Toward a Mathematical Foundation for Information and Decision Sciences

通过结合来自“混沌动力系统”、微分几何和对称的概念，将创建一个共同的数学基础，以服务于来自信息科学和决策科学的几个看似不同的模型。这样的基础允许思想、概念和技术在几个不同的学科之间的转移，并导致技术的发展，以解决跨越信息科学的问题。要解决的问题种类包括从投票和决策科学中分析程序，从概率论和统计学中分析技术，以及设计经济学的机制和激励结构。本研究获得的结果将是跨学科的，因为重点是描述模型的“各种定义属性”的组合对称性，而不是特定模型的特定属性。

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.