TOWARD A GENERAL-THEORY OF INFORMATION AGGREGATION

Information aggregation is a pervasive issue in the field of decision making. In this paper we begin an attempt to develop a comprehensive theory of this process. We investigate the use of a penalty function to help guide in the aggregation process. It is suggested that an aggregated value which violates a given piece of data is charged a penalty. The problem of aggregation can be seen as finding the aggregated value with the least penalty. We show that logical inference systems are characterized by infinite penalty functions. This implies that deviation from the data are not easily accepted. Probability theory is characterized by equal finite penalty costs. Nonmonotonic logics appear to be characterized by a case in which we have at least two different levels of penalties of differing magnitudes. We discuss the relationship between the relevance or bearing a piece of data has on the problem and the penalty cost associated with it. We see the central role of the intersection operation.