Properties of Egalitarian Sequences of Committees: Theory and Experiments

We study the task of electing egalitarian sequences of $τ$ committees given a set of agents with additive utilities for candidates available on each of $τ$ levels. We introduce several rules for electing an egalitarian committee sequence as well as properties for such rules. We settle the computational complexity of finding a winning sequence for our rules and classify them against our properties. Additionally, we transform sequential election data from existing election data from the literature. Using this data set, we compare our rules empirically and test them experimentally against our properties.