A note on the collective identity of indistinguishable entities: a view from the stable marriage problem

Authors:
Yoshiteru Ishida
Affiliations:
Department of Computer Science and Engineering, Toyohashi University of Technology, Toyohashi, Japan
Venue:
KES'11 Proceedings of the 15th international conference on Knowledge-based and intelligent information and engineering systems - Volume Part IV
Year:
2011

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Abstract

This note formalizes a conjecture that entities of similar kinds behave similarly, and hence a collective of similar entities may be treated as one entity (a collective identity). We previously reported that this conjecture may be formalized as an additive symmetry exhibited by two or more similar species in the Lotka-Volterra model. This note reports on a formalization based on the Stable Marriage Problem. That is, similar individuals exhibit the additive symmetry and may be treated as one collective entity (called "generalized individual"). This formalization allows us to relate the collectives with concepts such as decomposability and diversity based on the similarity and distinguishability.