The University of New Mexico
Christopher K. Butler
Group Interactions
WORKING PAPER
2009

Abstract

Predicting social outcomes on the basis of numerous individual-level interactions is an exhaustive task that only a computer can complete. Even a computer takes exponentially longer to compute all the interactions as the number of actors increases. In addition, the measurement of relevant information (minimally, preferences, but often power and salience as well) becomes increasingly dicult as the number of actors gets larger. I propose a dierent way of thinking about these large number of interactions for bargaining in a single issue space by re-conceptualizing the interactions as between probability distributions at opposite ends of the issue area rather than between individuals. The measurement of individual information is presumed to be a sample of the opposing distributions rather than a complete picture of all the relevant actors. This sampling can be used to describe each opposing distribution. Each distribution is thought of as a heterogeneous group of individuals. The density of the distribution at a given position represents the proportion of individuals desiring that position as their ideal position. This presumes that all individuals at a given position would be similarly a ected by bargaining. The joint distribution of the two opposing distributions both summarizes the total \society" and provides the basis of a probability density function of prediction (rather than a point prediction). Once the framework of this type of analysis is established, a particular model of distributional interaction is put forward to demonstrate how the framework can be used to generate dynamic predictions over time.

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Department of Political Science The University of New Mexico Department of Political Science The University of New Mexico