Diversity, Agreement, and Polarization in Elections

Abstract: We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such measures for the other two notions are lacking. We attempt to rectify this issue by designing appropriate measures, providing means of their (approximate) computation, and arguing that they, indeed, capture diversity and polarization well. In particular, we present "maps of preference orders" that highlight relations between the votes in a given election and which help in making arguments about their nature.