ABSTRACT The Structure of Norms and Legal Uncertainty: A Framework for the Functional Analysis of Law as Transformed in Multi-Member Decision Mechanisms Gunnar Nordén 2016 Doctrinal studies of law describe relationships between conditioning legal facts and con- sequences, distinguishing between substantive and procedural norms. The latter consti- tute 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 im- plied 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) behav- ior. 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 devel- oped using formal representation of norms and by ex ante identification of judges (arbi- trators) 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 substan- tive norms. Under ordinary-level uncertainty, they may reach different conclusions under the same substantive norm. In correspondence with standard conceptions of legal deci- sion-making, judges applying law vote directly on outcomes or on substantive norm ele- ments, not abstractly over substantive norms. The commitment notion assumes judges vote independently (non-strategically) as uncertainty is resolved. Both majority and su- per-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 (un- certainty 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. ii 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 prob- lems 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 systematical- ly with decision mechanisms. This sensitivity, exacerbated by epistemic uncertainty, ac- centuates 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 sug- gested 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 dom- inance 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. iii iv The Structure of Norms and Legal Uncertainty: A Framework for the Functional Analysis of Law as Transformed in Multi- Member Decision Mechanisms A Dissertation Presented to the Faculty of the Law School of Yale University In Candidacy for the Degree of Doctor of the Science of Law By Gunnar Nordén Dissertation Committee Supervisor: Richard R.W. Brooks Readers: Ian Ayres and Daniel Markovits June 2016 © 2016 Gunnar Nordén All rights reserved. vi TABLE OF CONTENTS ABSTRACT ........................................................................................................ vii LIST OF FIGURES ............................................................................................... x LIST OF TABLES ............................................................................................... vii LIST OF EXAMPLES ........................................................................................ viii ACKNOWLEDGEMENTS ................................................................................ xiv PART ONE: INTRODUCTION ..................................................................... 15 1 Background ............................................................................................. 15 2 Conceptual framework, approach, and main themes .............................. 25 3 Organization and outline ......................................................................... 32 PART TWO: REPRESENTATION OF NORMS .............................................. 39 1 Basic concepts and notation .................................................................... 39 2 Legal norms: definitions and examples .................................................. 42 3 Rules and standards: local and global definitions ................................... 53 4 Convex combinations of norms (mixed norms)...................................... 60 5 Meta-norms ............................................................................................. 63 PART THREE: TRANSFORMATION OF NORMS IN MULTI- MEMBER DECISION MECHANISMS ......................................................... 69 1 Introduction ............................................................................................. 69 1.1 Legal aggregation methods ........................................................ 70 1.2 Modeling the decision process ................................................... 74 2 Dichotomous environments: basic legal geometries ............................... 76 3 Polychotomous environments and the classical rule .............................. 84 4 Higher-dimensional norms and voting protocols .................................... 88 5 Unitary versus bifurcated trials ............................................................... 94 6 Theoretical norm element determination .............................................. 104 vii 7 Majority mechanisms ............................................................................ 109 PART FOUR: EQUILIBRIUM UNDER TRANSFORMED (PURE) NORMS............................................................................................ 119 1 Equilibrium analysis ............................................................................. 119 2 Introductory example: final-offer arbitration ........................................ 122 3 The model of precaution ....................................................................... 128 4 Equilibrium analysis I: the structure of solutions ................................. 130 4.1 Large panels ............................................................................. 133 4.2 Finite panels ............................................................................. 134 4.3 Comparative statics: panel size ................................................ 142 5 Equilibrium analysis II: uniform distributions .....................................