The Mathematics of Aggregation, Interdependence, Organizations and Systems of Nash equilibria (NE): A replacement for Game Theory

William F. Lawless and Donald A. Sofge

Traditional social science research has been unable to satisfactorily aggregate individual level data to group, organization and systems levels, making it one of social science’s biggest challenges, if not the most important (Giles, 2011). For game and social theory, we believe that the fault can be attributed to the lack of valid distance measures (e.g., the arbitrary ordering of cooperation and competition precludes a Hilbert space distance metric for gradations in these social behaviors, making theory normative). As an alternative, we offer a theory of social interdependence with countable mathematics based on bistable or multi-stable perspectives patterned after quantum information theory. The evidence that is available is supportive. It indicates that meaning is a one-sided, stable, classical interpretation, not only making the correspondence between beliefs and objective reality in social settings incomplete, but necessarily sweeping aside many static theories from earlier eras (e.g., Axelrod’s evolution of cooperation; Simon’s bounded rationality). This result alone indicates for democracies that system interpretations evolve to become orthogonal (Nash equilibria), that orthogonal interpretations generate the information that uniquely promotes social evolution, but that in dictatorships, dependent as they are on the enforcement of social cooperation and the suppression f opposing points of view, evolution stops or slows, such as in China, Iran or Cuba, causing capital and energy to be wasted, misdirected or misallocated as government leaders suppress the interpretations that they alone have the authority to label as unethical, immoral, or irreligious.

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