Open AccessMultinary group identification
Author(s) -
Cho Wonki Jo,
Ju BiungGhi
Publication year - 2017
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2156
Subject(s) - axiom , independence (probability theory) , independence of irrelevant alternatives , identification (biology) , group (periodic table) , arrow , arrow's impossibility theorem , mathematical economics , impossibility , mathematics , axiom independence , group identification , social psychology , social choice theory , psychology , computer science , law , political science , statistics , botany , chemistry , organic chemistry , biology , geometry , programming language
Group identification refers to the problem of classifying individuals into groups (e.g., racial or ethnic classification). We consider a multinary group identification model where memberships to three or more groups are simultaneously determined based on individual opinions on who belong to what groups. Our main axiom requires that membership to each group, say the group of J's, should depend only on the opinions on who is a J and who is not (that is, independently of the opinions on who is a K or an L). This shares the spirit of Arrow's independence of irrelevant alternatives and, therefore, is termed independence of irrelevant opinions . Our investigation of multinary group identification and the independence axiom reports a somewhat different message from the celebrated impossibility result by Arrow (1951). We show that the independence axiom, together with symmetry and non‐degeneracy, implies the liberal rule (each person self‐determines her own membership). This characterization provides a theoretical foundation for the self‐identification method commonly used for racial or ethnic classifications.