Title: Allowing abstentions in ranking methods with generalised ballots

Authors: James E. Falk; Lowell Bruce Anderson; Susan Palocsay

Addresses: School of Engineering and Applied Science, The George Washington University, Washington DC 20052, USA; Industrial Engineering Department, Bogazici University, 34342, Bebek-Istanbul, Turkey ' Institute for Defense Analyses, 4850 Mark Center Drive, Alexandria, VA 22311, USA ' Computer Information Systems and Business Analytics Department, James Madison University, Harrisonburg, VA 22807, USA

Abstract: 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.

Keywords: group decision making; generalised ballots; paired comparisons; reducibility; abstentions; ranking methods; voters; voter opinions.

DOI: 10.1504/IJAMS.2013.057111

International Journal of Applied Management Science, 2013 Vol.5 No.4, pp.322 - 339

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 11 Oct 2013 *

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