An Introductory Course to Judgment Aggregation

Reaching some form of consensus is often necessary for autonomous agents that want to coordinate their actions or otherwise engage in joint activities. One way to reach a consensus is by aggregating individual information, such as decisions, beliefs, preferences and constraints. Judgment aggregation is a social choice method, which generalises voting, that studies the aggregation of individual judgments regarding the truth-value of logically related propositions. As such, judgment aggregation is applicable for consensus reaching problems in multi agent systems. As other social choice theory, judgment aggregation research is abundant with impossibility results. However, the aim of this tutorial is to give an introduction to the methods of judgment aggregation, not the impossibility results. In particular, the tutorial will introduce the basic frameworks that model judgment aggregation problems and give an overview of the judgment aggregation functions so far developed as well as their social theoretic and computational complexity properties. The focus of the tutorial are consensus reaching problems in multi agent systems that can be modelled as judgment aggregation problems. The desirable properties of a judgment aggregation method applied to these problems are not necessarily the same as properties desirable in legal or political contexts, which is considered to be the native domain of judgment aggregation. After this tutorial the participants are expected to be able to read and understand judgment aggregation literature and have a grasp on the state-of-the-art and open questions in judgment aggregation research of interest to multi agent systems.

[1]  Gabriella Pigozzi,et al.  Aggregation in multiagent systems and the problem of truth-tracking , 2007, AAMAS '07.

[2]  F. Dietrich,et al.  Judgment Aggregation By Quota Rules , 2007 .

[3]  Marcus Pivato,et al.  Majority Rule in the Absence of a Majority , 2013, J. Econ. Theory.

[4]  C. List,et al.  Aggregating Sets of Judgments: An Impossibility Result , 2002, Economics and Philosophy.

[5]  J. Nash,et al.  A Context-Sensitive Voting Protocol Paradigm for Multimember Courts , 2003 .

[6]  Ron Holzman,et al.  Aggregation of binary evaluations with abstentions , 2010, J. Econ. Theory.

[7]  Iyad Rahwan,et al.  Interval Methods for Judgment Aggregation in Argumentation , 2014, KR.

[8]  Christian List,et al.  Majority voting on restricted domains , 2010, J. Econ. Theory.

[9]  Peter C. Fishburn,et al.  Aggregation of equivalence relations , 1986 .

[10]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[11]  Marija Slavkovik.  Not all Judgment Aggregation Should be Neutral , 2014, ECSI.

[12]  Marc Pauly,et al.  Logical Constraints on Judgement Aggregation , 2006, J. Philos. Log..

[13]  C. List,et al.  Judgment aggregation: A survey , 2009 .

[14]  Leon van der Torre,et al.  Selecting judgment aggregation rules for NAO robots: an experimental approach , 2012, AAMAS.

[15]  Gabriella Pigozzi,et al.  Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation , 2006, Synthese.

[16]  Philippe Mongin,et al.  Factoring out the impossibility of logical aggregation , 2008, J. Econ. Theory.

[17]  Christian List,et al.  A possibility theorem on aggregation over multiple interconnected propositions , 2003, Math. Soc. Sci..

[18]  Ulrich Endriss,et al.  Group Manipulation in Judgment Aggregation , 2016, AAMAS.

[19]  Luc Bovens,et al.  Democratic Answers to Complex Questions – An Epistemic Perspective , 2006, Synthese.

[20]  Franz Dietrich,et al.  A generalised model of judgment aggregation , 2007, Soc. Choice Welf..

[21]  Christian List,et al.  Arrow’s theorem in judgment aggregation , 2005, Soc. Choice Welf..

[22]  Christian List,et al.  Judgment aggregation without full rationality , 2008, Soc. Choice Welf..

[23]  Ulrich Endriss,et al.  Collective Annotation of Linguistic Resources: Basic Principles and a Formal Model , 2013, ACL.

[24]  Guido Boella,et al.  Group Intention = Social Choice + Commitment , 2010, MALLOW.

[25]  James G. March,et al.  How Decisions Happen in Organizations , 1991, Hum. Comput. Interact..

[26]  Sébastien Konieczny,et al.  Merging Information Under Constraints: A Logical Framework , 2002, J. Log. Comput..

[27]  Richard Booth.  Judgment Aggregation in Abstract Dialectical Frameworks , 2015, Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation.

[28]  Gabriella Pigozzi,et al.  Judgment aggregation rules based on minimization , 2011, TARK XIII.

[29]  Alasdair Urquhart,et al.  Basic Many-Valued Logic , 2001 .

[30]  Robert B. Wilson.  On the theory of aggregation , 1975 .

[31]  Marija Slavkovik,et al.  Judgment Aggregation Rules and Voting Rules , 2013, ADT.

[32]  Lawrence G. Sager,et al.  The One and the Many: Adjudication in Collegial Courts , 1993 .

[33]  Ulrich Endriss,et al.  Lifting integrity constraints in binary aggregation , 2013, Artif. Intell..

[34]  Gabriella Pigozzi,et al.  A partial taxonomy of judgment aggregation rules and their properties , 2015, Social Choice and Welfare.

[35]  Ron Holzman,et al.  Aggregation of binary evaluations , 2010, J. Econ. Theory.

[36]  Ulrich Endriss,et al.  Binary Aggregation by Selection of the Most Representative Voters , 2014, AAAI.

[37]  Christian List,et al.  Propositionwise judgment aggregation: the general case , 2013, Soc. Choice Welf..

[38]  Conal Duddy,et al.  A measure of distance between judgment sets , 2012, Soc. Choice Welf..

[39]  Marcus Pivato,et al.  The Condorcet set: Majority voting over interconnected propositions , 2014, J. Econ. Theory.

[40]  Wojciech Jamroga,et al.  Distance-based rules for weighted judgment aggregation , 2012, AAMAS.

[41]  Daniel N. Osherson,et al.  Methods for distance-based judgment aggregation , 2009, Soc. Choice Welf..

[42]  Ulrich Endriss,et al.  Judgment Aggregation under Issue Dependencies , 2016, AAAI.

[43]  Ulrich Endriss,et al.  Complexity of Judgment Aggregation , 2012, J. Artif. Intell. Res..

[44]  Ulrich Endriss,et al.  Succinctness of Languages for Judgment Aggregation , 2016, KR.

[45]  Christian List,et al.  A liberal paradox for judgment aggregation , 2008, Soc. Choice Welf..

[46]  Stephan Hartmann,et al.  Judgment aggregation and the problem of tracking the truth , 2011, Synthese.

[47]  Wojciech Jamroga,et al.  A Deliberation Procedure for Judgment Aggregation Problems , 2016, ArXiv.

[48]  P. Fishburn,et al.  Algebraic aggregation theory , 1986 .

[49]  Ulrich Endriss,et al.  Collective Rationality in Graph Aggregation , 2014, ECAI.

[50]  Gabriella Pigozzi,et al.  Judgment aggregation and the problem of truth-tracking , 2007, TARK '07.

[51]  Gabriella Pigozzi,et al.  A Complete Conclusion-Based Procedure for Judgment Aggregation , 2009, ADT.

[52]  Noga Alon,et al.  Bundling Attacks in Judgment Aggregation , 2013, AAAI.

[53]  Franz Dietrich.  Scoring rules for judgment aggregation , 2014, Soc. Choice Welf..

[54]  Wojciech Jamroga,et al.  Distance-based Judgment Aggregation of Three-valued Judgments with Weights , 2011 .

[55]  Gabriella Pigozzi,et al.  Judgment Aggregation: A Primer , 2014, Judgment Aggregation.

[56]  Iyad Rahwan,et al.  Collective argument evaluation as judgement aggregation , 2010, AAMAS.

[57]  Philippe Mongin,et al.  The premiss-based approach to judgment aggregation , 2010, J. Econ. Theory.

[58]  Yan Zhang,et al.  Knowledge forgetting: Properties and applications , 2009, Artif. Intell..

[59]  Gabriella Pigozzi,et al.  On judgment aggregation in abstract argumentation , 2009, Autonomous Agents and Multi-Agent Systems.

[60]  Piotr Faliszewski,et al.  Distance rationalization of voting rules , 2015, Soc. Choice Welf..

[61]  Emil L. Post.  Introduction to a General Theory of Elementary Propositions , 1921 .

[62]  Sébastien Konieczny,et al.  Logic Based Merging , 2011, J. Philos. Log..

[63]  Umberto Grandi,et al.  Combinatorial Aggregation , 2011, IJCAI.

[64]  Ulrich Endriss,et al.  Complexity of judgment aggregation: safety of the agenda , 2010, AAMAS.

[65]  Marija Slavkovik,et al.  Measuring Dissimilarity between Judgment Sets , 2014, JELIA.

[66]  Marija Slavkovik,et al.  How Hard is it to Compute Majority-Preserving Judgment Aggregation Rules? , 2014, ECAI.

[67]  Piotr Faliszewski,et al.  Properties of multiwinner voting rules , 2014, Social Choice and Welfare.

[68]  Ulrich Endriss,et al.  Complexity of the Winner Determination Problem in Judgment Aggregation: Kemeny, Slater, Tideman, Young , 2015, AAMAS.

[69]  Hitoshi Matsushima,et al.  Handbook of Social Choice and Welfare, Volume 1 (Book) , 2004 .

[70]  Franz Dietrich,et al.  Judgment aggregation and agenda manipulation , 2016, Games Econ. Behav..

[71]  Sébastien Konieczny,et al.  Counting votes for aggregating judgments , 2014, AAMAS.

[72]  Guido Boella,et al.  Recognition-primed group decisions via judgement aggregation , 2012, Synthese.

[73]  Sébastien Konieczny,et al.  Belief Merging versus Judgment Aggregation , 2015, AAMAS.

[74]  Iyad Rahwan,et al.  Judgment Aggregation in Multi-Agent Argumentation , 2014, J. Log. Comput..

[75]  Marija Slavkovik,et al.  Agenda Separability in Judgment Aggregation , 2016, AAAI.

[76]  Jörg Rothe,et al.  Complexity of manipulation and bribery in judgment aggregation for uniform premise-based quota rules , 2015, Math. Soc. Sci..

[77]  Christian List,et al.  STRATEGY-PROOF JUDGMENT AGGREGATION* , 2005, Economics and Philosophy.

[78]  Elena Deza,et al.  Encyclopedia of Distances , 2014 .

[79]  Lawrence G. Sager.  Handbook of Computational Social Choice , 2015 .

[80]  Lawrence G. Sager,et al.  Unpacking the Court , 1986 .

[81]  Hans Peters,et al.  Judgment aggregation in search for the truth , 2014, Games Econ. Behav..