MOVE - URRUTIA ELEJLDE WORKSHOP on JUDGEMENT AGGREGATION
14th, 15th and 16th November 2009, Casa Convalescència (Barcelona)
EXECUTIVE SUMMARY
Tutorial 1. An introduction to the Theory of Judgement Aggregation. Part I Ron Holzman (Technion - Israel Institute of Technology) The first lecture provides the non-expert audience the basic tools for understanding the theory of judgment aggregation. Professors Holzman and Mongin introduce some basic concepts of mathematical logics and judgment aggregation theory such as propositional calculus, the notion of proposition, consistency or entailment. |
Tutorial 2. Aggregation of Non-Binary Judgements. Part II Professor List provides an introductory tutorial of the theory of judgment aggregation. He introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems. |
Tutorial 3. Have we Resolved the Doctrinal Paradox? Professor Mongin investigates whether premiss-based aggregation is compatible with conclusion-based aggregation, assuming that some formulas of the agenda are singled out as premisses, and that Independence (formula-wise aggregation) holds for them, while Unanimity Preservation holds on the whole agenda. He states necessary and sufficient conditions under which this assumption leads to dictatorship (resp. oligarchy), either just on the premisses or on the whole agenda. This presentation was based on joint work with Franz Dietrich. |
Tutorial 4. Aggregation of Abstract Evaluations. In this lecture, Professor Holzman presents the results from two of his papers on the aggregation of binary evaluations (with and without abstentions). That situation fits in a social choice problem where not all the alternatives are feasible. The main purpose of the lecture is to characterize what he calls the impossibility domains, i.e. the domains that under some axioms on the aggregation process lead us to dictatorial mechanisms. For that, Professor Holzman presents two approaches to the problem: one where the alternatives are expressed in vectors of zeros and ones (the abstract approach), and the other where alternatives are presented in a propositional form (the logic approach). He shows that both approaches are equivalent. |
Tutorial 5. Aggregation in Property Spaces. In this lecture, Professor Puppe introduces the property space framework and provides a general characterization of all independent aggregators under monotonicity (the "Intersection Property"). In particular, he discusses important spaces that can be analyzed with this approach, including median spaces and quasi-median Spaces, addressing the possibility of neutral and/or anonymous agregation under monotonicity. He also covered the relation to the classical literature on strategy-proofness with single-peaked preferences. |
Tutorial 6. The impossibility of a Paretian Rational. In this lecture, Professor Nehring presents two models of aggregation: one is a purely judgment-oriented and the other is choice oriented, discussing the conflict between the Pareto criterion and reason baseness. In particular, Professor Nehring considers situations in which a group takes a collective decision by aggregating individual’s judgments on a set of criteria according to some agreed-upon decision functions. Assuming the criteria and the decision to be binary, Professor Nehring demonstrates that, except when the aggregation rule is dictatorial or the decision rule is particularly simple, such reason-based social choice must violate the Pareto principle. In the second part of the paper, the normative implications of this impossibility result are discussed. We argue that the normative case for the Pareto Principle is strong in situations of “shared self-interest”, but weak in situations of “shared responsibility”. |
Tutorial 7. Contributed Papers. In the contributed papers’ session, several complementary approaches were discussed. Amoros presents a model where from a set of contestants there is a set of deserving winners with the possibility that jurors may have biased preferences against some of the deserving winners. Plaza presents a computer science point of view to the problem of judgment aggregation. In particular, he presents models of multi-agent systems, where a group of agents needs to reach an agreement. In his lecture, Grandi analyzes the computational complexity of the problem of judgment aggregation. Finally, Mora presents a preference aggregation’s problem, where the nature of preferences is qualitative and the outcome has a quantitative nature. |
Tutorial 8. Extensions Aggregation of Non-Binary Evaluations Judgement Aggregation in the Light of Model Theory In this session, Professors Dokow and Eckert conclude the workshop with some final remarks on the topic. Professor Dokow extends the projects presented in the workshop by professor Holzman, by considering non-binary evaluations instead of binary ones. Professor Eckert satisfactorily claims that particular tools from model theory may be very useful for enhancing our understanding of judgment aggregation theory. |
