Socially desirable approximations for Dodgson's voting rule

In 1876 Charles Lutwidge Dodgson suggested the intriguing voting rule that today bears his name. Although Dodgson’s rule is one of the most well-studied voting rules, it suffers from serious deficiencies, both from the computational point of view—it is NP-hard even to approximate the Dodgson score within sublogarithmic factors—and from the social choice point of view—it fails basic social choice desiderata such as monotonicity and homogeneity. In a previous paper [Caragiannis et al., SODA 2009] we have asked whether there are approximation algorithms for Dodgson’s rule that are monotonic or homogeneous. In this paper we give definitive answers to these questions. We design a monotonic exponential-time algorithm that yields a 2-approximation to the Dodgson score, while matching this result with a tight lower bound. We also present a monotonic polynomial-time O(log m)-approximation algorithm (where m is the number of alternatives); this result is tight as well due to a compl...

• Type: Conference
• Year: 2010
• Where: SIGECOM
• Authors: Ioannis Caragiannis, Christos Kaklamanis, Nikos Karanikolas, Ariel D. Procaccia
• Keywords: Dodgson Score, Dodgson’s Rule, ECommerce, SIGECOM 2010, Voting Rule