Succinctness of Languages for Judgment Aggregation

Ulle Endriss (1) , Umberto Grandi (2) , Ronald de Haan (3) , Jérôme Lang (2, 4)

1 ILLC - Institute for Logic, Language and Computation
2 IRIT - Institut de recherche en informatique de Toulouse
3 TU Wien - Vienna University of Technology = Technische Universität Wien
4 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

We review several different languages for collective decision making problems, in which agents express their judgments, opinions, or beliefs over elements of a logically structured domain. Several such languages have been proposed in the literature to compactly represent the questions on which the agents are asked to give their views. In particular, the framework of judgment aggregation allows agents to vote directly on complex, logically related formulas, whereas the setting of binary aggregation asks agents to vote on propositional variables, over which dependencies are expressed by means of an integrity constraint. We compare these two languages and some of their variants according to their relative succinctness and according to the computational complexity of aggregating several individual views expressed in such languages into a collective judgment. Our main finding is that the formula-based language of judgment aggregation is more succinct than the constraint-based language of binary aggregation. In many (but not all) practically relevant situations, this increase in succinctness does not entail an increase in complexity of the corresponding problem of computing the outcome of an aggregation rule.

Mots clés: Social choice theory; Combinatorial domains; Computational complexity

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Ulle Endriss, Umberto Grandi, Ronald de Haan, Jérôme Lang. Succinctness of Languages for Judgment Aggregation. 15th International Conference on Principles of Knowledge Representation and Reasoning (KR 2016), co-located with DL 2016 and NMR 2016, Apr 2016, Cape Town, South Africa. pp.176-185. ⟨hal-03625799⟩