Autonomous Agents and Multi-Agent Systems

, Volume 22, Issue 1, pp 4–30 | Cite as

On the logic of preference and judgment aggregation

  • Thomas Ågotnes
  • Wiebe van der Hoek
  • Michael Wooldridge


Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow’s theorem and Condorcet’s paradox—which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation—including classical preference aggregation. As a case study we present a logical study of, including a formal proof of, the neutrality lemma, the main ingredient in a well-known proof of Arrow’s theorem.


Judgment aggregation Preference aggregation Modal logic Complexity Completeness 


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Thomas Ågotnes
    • 1
  • Wiebe van der Hoek
    • 2
  • Michael Wooldridge
    • 2
  1. 1.Department of Information Science and Media StudiesUniversity of BergenBergenNorway
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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