Andreas Blass

University of Michigan, Ann Arbor

March 3,
refreshments at 3:45pm


I plan to talk about both finite and infinite combinatorics of the following situation. A set of voters is to choose between two alternatives. If a majority of the voters chooses one alternative, then their choice wins. But if the vote is a tie, then the decision is made by a "tie-breaker" rule, which specifies which sets of half the voters are winning coalitions.

If the number of voters is finite, the results I'll discuss are mostly about fairness. To what extent can a tie-breaker treat all voters alike? Or even treat equal-sized (small) sets of voters alike?

If the number of voters is infinite, most of the questions from the finite case become trivial, but many new questions arise, which have no analog in the finite case. I'll discuss some questions about which sets of voters might hold the balance of power in "close" elections.

Speaker's Contact Info: ablass(at-sign)umich.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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