John Cullinan

A Borda count for partially ordered ballots

The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure, called the partial Borda count, that extends the classic Borda count to allow for arbitrary partially ordered preference rankings. We characterize the partial Borda count in the context of weighting procedures and in the context of social choice functions.

SYMPLECTIC STABILIZERS WITH APPLICATIONS TO ABELIAN VARIETIES

Fix a prime number l > 2 and let V be a four-dimensional Fl-vector space. We classify subgroups G of Sp(V) with the property that every g ∈ G stabilizes a one-dimensional subspace of V, yet G itself is not of parabolic type. This classification is motivated by its application to the mod l representation of abelian surfaces, following a program outlined by Sutherland.