Skip to main content

Democratix: A Declarative Approach to Winner Determination

  • Conference paper
  • First Online:
Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 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

  1. Ali, A., Meila, M.: Experiments with Kemeny ranking: what works when? Math. Soc. Sci. 64(1), 28–40 (2012)

    Article  MathSciNet  Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. Bennett, J., Lanning, S.: The Netflix prize. In: Proceedings of KDD Cup and Workshop (2007)

    Google Scholar 

  4. Betzler, N., Guo, J., Niedermeier, R.: Parameterized computational complexity of Dodgson and Young elections. Inf. Comput. 208(2), 165–177 (2010)

    Article  MathSciNet  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. Bouveret, S.: Whale\(^3\): Which alternative is elected (2013). http://whale3.noiraudes.net/whale3/

  7. Brandt, F., Geist, C.: Finding strategyproof social choice functions via SAT solving. In: Proceedings of AAMAS 2014, pp. 1193–1200. IFAAMAS (2014)

    Google Scholar 

  8. 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)

    Google Scholar 

  9. 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)

    Google Scholar 

  10. Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)

    Article  Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Article  MathSciNet  Google Scholar 

  13. Conitzer, V., Davenport, A., Kalagnanam, J.: Improved bounds for computing Kemeny rankings. In: Proceedings of AAAI 2006, pp. 620–626. AAAI Press (2006)

    Google Scholar 

  14. 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)

    Google Scholar 

  15. Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: Proceedings of WWW 2001, pp. 613–622. ACM (2001)

    Google Scholar 

  16. 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)

    Google Scholar 

  17. Gebser, M., Janhunen, T., Rintanen, J.: ASP encodings of acyclicity properties. In: Proceedings of KR 2014. AAAI Press (2014)

    Google Scholar 

  18. 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)

    Book  Google Scholar 

  19. 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)

    Article  MathSciNet  Google Scholar 

  20. 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)

    Article  MathSciNet  Google Scholar 

  21. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generat. Comput. 9(3/4), 365–386 (1991)

    Article  Google Scholar 

  22. 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)

    Google Scholar 

  23. 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)

    Article  MathSciNet  Google Scholar 

  24. Hemaspaandra, E., Spakowski, H., Vogel, J.: The complexity of Kemeny elections. Theor. Comput. Sci. 349(3), 382–391 (2005)

    Article  MathSciNet  Google Scholar 

  25. 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)

    Google Scholar 

  26. 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)

    Article  MathSciNet  Google Scholar 

  27. Mao, A., Procaccia, A., Chen, Y.: Better human computation through principled voting. In: Proceedings of AAAI 2013, pp. 1142–1148. AAAI Press (2013)

    Google Scholar 

  28. 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)

    Chapter  Google Scholar 

  29. Narodytska, N., Walsh, T., Xia, L.: Combining voting rules together. In: Proceedings of ECAI 2012. FAIA, vol. 242, pp. 612–617. IOS Press (2012)

    Google Scholar 

  30. Niemelä, I.: Logic programming with stable model semantics as a constraint programming paradigm. Ann. Math. Artif. Intell. 25(3–4), 241–273 (1999)

    Article  Google Scholar 

  31. O’Neill, J.: www.OpenSTV.org (2013)

    Google Scholar 

  32. 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)

    Article  MathSciNet  Google Scholar 

  33. Rothe, J., Spakowski, H., Vogel, J.: Exact complexity of the winner problem for Young elections. Theor. Comput. Syst. 36(4), 375–386 (2003)

    Article  MathSciNet  Google Scholar 

  34. Simjour, N.: Parameterized enumeration of neighbour strings and Kemeny aggregations. Ph.D. thesis, University of Waterloo (2013)

    Google Scholar 

  35. Tang, P., Lin, F.: Computer-aided proofs of Arrow’s and other impossibility theorems. Artif. Intell. 173(11), 1041–1053 (2009)

    Article  MathSciNet  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Günther Charwat or Andreas Pfandler .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23114-3_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23113-6

  • Online ISBN: 978-3-319-23114-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics