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CONSTRAINT

a relation between two sets such that the variety that exists under one condition is less than the variety that exists under another. (Ashby, 1956 p. l27) The total variety possible is defined by the variables which were selected by the observer. Constraints reduce this variety to the variety actually observed. As Ashby says, "The cybernetician looks at what does not happen." The constraints, or the interaction rules operating over a set of variables, determine what does not happen. (Umpleby)

Constraints are limitations imposed by nature or by man that do not permit certain actions to be taken. Constraints may mean that certain objectives cannot be achieved. The actions, alternatives, consequences, and objectives that are not precluded by the constraints are referred to as [feasible.] In a particular analysis study, some constraints may have to be considered [stiff] or unquestionable, others--from among those imposed by prior decisions--may be [elastic] or removable if the analysis proves a good case for it. For example, the natural water supply in a region is a stiff constraint, while the money or manpower allocated to fulfill a certain task may be an elastic constraint. It is useful to distinguish [short-run] and [long-run] constraints: for example, existing legislation is a constraint in the short run, but not necessarily in the long run. In mathematical terms, if the notions of action space, CONSEQUENCE space, and objective space are introduced, the constraints determine a [feasible set] in each of those spaces. (IIASA)

The difference between a set and a subset indicating that the variety that exists under one condition is less than the variety that exists under another (after Ashby). For an observer, constraints become apparent when he finds that a system can assume fewer states than are logically possible or hypothesized by him. Within a cartesian product a constraint is the complement of a relation, the former contains all states excluded by the latter. information is a measure of the constraint imposed by a condition or message. (Krippendorff)
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