Abstract
Given a profile of ranking lists over a finite set of alternatives, probabilistic social choice seeks to select a probability function over the alternatives on the basis of the pairwise comparison voting data. In this paper, we establish a differentially private formalism for probabilistic social choice in the shuffle model. In the shuffle model, individual voters submit their locally randomized data anonymously through a trusted shuffler which randomly permutes these individual data. Anonymity here plays a double role as a fairness condition and privacy amplification. The crucial step in our construction is to employ spectral clustering to find data-independent cluster centers and then to approximately round each input ranking order to these centers. We proceed to define a local differentially private randomizer plus the shuffler and then implement standard probabilistic social choice protocols such as maximal lottery and random dictatorship. Moreover, we analyze both privacy and utility of the proposed shuffle model and run some experiments to show the effectiveness of our formalism. In the last section, we discuss some related works and future directions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ao, L., Lu, Y., Xia, L., Zikas, V.: How private are commonly-used voting rules? In: UAI2020, pp. 629–638. PMLR (2020)
Balle, B., Bell, J., Gascón, A., Nissim, K.: The privacy blanket of the shuffle model. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 638–667. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_22
Balle, B., Bell, J., Gascón, A., Nissim, K.: Private summation in the multi-message shuffle model. In: CCS 2020, pp. 657–676 (2020)
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)
Brandl, F., Brandt, F., Seedig, H.G.: Consistent probabilistic social choice. Econometrica 84(5), 1839–1880 (2016)
Brandl, F., Brandt, F., Stricker, C.: An analytical and experimental comparison of maximal lottery schemes. Soc. Choice Welfare 58(1), 5–38 (2021). https://doi.org/10.1007/s00355-021-01326-x
Brandt, F.: Rolling the dice: recent results in probabilistic social choice. In: Trends in Computational Social Choice, pp. 3–26 (2017)
Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D.: Handbook of Computational Social Choice. Cambridge University Press, Cambridge (2016)
Cheu, A.: Differential privacy in the shuffle model. Ph.D. thesis, Northeastern University (2021)
Cheu, A., Smith, A., Ullman, J., Zeber, D., Zhilyaev, M.: Distributed differential privacy via shuffling. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 375–403. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_13
Cheu, A., Ullman, J.: The limits of pan privacy and shuffle privacy for learning and estimation. In: STOC 2021, pp. 1081–1094 (2021)
Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Found. Trends Theor. Comput. Sci. 9(3–4), 211–407 (2014)
Erlingsson, Ú., Feldman, V., Mironov, I., Raghunathan, A., Talwar, K., Thakurta, A.: Amplification by shuffling: from local to central differential privacy via anonymity. In: SODA 2019, pp. 2468–2479. SIAM (2019)
Fishburn, P.C.: Probabilistic social choice based on simple voting comparisons. Rev. Econ. Stud. 51(4), 683–692 (1984)
Ghazi, B., Kumar, R., Manurangsi, P., Pagh, R., Sinha, A.: Differentially private aggregation in the shuffle model: almost central accuracy in almost a single message. In: ICML 2021, pp. 3692–3701. PMLR (2021)
Gibbard, A.: Manipulation of schemes that mix voting with chance. Econometrica 45(3), 665–81 (1977)
Hay, M., Elagina, L., Miklau, G.: Differentially private rank aggregation. In: ICDM 2017, pp. 669–677. SIAM (2017)
Jiao, Y., Vert, J.P.: The Kendall and Mallows Kernels for permutations. IEEE Trans. Pattern Anal. Mach. Intell. 40(7), 1755–1769 (2018)
Jiao, Y., Vert, J.P.: The weighted Kendall and high-order Kernels for permutations. In: ICML 2018, pp. 2314–2322. PMLR (2018)
Kairouz, P., Bonawitz, K., Ramage, D.: Discrete distribution estimation under local privacy. In: Balcan, M., Weinberger, K.Q. (eds.) ICML 2016, New York City, NY, USA, 19–24 June 2016, vol. 48, pp. 2436–2444. JMLR.org (2016)
Liu, J., Han, J.: Spectral clustering. In: Data Clustering, pp. 177–200. Chapman and Hall/CRC (2018)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS 2002, pp. 849–856 (2002)
Prasad, A., Pareek, H., Ravikumar, P.: Distributional rank aggregation, and an axiomatic analysis. In: ICML 2015, pp. 2104–2112. PMLR (2015)
Rivest, R.L., Shen, E.: An optimal single-winner preferential voting system based on game theory. In: Proceedings of 3rd International Workshop on Computational Social Choice, pp. 399–410 (2010)
Shang, S., Wang, T., Cuff, P., Kulkarni, S.: The application of differential privacy for rank aggregation: privacy and accuracy. In: FUSION 2014, pp. 1–7. IEEE (2014)
Sweeney, L.: Weaving technology and policy together to maintain confidentiality. J. Law Med. Ethics 25(2–3), 98–110 (1997)
Torra, V.: Random dictatorship for privacy-preserving social choice. Int. J. Inf. Secur. 19(5), 537–545 (2020)
Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)
Wang, T., Blocki, J., Li, N., Jha, S.: Locally differentially private protocols for frequency estimation. In: Kirda, E., Ristenpart, T. (eds.) 26th USENIX Security Symposium, USENIX Security 2017, Vancouver, BC, Canada, 16–18 August 2017, pp. 729–745. USENIX Association (2017)
Warner, S.: Randomized response: a survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60(309), 63–69 (1965)
Yan, D., Huang, L., Jordan, M.I.: Fast approximate spectral clustering. In: KDD 2009, pp. 907–916 (2009)
Yan, Z., Li, G., Liu, J.: Private rank aggregation under local differential privacy. Int. J. Intell. Syst. 35(10), 1492–1519 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Ding, Q., Sun, K., Jiang, L., Zhou, H., Zhou, C. (2023). Differentially Private Probabilistic Social Choice in the Shuffle Model. In: Huynh, VN., Le, B., Honda, K., Inuiguchi, M., Kohda, Y. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2023. Lecture Notes in Computer Science(), vol 14375. Springer, Cham. https://doi.org/10.1007/978-3-031-46775-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-46775-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-46774-5
Online ISBN: 978-3-031-46775-2
eBook Packages: Computer ScienceComputer Science (R0)