The rarity of consistent aggregators

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Baharad, E (Author) Other; Neeman, Z (Author) Other; Rubinchik, A (Author) Other

Journal

Title: MATHEMATICAL SOCIAL SCIENCES

Vol. 108

Pages: 146-149

ISSN: 0165-4896

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-017-3SJ

DOI: 10.1016/j.mathsocsci.2019.09.007

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 4