2010/08/06 by John C. McCabe-Dansted, McCabe-Dansted, John C.
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #91B12 #Absurdity #Calculus (dental) #Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #Computer science #Electoral Systems and Political Participation #Epistemology #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Mathematical economics #Mathematics #Philosophy #cs.GT #math.CO #msc:91B12
paper · pdf · doi:10.48550/arxiv.1008.1501
Expanded draft of paper presented at COMSOC 2008
arxiv created 2010/08/06 · openalex publication_date 2010/08/06 · arxiv updated 2010/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With the Dodgson rule, cloning the electorate can change the winner, which Young (1977) considers an "absurdity". Removing this absurdity results in a new rule (Fishburn, 1977) for which we can compute the winner in polynomial time (Rothe et al., 2003), unlike the traditional Dodgson rule. We call this rule DC and introduce two new related rules (DR and D&). Dodgson did not explicitly propose the "Dodgson rule" (Tideman, 1987); we argue that DC and DR are better realizations of the principle behind the Dodgson rule than the traditional Dodgson rule. These rules, especially D&, are also effective approximations to the traditional Dodgson's rule. We show that, unlike the rules we have considered previously, the DC, DR and D& scores differ from the Dodgson score by no more than a fixed amount given a fixed number of alternatives, and thus these new rules converge to Dodgson under any reasonable assumption on voter behaviour, including the Impartial Anonymous Culture assumption.