A single measure for point and interval predictions of coalition theories

Abstract

Some theories of coalition formation (e.g., the weighted probability model) make specific point predictions about the probabilities that various coalitions will form, while others predict only that some coalitions should be more likely than others, without making specific predictions about probabilities. Similarly, some theories make point predictions about the distribution of rewards within a coalition, while others (e.g., the bargaining set) make range predictions rather than point predictions. These theories apply to decision processes of living systems at the levels of groups, organizations, societies, and supranational systems. A measure is developed for evaluating competitively these otherwise incomparable types of predictions. The measure, E, is the mean squared distance between the experimental distribution of proportions and the whole set of probability distributions consistent with the prediction. A “proportional reduction in error” version of E is also suggested.