Abstract
Computing the winners of an election is an important task in voting and preference aggregation. The declarative nature of answer-set programming (ASP) and the performance of state-of-the-art solvers render ASP very well-suited to tackle this problem. In this work we present a novel, reduction-based approach for a variety of voting rules, ranging from tractable cases to problems harder than NP. The encoded voting rules are put together in the extensible tool Democratix, which handles the computation of winners and is also available as a web application. To learn more about the capabilities and limits of the approach, the encodings are evaluated thoroughly on real-world data as well as on random instances.
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Notes
- 1.
Note that these rules can be simplified by using the so-called choice rule (see, e.g., [11]). Currently, this construct is, however, not supported by all ASP solvers.
References
Ali, A., Meila, M.: Experiments with Kemeny ranking: what works when? Math. Soc. Sci. 64(1), 28–40 (2012)
Alviano, M., Dodaro, C., Faber, W., Leone, N., Ricca, F.: WASP: a native ASP solver based on constraint learning. In: Cabalar, P., Son, T.C. (eds.) LPNMR 2013. LNCS, vol. 8148, pp. 54–66. Springer, Heidelberg (2013)
Bennett, J., Lanning, S.: The Netflix prize. In: Proceedings of KDD Cup and Workshop (2007)
Betzler, N., Guo, J., Niedermeier, R.: Parameterized computational complexity of Dodgson and Young elections. Inf. Comput. 208(2), 165–177 (2010)
Betzler, N., Bredereck, R., Niedermeier, R.: Theoretical and empirical evaluation of data reduction for exact Kemeny rank aggregation. Auton. Agent. Multi-Agent Syst. 28(5), 721–748 (2014)
Bouveret, S.: Whale\(^3\): Which alternative is elected (2013). http://whale3.noiraudes.net/whale3/
Brandt, F., Geist, C.: Finding strategyproof social choice functions via SAT solving. In: Proceedings of AAMAS 2014, pp. 1193–1200. IFAAMAS (2014)
Brandt, F., Chabin, G., Geist, C.: Pnyx: a powerful and user-friendly tool for preference aggregation. In: Proceedings of AAMAS 2015, pp. 1915–1916. IFAAMAS (2015)
Bredereck, R.: Fixed-parameter algorithms for computing Kemeny scores - theory and practice. Pre-diploma thesis, Department of Mathematics and Computer Science, University of Jena (2009)
Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F., Schaub, T.: ASP-Core-2: 4th ASP competition official input language format (2013)
Caragiannis, I., Covey, J., Feldman, M., Homan, C., Kaklamanis, C., Karanikolas, N., Procaccia, A., Rosenschein, J.: On the approximability of Dodgson and Young elections. Artif. Intell. 187, 31–51 (2012)
Conitzer, V., Davenport, A., Kalagnanam, J.: Improved bounds for computing Kemeny rankings. In: Proceedings of AAAI 2006, pp. 620–626. AAAI Press (2006)
Davenport, A., Kalagnanam, J.: A computational study of the Kemeny rule for preference aggregation. In: Proceedings of AAAI 2004, pp. 697–702. AAAI Press (2004)
Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: Proceedings of WWW 2001, pp. 613–622. ACM (2001)
Eiter, T., Ianni, G., Krennwallner, T.: Answer set programming: a primer. In: Tessaris, S., Franconi, E., Eiter, T., Gutierrez, C., Handschuh, S., Rousset, M.-C., Schmidt, R.A. (eds.) Reasoning Web. LNCS, vol. 5689, pp. 40–110. Springer, Heidelberg (2009)
Gebser, M., Janhunen, T., Rintanen, J.: ASP encodings of acyclicity properties. In: Proceedings of KR 2014. AAAI Press (2014)
Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Answer Set Solving in Practice. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan and Claypool, San Rafael (2012)
Gebser, M., Kaufmann, B., Kaminski, R., Ostrowski, M., Schaub, T., Schneider, M.: Potassco: the Potsdam answer set solving collection. AI Comm. 24(2), 107–124 (2011)
Geist, C., Endriss, U.: Automated search for impossibility theorems in social choice theory: ranking sets of objects. J. Artif. Intell. Res. 40, 143–174 (2011)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generat. Comput. 9(3/4), 365–386 (1991)
Ghosh, S., Mundhe, M., Hernandez, K., Sen, S.: Voting for movies: the anatomy of a recommender system. In: Proceedings of Agents 1999, pp. 434–435. ACM (1999)
Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Exact analysis of Dodgson elections: Lewis Carroll’s 1876 voting system is complete for parallel access to NP. J. ACM 44(6), 806–825 (1997)
Hemaspaandra, E., Spakowski, H., Vogel, J.: The complexity of Kemeny elections. Theor. Comput. Sci. 349(3), 382–391 (2005)
Konczak, K.: Voting theory in answer set programming. In: Proceedings of WLP 2006. INFSYS Research Report, vol. 1843–06-02, pp. 45–53. Technische Universität Wien (2006)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Log. 7(3), 499–562 (2006)
Mao, A., Procaccia, A., Chen, Y.: Better human computation through principled voting. In: Proceedings of AAAI 2013, pp. 1142–1148. AAAI Press (2013)
Mattei, N., Walsh, T.: PrefLib: a library for preferences. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds.) ADT 2013. LNCS (LNAI), vol. 8176, pp. 259–270. Springer, Heidelberg (2013)
Narodytska, N., Walsh, T., Xia, L.: Combining voting rules together. In: Proceedings of ECAI 2012. FAIA, vol. 242, pp. 612–617. IOS Press (2012)
Niemelä, I.: Logic programming with stable model semantics as a constraint programming paradigm. Ann. Math. Artif. Intell. 25(3–4), 241–273 (1999)
O’Neill, J.: www.OpenSTV.org (2013)
Ricca, F., Grasso, G., Alviano, M., Manna, M., Lio, V., Iiritano, S., Leone, N.: Team-building with answer set programming in the Gioia-Tauro seaport. Theor. Pract. Log. Prog. 12(03), 361–381 (2012)
Rothe, J., Spakowski, H., Vogel, J.: Exact complexity of the winner problem for Young elections. Theor. Comput. Syst. 36(4), 375–386 (2003)
Simjour, N.: Parameterized enumeration of neighbour strings and Kemeny aggregations. Ph.D. thesis, University of Waterloo (2013)
Tang, P., Lin, F.: Computer-aided proofs of Arrow’s and other impossibility theorems. Artif. Intell. 173(11), 1041–1053 (2009)
Acknowledgements
The authors are grateful to the anonymous COMSOC-2014 and ADT-2015 referees for their very helpful comments and suggestions. This work was supported by the Austrian Science Fund (FWF): P25518, P25607, Y968; and the German Research Foundation (DFG): ER 738/2–1.
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Charwat, G., Pfandler, A. (2015). Democratix: A Declarative Approach to Winner Determination. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_16
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DOI: https://doi.org/10.1007/978-3-319-23114-3_16
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