Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

Consensus theories: an oriented survey

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2010.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2010.57 - ISSN : 1955-611XThis article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Cet article présente une vue d'ensemble de sept directions de recherche en théorie du consensus : résultats arrowiens, règles d'agrégation définies au moyen de fédérations, règles définies au moyen de distances, solutions de tournoi, domaines restreints, théories abstraites du consensus, questions de complexité et d'algorithmique. Ce panorama est orienté dans la mesure où il présente principalement – mais non exclusivement – les travaux les plus significatifs obtenus – quelquefois avec d'autres chercheurs – par une équipe de chercheurs français qui sont – ou ont été – membres pléniers ou associés du Centre d'Analyse et de Mathématique Sociale (CAMS)

The Structure of Norms and Legal Uncertainty: A Framework for the Functional Analysis of Law as Transformed in Multi-Member Decision Mechanisms

Doctrinal studies of law describe relationships between conditioning legal facts and con-sequences, distinguishing between substantive and procedural norms. The latter constitute decision mechanisms that maintain the legal system’s norms. These mechanisms generate binding decisions—ordered pairs of facts and consequences—that may obtain the status of res judicata and become part of the norm system in the extensive sense. Functional analyses of law undertake to study agent equilibrium behavior under given norms, perceived as incentive structures. Characteristically, norms that are maintained through adjudication (or arbitration) are not complete or unambiguous: In the ex ante sense, consequences are not uniquely implied by relevant conditioning facts. This indeterminacy has profound implications: first, in multi-member decision mechanisms norm structures are systematically transformed; second, these transformed norms or incentive structures guide agent (equilibrium) behavior. These observations challenge the approach that currently prevails in legal theory, namely of considering substantive norms as abstract entities independent of procedural mechanisms. They also suggest opportunities for widening the scope of functional or repercussion analyses of law. This dissertation develops an analytical framework that seeks to enable the study of norm transformation in multi-member judicial decision mechanisms. The framework’s relevance is demonstrated through numerous examples showing how equilibrium out-comes vary with mechanisms shaping the incentive structures. The framework is developed using formal representation of norms and by ex ante identification of judges (arbitrators) and norms. These representations combine functional relations with basic notions from probability theory that are simple enough to be operative in equilibrium analyses, and, at the same time, rich enough to embody detailed aspects of procedural law. The framework facilitates: (i) distinction between “meta-norms” (the doctrine of sources and judicial method) and “ordinary norms” (doctrine in the customary sense); (ii) depiction of (possible) indeterminacy at both levels; (iii) modeling of multi-member decision-making; and (iv) simultaneous consideration of epistemic uncertainty. The identification of norms and judges envisions judging as commitment, in contrast to a preference-based, rational choice account. The approach combines insights from logical aggregation, case-space, and evolutionary theories. Under meta-level uncertainty, judges may base decisions on different substantive norms. Under ordinary-level uncertainty, they may reach different conclusions under the same substantive norm. In correspondence with standard conceptions of legal decision-making, judges applying law vote directly on outcomes or on substantive norm elements, not abstractly over substantive norms. The commitment notion assumes judges vote independently (non-strategically) as uncertainty is resolved. Both majority and super-majority aggregation rules are studied (the latter require default state specifications). Implications of sequential decision-making (bifurcation) and separation of (collective) decisions on law and facts are also analyzed. The framework is applied to a detailed analysis of the model of precaution, which has a prevalent and unifying role in many areas of law. Equilibrium precautionary investment is derived under uncertain negligence standards, and under mixed norms (uncertainty between strict liability and negligence). Continuous comparative statics reflects the parametric representation of uncertainty on both the meta and ordinary level. Discrete comparative statics reflects decision mechanism size. A condensed analysis of final-offer arbitration demonstrates that the framework is applicable to strategic environments. The norm representation enables one to distinguish between primary norms ex-pressing obligations and power-conferring secondary norms, which express discretion or options. This distinction is reflected in suggested law-in-force notions, with discretion motivating a forward-looking, means-end approach (in fact, partly due to logical problems arising under aggregation). Examples used to illustrate the benefits from detailed attention to norms structures include entitlement-protection in exchange economies and legal commitment mechanisms in strategic environments. Under indeterminacy, norm structures and induced equilibria vary systematically with decision mechanisms. This sensitivity, exacerbated by epistemic uncertainty, accentuates the question of evaluative criteria as discussed in legal and political philosophy. In reference to observed authority structures, the majority outcome in large panels is suggested as a benchmark, making possible a study of the link between (finite, real-world) mechanism choice and Type I and II error generation. Some analytical results may be of independent interest. Judicial panels trans-form marginal dimensions of incentive structures. This is important when conditioning legal fact sets are choice or strategy spaces for optimizing agents (level transformations correspond to Condorcet-type theorems). Second-order stochastic dominance is used to describe panel size effects on a domain of substantive norms. First-order stochastic dominance is used to compare unitary and bifurcated trials. Due to analytical challenges, some results are based on asymptotic theory. The equilibrium analyses are supported by simulations

The Routledge Handbook of Philosophy of Economics

The most fundamental questions of economics are often philosophical in nature, and philosophers have, since the very beginning of Western philosophy, asked many questions that current observers would identify as economic. The Routledge Handbook of Philosophy of Economics is an outstanding reference source for the key topics, problems, and debates at the intersection of philosophical and economic inquiry. It captures this field of countless exciting interconnections, affinities, and opportunities for cross-fertilization. Comprising 35 chapters by a diverse team of contributors from all over the globe, the Handbook is divided into eight sections: I. Rationality II. Cooperation and Interaction III. Methodology IV. Values V. Causality and Explanation VI. Experimentation and Simulation VII. Evidence VIII. Policy The volume is essential reading for students and researchers in economics and philosophy who are interested in exploring the interconnections between the two disciplines. It is also a valuable resource for those in related fields like political science, sociology, and the humanities.</p