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Iterative Deliberation via Metric Aggregation

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Algorithmic Decision Theory (ADT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13023))

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Abstract

We investigate an iterative deliberation process for an agent community wishing to make a joint decision. We develop a general model consisting of a community of n agents, each with their initial ideal point in some metric space (Xd), such that in each iteration of the iterative deliberation process, all agents move slightly closer to the current winner, according to some voting rule \(\mathcal {R}\). For several natural metric spaces and suitable voting rules for them, we identify conditions under which such an iterative deliberation process is guaranteed to converge.

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Notes

  1. 1.

    Indeed, the result of such deliberation may be the opposite – that the right-winger would be radicalized; we do not focus on such cases, but mention them in Sect. 8.

  2. 2.

    Indeed, for some sparse spaces these two constraints may not be always satisfiable, as agents moving towards the current winner may need to jump “too far”. In the metric spaces we consider in this paper there is always at least a specific \(\epsilon \) for which these constraints are indeed satisfiable.

  3. 3.

    We use “T” and not the standard “d”, as “d” is taken by the metric space (Xd).

References

  1. Arrow, K.: Advances in the Spatial Theory of Voting. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  2. Austen-Smith, D., Feddersen, T.: Deliberation and voting rules. In: Austen-Smith, D., Duggan, J. (eds.) Social Choice and Strategic Decisions. SCW, pp. 269–316. Springer, Heidelberg (2005). https://doi.org/10.1007/3-540-27295-X_11

    Chapter  MATH  Google Scholar 

  3. Austen-Smith, D., Feddersen, T.J.: Deliberation, preference uncertainty, and voting rules. Am. Polit. Sci. Rev., 209–217 (2006)

    Google Scholar 

  4. Brandt, F., Conitzer, V., Endriss, U., Procaccia, A.D., Lang, J.: Handbook of Computational Social Choice. Cambridge University Press, Cambridge (2016)

    Google Scholar 

  5. Bulteau, L., Shahaf, G., Shapiro, E., Talmon, N.: Aggregation over metric spaces: proposing and voting in elections, budgeting, and legislation. J. Artif. Intell. Res. 70, 1413–1439 (2021)

    Article  MathSciNet  Google Scholar 

  6. Cohen, J., Bohman, J., Rehg, W.: Deliberation and democratic legitimacy, 1997, pp. 67–92 (1989)

    Google Scholar 

  7. Elkind, E., Grossi, D., Shapiro, E., Talmon, N.: United for change: deliberative coalition formation to change the status quo. In: Proceedings of AAAI 2021, vol. 35, pp. 5339–5346 (2021)

    Google Scholar 

  8. Fain, B., Goel, A., Munagala, K., Sakshuwong, S.: Sequential deliberation for social choice. In: Devanur, N.R., Lu, P. (eds.) WINE 2017. LNCS, vol. 10660, pp. 177–190. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71924-5_13

    Chapter  Google Scholar 

  9. Faliszewski, P., Gonen, R., Kouteckỳ, M., Talmon, N.: Opinion diffusion and campaigning on society graphs. In: Proceedings of IJCAI 2018, pp. 219–225 (2018)

    Google Scholar 

  10. Faliszewski, P., Skowron, P., Slinko, A., Szufa, S., Talmon, N.: How similar are two elections? In: Proceedings of AAAI 2019, vol. 33, pp. 1909–1916 (2019)

    Google Scholar 

  11. Faliszewski, P., Skowron, P., Slinko, A., Szufa, S., Talmon, N.: Isomorphic distances among elections. In: Proceedings of CSR 2020, pp. 64–78 (2020)

    Google Scholar 

  12. Faliszewski, P., Skowron, P., Slinko, A., Talmon, N.: Multiwinner voting: a new challenge for social choice theory. Trends Comput. Soc. Choice 74, 27–47 (2017)

    Google Scholar 

  13. Faliszewski, P., Slinko, A., Talmon, N.: Multiwinner rules with variable number of winners. In: Proceedings of ECAI 2020 (2020)

    Google Scholar 

  14. Garg, N., Kamble, V., Goel, A., Marn, D., Munagala, K.: Iterative local voting for collective decision-making in continuous spaces. J. Artif. Intell. Res. 64, 315–355 (2019)

    Article  MathSciNet  Google Scholar 

  15. Grandi, U.: Social choice and social networks. Trends Comput. Soc. Choice, 169–184 (2017)

    Google Scholar 

  16. Hogrebe, T.: Complexity of distances in elections: doctoral consortium. In: Proceedings of AAMAS 2019, pp. 2414–2416 (2019)

    Google Scholar 

  17. Lang, J., Xia, L.: Voting in combinatorial domains. In: Handbook of Computational Social Choice, pp. 197–222. Cambridge University Press, Cambridge (2016)

    Google Scholar 

  18. Lizzeri, A., Yariv, L.: Sequential deliberation (2010). SSRN 1702940

    Google Scholar 

  19. Meir, R.: Iterative voting. Trends in Comput. Soc. Choice, 69–86 (2017)

    Google Scholar 

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Acknowledgments

Nimrod Talmon and Eyal Leizerovich were supported by the Israel Science Foundation (ISF; Grant No. 630/19).

Most importantly, we thank the Hoodska Explosive for years of fun.

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Zvi, G.B., Leizerovich, E., Talmon, N. (2021). Iterative Deliberation via Metric Aggregation. In: Fotakis, D., Ríos Insua, D. (eds) Algorithmic Decision Theory. ADT 2021. Lecture Notes in Computer Science(), vol 13023. Springer, Cham. https://doi.org/10.1007/978-3-030-87756-9_11

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  • DOI: https://doi.org/10.1007/978-3-030-87756-9_11

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  • Online ISBN: 978-3-030-87756-9

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