Many-valued judgment aggregation: characteriing the possibility/impossibility boundary for an important class of agendas

A general model of judgment aggregation is presented in which judgments on propositions are not binary but come in degrees. The primitives of the model are a set of propositions, an entailment relation, and a “triangular norm” which establishes a lower bound on the degree to which a proposition is true whenever it is entailed by a set of propositions. For an important class of agendas, we identify a necessary and sufficient condition for judgment aggregation to be free from veto power. This condition says that the triangular norm used to establish the lower bound must contain a zero divisor.

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

[2]  Conal Duddy,et al.  Arrow’s theorem and max-star transitivity , 2011, Soc. Choice Welf..

[3]  Ashley Piggins,et al.  Instances of Indeterminacy , 2007 .

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

[5]  Klaus Nehring,et al.  Abstract Arrowian aggregation , 2010, J. Econ. Theory.

[6]  Christian Eitzinger,et al.  Triangular Norms , 2001, Künstliche Intell..

[7]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

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

[9]  Martin van Hees,et al.  The limits of epistemic democracy , 2007, Soc. Choice Welf..

[10]  Christian List,et al.  The aggregation of propositional attitudes: towards a general theory , 2008 .

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

[12]  C. Puppe,et al.  The Handbook of Rational and Social Choice , 2009 .

[13]  Ron Holzman,et al.  Aggregation of non-binary evaluations , 2010, Adv. Appl. Math..

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

[15]  Philippe Mongin,et al.  An interpretive account of logical aggregation theory , 2011 .

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

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