Measuring Nearly Single-Peakedness of an Electorate: Some New Insights

Abstract

After introducing a new distance measure of a preference profile to single-peakedness, directly derived from the very definition of single-peaked preferences by Black [4], we undertake a brief comparison with other popular distance measures to single-peakedness. We then tackle the computational aspects of the optimization problem raised by the proposed measure, namely we show that the problem is NP-hard and we propose an integer programming formulation. Finally, we carry out numerical tests on real and synthetic voting data. The obtained results show the interest of the proposed measure, but also shed new light on the advantages and drawbacks of some popular distance measures.