Theoretical Economics 12 (2017), 513–531
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Multinary group identification
Wonki Jo Cho, Biung-Ghi Ju
Abstract
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.
Keywords: Group identification, independence of irrelevant opinions, symmetry, liberalism, one-vote rules
JEL classification: C0,D70,D71,D72
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