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