Decomposition of the Group Members into Two-subgroups Based on the Correctness Probability of Collective Choice: Two-Decomposition Theorem of the Complete Homogeneous Group

Abstract

Some relationship among the individual choice competence, the number of individuals in the group, its decision rule and the collective choice competence was initially investigated in Condorcet’ s Jury Theorem. Although several researchers has developed the theorem in different directions, they in common assume implicitly one collective choice area and introduce only the individual choice competence for the area. In reality, however, there may exist multiple collective choice areas such as ‘management strategy and staff distribution’ and the individual choice competencies may be different for the corresponding area such that ‘he/she is good at management strategy but not staff distribution’. Under these existence and difference, how does the group assign what members in it to what collective choice area? This “group decomposition problem” can not be treated with in the collective choice models under Jury Theorem and its developed results because one collective choice area and one individual choice competence for it are assumed. This paper extends the basic model under Jury Theorem to the model of two collective choice are as and formulates in general the group two-decomposition problem. It also gives a solution to this problem under the complete homogeneity assumption that all of the members in the group have the same competence of individual choice for all of the collective choice areas. Finally, some unsolved problems are showed. © 1991, Japanese Association For Mathematical Sociology. All rights reserved.