Erik Aas: Banzhaf vectors

For any simplicial complex on n nodes, one can define its Banzhaf vector, which is a nonnegative integer vector with n components. The i-th component is supposed to measure the political power of node (=voter) i in the simplicial complex (=voting game). I will give a survey of this statistic, including:

• enumerating the set of all Banzhaf vectors of all simplicial complexes, respectively of the weighted complexes (to be defined).
• the inverse problem of constructing a simplicial complex of a given class with a given Banzhaf vector.
• connections to computer science.