Agenda Separability in Judgment Aggregation

One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in the same agenda. Independence, although considered a desirable property, is too strong, because together with mild additional conditions it implies dictatorship. We propose here a weakening of independence, named agenda separability: a judgment aggregation rule satisfies it if, whenever the agenda is composed of several independent sub-agendas, the resulting collective judgment sets can be computed separately for each sub-agenda and then put together. We show that this property is discriminant, in the sense that among judgment aggregation rules so far studied in the literature, some satisfy it and some do not. We briefly discuss the implications of agenda separability on the computation of judgment aggregation rules.

[1]  H. Young.  Social Choice Scoring Functions , 1975 .

[2]  Pierre Marquis,et al.  Conditional independence in propositional logic , 2002, Artif. Intell..

[3]  R. Parikh.  Beliefs, belief revision, and splitting languages , 1999 .

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

[5]  Ulrich Endriss.  Judgment Aggregation , 2016, Handbook of Computational Social Choice.

[6]  Norman Y. Foo,et al.  Distance Semantics for Relevance-Sensitive Belief Revision , 2004, KR.

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

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

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

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

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

[12]  Miroslaw Truszczynski,et al.  Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation , 2015, Lecture Notes in Computer Science.

[13]  Ulrich Endriss,et al.  Axiomatic analysis of aggregation methods for collective annotation , 2014, AAMAS.

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

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

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

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

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

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

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

[21]  Rohit Parikh,et al.  An Inconsistency Tolerant Model for Belief Representation and Belief Revision , 1999, IJCAI.

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

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

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

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

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

[27]  Adnan Darwiche,et al.  A Logical Notion of Conditional Independence: Properties and Application , 1997, Artif. Intell..

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

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

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

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