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Succinctness of Languages for Judgment Aggregation

Endriss, Ulle; Grandi, Umberto; de Haan, Ronald; Lang, Jérôme (2016), Succinctness of Languages for Judgment Aggregation, in Baral, Chitta; Delgrande, James; Wolter, Frank, KR'16 Proceedings of the Fifteenth International Conference on Principles of Knowledge Representation and Reasoning, AAAI Press : Palo Alto (USA), p. 176-186

Type
Communication / Conférence
External document link
http://dl.acm.org/citation.cfm?id=3032049
Date
2016
Conference title
15th International Conference on Principles of Knowledge Representation and Reasoning (KR'16)
Conference date
2016-04
Conference city
Cape Town
Conference country
South Africa
Book title
KR'16 Proceedings of the Fifteenth International Conference on Principles of Knowledge Representation and Reasoning
Book author
Baral, Chitta; Delgrande, James; Wolter, Frank
Publisher
AAAI Press
Published in
Palo Alto (USA)
ISBN
978-1-57735-755-1
Number of pages
642
Pages
176-186
Metadata
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Author(s)
Endriss, Ulle
Institute for Logic, Language and Computation [ILLC]
Grandi, Umberto cc

de Haan, Ronald

Lang, Jérôme
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
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.
Subjects / Keywords
social choice theory; combinatorial domains; computational complexity

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