Toward a Mathematical Foundation for Information and Decision Sciences

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By combining concepts coming from "chaotic dynamical systems," differential geometry, and symmetry, a common mathematical foundation will be created to serve for several, seemingly different models coming rom the informational and decision sciences. Such a foundation permits the transfer of ideas, concepts, and techniques among several different disciplines, and it leads to the development of techniques to solve issues that span the informational sciences. The kinds of problems to be addressed include the analysis of procedures from voting and the decision sciences, techniques from probability and statistics, as well as the design of mechanisms and incentive structures for economics. The reason the results obtained in this research will be interdisciplinary is that the emphasis is on characterizing the combinatoric symmetries of "kinds of defining properties" for models as opposed to the particular properties of a specific model.