institutions and natural resource. Exploiting a sample of more than 600 political leadership durations in up to 152 countries, we find that both institutions and resource types matter for the effect that natural resource wealth has on political survival: (i) wealth derived from natural resources affects political survival in intermediate and autocratic, but not in democratic, polities; and (ii) while oil and non-lootable diamonds are associated with positive effects on the duration in political office, minerals are associated with negative duration effects.     

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.     

Environmental (De-) Regulation, Competition, and Policy Rules

This article analyzes some problems regarding our knowledge of environmental policy. Sustainable development as the prospective enlargement of the political agenda has been identified as a long-term challenge for economic policy which could get trapped in a new form of interventionism. The evolutionary market approach that is presented here focuses on development risks of environmental policy that are mostly neglected in standard theory. A transfer of the Hayekian concept of negative rules to the realm of environmental policy is critically discussed. A straight-forward transfer of Hayek's theory stressing the importance of negative rules cannot be recommended, since even the negative rules carry some development risks in the realm of environmental policy. Some preliminary political consequences are drawn which are appropriate to limit the extension of environmental targets in the future.     

Convergence Results for Unanimous Voting

This paper derives a necessary condition for unanimous voting to converge to the perfect information outcome when voters are only imperfectly informed about the alternatives. Under some continuity assumptions, the condition is also sufficient for the existence of a sequence of equilibria that exhibits convergence. The requirement is equivalent to that found by Milgrom [1979, Econometrica47, 679-688] for information aggregation in single-prize auctions. An example illustrates that convergence may be reasonably fast for small committees. However, if voters have common preferences, unanimity is not the optimal voting rule. Unanimity rule makes sense only as a way to ensure minority views are respected. Journal of Economic Literature Classification Numbers: D72, D82, D44.     

On the determinants of local government performance: A two-stage nonparametric approach

This article analyzes the efficiency of local governments in the Comunitat Valenciana (Spain) and their main explanatory variables. The analysis is performed in two stages. Firstly, efficiency is measured via (nonparametric) activity analysis techniques. Specifically, we consider both Data Envelopment Analysis (DEA) and Free Disposable Hull (FDH) techniques. The second stage identifies some critical determinants of efficiency, focusing on both political and fiscal policy variables. In contrast to previous two-stage research studies, our approach performs the latter attempt via nonparametric smoothing techniques, rather than econometric methods such as OLS or Tobit related techniques. Results show that efficiency scores, especially under the nonconvexity assumption (FDH), are higher for large municipalities. Thus, there is empirical evidence to suggest that resources may be better allocated by large municipalities. However, the inefficiency found is not entirely attributable to poor management, as second-stage analysis reveals both fiscal and political variables to be explicably related to municipality performance. Moreover, the explanatory variables’ impact on efficiency is robust to the chosen technique—either convex DEA or nonconvex FDH.     

The Political Economy of Policy Vacuums: The European Commission on Demographic Change

ABSTRACT

Supranational organisations can only confront politico-economic issues that are recognised as important. Typically, issues gain recognition either when they provide an external shock to the system, shaking political actors into action, or when they are framed as important in policy networks concerned with developing the appropriate scientific approach. Ideally political and scientific actors align in creating pressures to recognise the issue as salient and to mobilise organisational responses. Issues differ in their capacity to be driven by both political and scientific pressures, creating crisis management, technocratic, and reform agenda outcomes. Here we explore a further variation, where pressures around an issue are insufficient, creating a policy vacuum. We examine one such policy vacuum in Europe: demographic change. This issue belongs to no particular Directorate-General in the European Commission, but is subject to policy frames from DG EMPL and DG ECFIN. Without sufficient political and scientific pressures, no particular policy position is occupied and advocated despite recognition of the issue’s importance. We discuss the role of policy vacuums and the need for their identification in political economy research.     

科学、价值与判断在环境影响评估架构中之整合

公共政策研拟，尤其是环境影响评估，不仅牵涉技术性科学层面，同时涵盖社会性价值评估与政策性决策判断。旨在探讨如何将科学、价值与判断等因素合理融合于环境影响评估作业过程中，并据此研拟一环境影响评估架构，作为中国台湾地区环保部门开发案审核依据之参考。本文所研拟之环境影响评估架构的理论基础包括社会选择理论、社会判断理论及多属性评估方法。通过社会选择理论分析环境政策制定的机制；通过社会判断理论解释科学与价值如何整合于政策制定及其可行性中；而通过多属性评估方法建立开发案评选的集体决策技术。以山坡地开发为例说明此架构在实践中的应用。