MEASURING COMPLEXITY

ABSTRACT Metrics (i.e., numerical values) that measure complexity in problematic situations have numerous benefits in understanding complexity and comparing situations. But such measures have been elusive because of misperceptions of what constitutes complexity. The key to measuring complexity is to understand its nature. Once its nature is understood, it becomes clear that various linguistic adjustments are required to support definitions of metrics, and to understand their significance. Since the resolution of complexity typically demands significant resources, of the type available in organizations, it is advisable to start to work on complexity with an organizational model in mind. Because of the wide variation in organizations, a surrogate must be chosen that is sufficiently reliable and flexible to be functional. This surrogate is the Coherent Organization, a virtual organization having three levels: producing, strategizing, and mediating between producers and strategists. A discovery team, comprised of well-informed stakeholders (none of which fully understands the problematic situation, but each of whom has something to contribute beyond a desire to see the complexity resolved) generates data to be used in computing five measures of complexity, while at the same time moving toward an understanding that will position the team to take on the challenge of designing an alternative intended to resolve the problematic situation. Friedman's Theorem of Non-Assured Model Consistency and Harary's Theorem of Assured Model Consistency provide the essential basis for two generating processes that are used to gather the data for computing the metrics. These are the Nominal Group Technique (NGT) and Interpretive Structural Modeling (ISM), both of which are embedded in a system of management of complexity called Interactive Management (IM). The necessary linguistic adjustments are embedded in this system, which has been tested for more than two decades .. The Miller Index measures the extent of the set of problems perceived by the Discovery team. The Spreadthink Index measures the extent of the differences of opinion within the team on relative importance of the various problems. The De Morgan Index measures the extent of paired relationships among the problems, and the Aristotle Index measures the density of logic embedded in the problematique arising from the group's work using ISM. The Situational Complexity Index is a composite measure of complexity, computed as the product of three other indices. Empirically-derived values of all of these indexes are shown and the rationale for their definition and use is given