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Introduction to Voting Theory
Student-Run Research| Speaker: | Sonny Mohammadzadeh, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Oct 11 2006, 12:10PM |
Description
Recent decades have shown a trend of mathematicians using various
methods of algebra, geometry, dynamical systems, and even representation
theory to study problems involving aggregation methods. One area that
has sparked interest is Voting Theory, the study of formally defined
voting systems. We will begin with Arrow's Impossibility Theorem, which
demonstrates that no voting system can possibly meet a certain set of
reasonable criteria. We will look at the most popular voting systems in
practice and under study including Borda Count, Condorcet, Plurality and
Single Transferable Voting. We will demonstrate faults of these systems
and paradox's that may occur from their use. We will then look in
detail into the methods of Donald Saari PhD. who studies voting
structures as naturally arising vector spaces, and hence admitting
geometries that can be analyzed. Saari's contributions have helped to
classify a large class of election paradoxes and suggest remedies to
these paradox's by exploiting symmetries of the associated vector
spaces.