Allowing abstentions in ranking methods with generalised ballots

There are many situations wherein a group of individuals (e.g., voters) must produce an ordered list of 'best' alternatives selected from a given group of alternatives (e.g., candidates). Standard approaches include ranked voting methods (RVMs) and methods of paired comparisons (MPCs). Typical 'ballots' for these approaches are distinctly different. Indeed, RVM ballots are simple rankings, with all unranked alternatives being considered inferior to all ranked alternatives. By comparison, MPC ballots are matrices whose off diagonal entries reflect the voter's opinion concerning only the row and column alternatives for that entry. Such methods generally do not require a voter to express an opinion concerning every pair of alternatives. In this paper we propose a straightforward methodology to allow voters to submit generalised ballots that can reflect the voter's opinions as precisely as those of MPC ballots, yet with the simplicity of traditional RVM ballots.