Plenary Talk: Elections and Representation

In this talk, I will introduce the mathematics and applications of election procedures and apportionment methods.

Elections are easy when there are only two candidates: vote by majority rule.  For three or more candidates, Kenneth Arrow’s Impossibility Theorem shows that no three-candidate election procedure satisfies a set of reasonable axioms, implying that there is no “best” election procedure.  After discussing the axiomatic approach in voting theory, we will review commonly used election procedures, including the use of ranked choice voting in East Pointe, Michigan as part of the resolution of a Voting Rights Act lawsuit.

In the context of the US House of Representatives, the apportionment problem is to determine the number of representatives each state receives in the House.  We will review the history and mathematics of apportioning the House, including its relationship to the Electoral College.  We will conclude with the recent use of apportionment methods to allocate delegates among candidates in the Democratic and Republican presidential primaries.

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