Donald G. Saari

University of California, Irvine

Election Year: 2001
Primary Section: 32, Applied Mathematical Sciences
Secondary Section: 54, Economic Sciences
Membership Type: Member

Research Interests

My research centers on dynamical systems, their applications to the physical and social sciences, and the development of new research tools motivated by dynamics. In the physical sciences I work on the Newtonian N-body problem by examining all possible ways N-body systems can evolve as time goes to infinity, the dynamic behavior of collisions and singularities, and the kinds of configurations the particles can form as determined by the integrals of motion and symmetry considerations. My recent research emphasizes dynamics in the social sciences, such as the properties of price mechanisms, equilibrium concepts such as the core, evolutionary models, and in particular, decision analysis. As an illustration of the latter, as known since 1770, an election outcome can reflect the procedure rather than the voters' preferences. By developing tools motivated by chaotic systems and symmetry concepts we now can analyze all possible standard voting and decision procedures. This includes discovering a benign interpretation for the seminal Arrow Theorem while extending it. A next goal is to extend these approaches so they can address decision problems coming from such areas as statistics, management, and engineering.

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