Abstract
Conflict of interest is the permanent companion of any population of agents (computational or biological). For that reason, the ability to compromise is of paramount importance, making voting a key element of societal mechanisms. A voting procedure often discussed in the literature and, due to its intuitiveness, also conceptually quite appealing is Charles Dodgson’s scoring rule, basically using the respective closeness to being a Condorcet winner for evaluating competing alternatives. In this paper, we offer insights into the practical limits of algorithms computing the exact Dodgson scores from a number of votes. While the problem itself is theoretically intractable, this work proposes and analyses five different solutions which try distinct approaches to practically solve the issue in an effective manner. Additionally, three of the discussed procedures can be run in parallel which has the potential of drastically improving computational performance on the problem.
Similar content being viewed by others
Notes
The source code of the project software is available from https://sourceforge.net/projects/dodgsonscoring/.
In a Borda count voters rank alternatives in order of preference. The outcome is determined by assigning each alternative, for each ballot, a number of points corresponding to the number of candidates ranked lower. The alternative with the highest number of points, summed up over all cast votes, is the winner.
Similar to [5], even values for n were omitted as the performance of multiprocessing algorithms is influenced by the probability of there being a Condorcet winner. Even numbers of agents make this significantly less likely due to ties, resulting in the graph spiking after every other value.
References
Brandt F, Conitzer V, Endriss U, Lang J, Procaccia A (eds) (2016) Handbook of computational social choice. Cambridge University Press, Cambridge
Caragiannis I, Kaklamanis C, Karanikolas N, Procaccia A (2014) Socially desirable approximations for Dodgson’s voting rule. ACM Trans Algorithms 10:6
Dodgson C (1876) Reprint of “A method of taking votes on more than two issues”. In: McLean I, Urken A (eds) Classics of social choice. The University of Michigan Press (reprinted in 1995)
Fellows M, Jansen BMP, Lokshtanov D, Rosamond FA, Saurabh S (2010) Determining the winner of a Dodgson election is hard. In: IARCS annual conference on foundations of software technology and theoretical computer science, Schloss Dagstuhl-LZI, Leibniz international Proceedings in informatics (LIPIcs), vol 8, pp 459–468
Gehrlein WV (1999) Approximating the probability that a condorcet winner exists. In: Proceedings of the National Decision Sciences Institute, pp 626–628
Hemaspaandra E, Hemaspaandra LA, Rothe J (1997) Exact analysis of Dodgson elections: Lewis Carroll’s 1876 voting system is complete for parallel access to NP. J Assoc Comput Mach 44:806–825
Homan CM, Hemaspaandra LA (2009) Guarantees for the success frequency of an algorithm for finding Dodgson-election winners. J Heuristics 15(4):403–423
McCabe-Dansted J, Pritchard G, Slinko A (2008) Approximability of Dodgson’s rule. Soc Choice Welf 31:311–330
Ratliff TC (2002) A comparison of Dodgson’s method and the Borda count. Econ Theory 20(2):357–372
Recknagel A (2015) An approach to efficiently calculating Dodgson-scores using heuristics and parallel computing, vol 1. Publications of the Institute of Cognitive Science (PICS), Institute of Cognitive Science, Osnabrück
Rothe J (ed) (2015) Economics and computation. An introduction to algorithmic game theory, computational social choice, and fair division. Springer Texts in Business and Economics, Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Recknagel, A., Besold, T.R. Towards Efficiently Implementing Dodgson’s Formally Intractable Voting Rule. Künstl Intell 31, 161–167 (2017). https://doi.org/10.1007/s13218-016-0454-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13218-016-0454-8