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Byzantine Preferential Voting

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Web and Internet Economics (WINE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11316))

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Abstract

In the Byzantine agreement problem, n nodes with possibly different input values aim to reach agreement on a common value in the presence of \(t<n/3\) Byzantine nodes which represent arbitrary failures in the system. This paper introduces a generalization of Byzantine agreement, where the input values of the nodes are preference rankings of three or more candidates. We show that consensus on preferences, which is an important question in social choice theory, complements already known results from Byzantine agreement. In addition, preferential voting raises new questions about how to approximate consensus vectors. We propose a deterministic algorithm to solve Byzantine agreement on rankings under a generalized validity condition, which we call Pareto-Validity. These results are then extended by considering a special voting rule which chooses the Kemeny median as the consensus vector. For this rule, we derive a lower bound on the approximation ratio of the Kemeny median that can be guaranteed by any deterministic algorithm. We then provide an algorithm matching this lower bound. To our knowledge, this is the first non-trivial generalization of multi-valued Byzantine agreement to multiple dimensions which can tolerate a constant fraction of Byzantine nodes.

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References

  1. Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. J. ACM 55(5), 23:1–23:27 (2008)

    Article  MathSciNet  Google Scholar 

  2. Arrow, K.J.: Social Choice and Individual Values, 1st edn. Cowles Foundation, New Haven (1951)

    MATH  Google Scholar 

  3. Arrow, K.J.: Social Choice and Individual Values, 2nd edn. Wiley, New York (1963)

    MATH  Google Scholar 

  4. Bartholdi, J., Tovey, C.A., Trick, M.A.: Voting schemes for which it can be difficult to tell who won the election. Soc. Choice Welfare 6(2), 157–165 (1989)

    Article  MathSciNet  Google Scholar 

  5. Bartholdi, J.J., Tovey, C.A., Trick, M.A.: The computational difficulty of manipulating an election. Soc. Choice Welfare 6(3), 227–241 (1989)

    Article  MathSciNet  Google Scholar 

  6. Bassett, G.W., Persky, J.: Robust voting. Public Choice 990(3), 299–310 (1999)

    Article  Google Scholar 

  7. Ben-Or, M.: Another advantage of free choice (extended abstract): completely asynchronous agreement protocols. In: Proceedings of the Second Annual ACM Symposium on Principles of Distributed Computing, PODC 1983, pp. 27–30 (1983)

    Google Scholar 

  8. Berman, P., Garay, J.A.: Asymptotically optimal distributed consensus. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds.) ICALP 1989. LNCS, vol. 372, pp. 80–94. Springer, Heidelberg (1989). https://doi.org/10.1007/BFb0035753

    Chapter  Google Scholar 

  9. Berman, P., Garay, J.A., Perry, K.J.: Towards optimal distributed consensus. In: 30th Annual Symposium on Foundations of Computer Science, FOCS, October 1989

    Google Scholar 

  10. Betzler, N., Niedermeier, R., Woeginger, G.J.: Unweighted coalitional manipulation under the Borda rule is NP-hard. In: IJCAI, vol. 11, pp. 55–60 (2011)

    Google Scholar 

  11. Bracha, G.: Asynchronous Byzantine agreement protocols. Inf. Comput. 75(2), 130–143 (1987)

    Article  MathSciNet  Google Scholar 

  12. Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D.: Handbook of Computational Social Choice, 1st edn. Cambridge University Press, New York (2016)

    Book  Google Scholar 

  13. Chauhan, H., Garg, V.K.: Democratic elections in faulty distributed systems. In: Frey, D., Raynal, M., Sarkar, S., Shyamasundar, R.K., Sinha, P. (eds.) ICDCN 2013. LNCS, vol. 7730, pp. 176–191. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35668-1_13

    Chapter  Google Scholar 

  14. Davies, J., Katsirelos, G., Narodytska, N., Walsh, T.: Complexity of and algorithms for Borda manipulation. In: AAAI, vol. 11, pp. 657–662 (2011)

    Google Scholar 

  15. Diaconis, P., Graham, R.L.: Spearman’s footrule as a measure of disarray. J. R. Stat. Soc. Ser. B (Methodol.) 39, 262–268 (1977)

    MathSciNet  MATH  Google Scholar 

  16. Doerr, B., Goldberg, L.A., Minder, L., Sauerwald, T., Scheideler, C.: Stabilizing consensus with the power of two choices. In: Proceedings of the Twenty-third Annual ACM Symposium on Parallelism in Algorithms and Architectures, SPAA (2011)

    Google Scholar 

  17. Dolev, D., Lynch, N.A., Pinter, S.S., Stark, E.W., Weihl, W.E.: Reaching approximate agreement in the presence of faults. J. ACM 33(3), 499–516 (1986)

    Article  MathSciNet  Google Scholar 

  18. Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: Proceedings of the 10th International Conference on World Wide Web, WWW 2001, pp. 613–622. ACM, New York (2001)

    Google Scholar 

  19. Fekete, A.D.: Asymptotically optimal algorithms for approximate agreement. Distrib. Comput. 4(1), 9–29 (1990)

    Article  MathSciNet  Google Scholar 

  20. Fischer, M.J., Lynch, N.A.: A lower bound for the time to assure interactive consistency. Inf. Process. Lett. 14(4), 183–186 (1982)

    Article  MathSciNet  Google Scholar 

  21. Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)

    Article  MathSciNet  Google Scholar 

  22. Kemeny, J.G.: Mathematics without numbers. Daedalus 88(4), 577–591 (1959)

    Google Scholar 

  23. Kemeny, J.G., Snell, J.L.: Mathematical Models in the Social Sciences. Introductions to Higher Mathematics, Blaisdell, Waltham (Mass.) (1962)

    Google Scholar 

  24. Kendall, M.G.: A new measure of rank correlation. Biometrika 30(1/2), 81–93 (1938)

    Article  Google Scholar 

  25. King, V., Saia, J.: Byzantine agreement in expected polynomial time. J. ACM 63(2), 13:1–13:21 (2016)

    Article  MathSciNet  Google Scholar 

  26. Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)

    Article  Google Scholar 

  27. May, K.O.: A set of independent necessary and sufficient conditions for simple majority decision. Econometrica 20(4), 680–684 (1952)

    Article  MathSciNet  Google Scholar 

  28. Melnyk, D., Wattenhofer, R.: Byzantine agreement with interval validity. In: 37th Annual IEEE International Symposium on Reliable Distributed Systems, SRDS (2018)

    Google Scholar 

  29. Mendes, H., Herlihy, M.: Multidimensional approximate agreement in Byzantine asynchronous systems. In: Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing, STOC (2013)

    Google Scholar 

  30. Mendes, H., Herlihy, M., Vaidya, N., Garg, V.K.: Multidimensional agreement in Byzantine systems. Distrib. Comput. 28(6), 423–441 (2015)

    Article  MathSciNet  Google Scholar 

  31. Pareto, V.: Manuale di Economia Politica con una Introduzione alla Scienza Sociale. Società Editrice Libraria (1919)

    Google Scholar 

  32. Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)

    Article  MathSciNet  Google Scholar 

  33. Procaccia, A.D., Rosenschein, J.S., Kaminka, G.A.: On the robustness of preference aggregation in noisy environments. In: Proceedings of the 6th International Joint Conference on Autonomous Agents and Multiagent Systems, p. 66. ACM (2007)

    Google Scholar 

  34. Srikanth, T., Toueg, S.: Simulating authenticated broadcasts to derive simple fault-tolerant algorithms. Distrib. Comput. 2(2), 80–94 (1987)

    Article  Google Scholar 

  35. Stolz, D., Wattenhofer, R.: Byzantine agreement with median validity. In: 19th International Conference on Principles of Distributed Systems, OPODIS (2015)

    Google Scholar 

  36. Tideman, N.: The single transferable vote. J. Econ. Perspect. 9(1), 27–38 (1995)

    Article  Google Scholar 

  37. Tseng, L.: Voting in the presence of Byzantine faults. In: 2017 IEEE 22nd Pacific Rim International Symposium on Dependable Computing (PRDC), January 2017

    Google Scholar 

  38. Vaidya, N.H., Garg, V.K.: Byzantine vector consensus in complete graphs. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, PODC (2013)

    Google Scholar 

  39. Wattenhofer, R.: Distributed Ledger Technology: The Science of the Blockchain, 2nd edn. CreateSpace Independent Publishing Platform, Scotts Valley (2017)

    Google Scholar 

  40. van Zuylen, A., Williamson, D.P.: Deterministic algorithms for rank aggregation and other ranking and clustering problems. In: Kaklamanis, C., Skutella, M. (eds.) WAOA 2007. LNCS, vol. 4927, pp. 260–273. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-77918-6_21

    Chapter  MATH  Google Scholar 

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Authors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Darya Melnyk, Yuyi Wang & Roger Wattenhofer

Authors
  1. Darya Melnyk
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  2. Yuyi Wang
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  3. Roger Wattenhofer
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Correspondence to Darya Melnyk .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    George Christodoulou

  2. Universität Augsburg, Augsburg, Germany

    Tobias Harks

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Melnyk, D., Wang, Y., Wattenhofer, R. (2018). Byzantine Preferential Voting. In: Christodoulou, G., Harks, T. (eds) Web and Internet Economics. WINE 2018. Lecture Notes in Computer Science(), vol 11316. Springer, Cham. https://doi.org/10.1007/978-3-030-04612-5_22

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  • DOI: https://doi.org/10.1007/978-3-030-04612-5_22

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  • Online ISBN: 978-3-030-04612-5

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