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Paradoxes of Democracy, Voting, and Social Choice
(Taught in Splash! 2007)
Come learn ideas with applications in mathematics, economics, engineering, and political science! What if, in hypothetical two-way races, Clinton beats Obama, Obama beats Edwards, and Edwards beats Clinton? Is this even possible? (Yes.) What would then be a fair way to decide the "best" preferences of Democrats? Whether it's a T-shirt design contest or a presidential election, voting converts preferences of individuals into a single preference for the community. We'll discuss Arrow's Impossibility Theorem, which states that there is no "perfect" way of doing so. We'll demonstrate a few of the mind-boggling flaws that every voting method must have. Finally, interesting paradoxes in fair division (in particular, apportioning Congressional seats) will be shown.