Abstract
This paper explores the problems that are associated with building a model (representation) of two systems which are central to the field of policy analysis. The systems are the Lockean and Dialectical Inquiring Systems (ISs). Given two or more belief systems, a Lockean IS will attempt to secure maximum agreement between them, whereas a Dialectical IS will attempt to secure maximum disagreement as the basis for forming a policy. It is shown that a representation of these two systems necessitates a notion of probability assignment in which the law of conditional probabilities, p(A)p(B\A) = p(B)p(A\B), does not hold. Cross impact analysis provides such a notion of probability and hence is necessary to the representation of what happens as a decision-maker goes from a Lockean state to a Dialectical state. The movement from a Lockean to a Dialectical state is termed Conflict Production or Generation whereas the movement from a Dialectical to a Lockean state is termed Conflict Resolution or Reduction. It is argued that the representation of these two systems is basic to the foundation of a mathematical approach to policy analysis.

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