The complexity of election problems with group-separable preferences

Piotr Faliszewski, Alexander Karpov, Svetlana Obraztsova

Abstract: We analyze the complexity of several \({{\mathrm {NP}}}\)-hard election-related problems under the assumptions that the voters have group-separable preferences. We show that under this assumption our problems typically remain \({{\mathrm {NP}}}\)-hard, but we provide more efficient algorithms if additionally the clone decomposition tree is of moderate height. We also show a polynomial-time algorithm for sampling group-separable elections uniformly at random.