The rarity of consistent aggregators

Eyal Baharad, Zvika Neeman, Anna Rubinchik

Research output: Contribution to journalArticlepeer-review


We demonstrate that the inconsistency associated with judgment aggregation, known as the “doctrinal paradox”, is not a rare exception. There are n individuals who have opinions about k propositions. Each opinion expresses the degree of belief or conviction and thus belongs to the unit interval [0,1]. We work with an arbitrary proposition aggregator that maps opinions about k propositions into an overall opinion in [0,1] and an arbitrary individual opinions aggregator mapping opinions of n individuals into a single judgement from a unit interval. We show that for any typical proposition aggregator, the set of individual opinion aggregators that are immune to the paradox is very small, i.e., is nowhere dense in the space of uniformly bounded functions. In addition, we offer several examples of judgement aggregation for which the paradox can be avoided.

Original languageEnglish
Pages (from-to)146-149
Number of pages4
JournalMathematical Social Sciences
StatePublished - Nov 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Aggregation of opinions
  • Doctrinal paradox

ASJC Scopus subject areas

  • Sociology and Political Science
  • General Social Sciences
  • General Psychology
  • Statistics, Probability and Uncertainty


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