TY - JOUR

T1 - The rarity of consistent aggregators

AU - Baharad, Eyal

AU - Neeman, Zvika

AU - Rubinchik, Anna

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - Aggregation of opinions

KW - Doctrinal paradox

UR - http://www.scopus.com/inward/record.url?scp=85086506494&partnerID=8YFLogxK

U2 - 10.1016/j.mathsocsci.2019.09.007

DO - 10.1016/j.mathsocsci.2019.09.007

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85086506494

SN - 0165-4896

VL - 108

SP - 146

EP - 149

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

ER -