Probabilistic theories of coalition formation in groups

Chertkoff's (1967) and Walker's (1973) theories of coalition formation for decision making, which attempt to predict the probabilities of the occurrence of coalitions in three-person group systems, are extended to apply to certain situations involving groups larger than these triads. These two extended theories and Komorita's (1974) weighted probability theory, which attempts to predict the probabilities of occurrence of coalitions in groups of any size, are compared according to how well they can account for the results of a number of previously reported experiments, both on triads and on larger groups. In general, this comparison shows that: (a) Chertkoff's theory cannot account for the results; (b) Walker's theory can account only for the results of experiments in which all the minimal winning coalitions are equal in size; and (c) Komorita's theory can account only for the results of experiments in which there is some difference in size among the minimal winning coalitions. It is suggested that the theories of Chertkoff and Walker do not attribute enough importance to size as a factor in coalition formation, while weighted probability theory attributes too much importance to this factor.