Majority voting is not good for heaven or hell, with mirrored performance

[2401.00592] Majority voting is not good for heaven or hell, with mirrored performance Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Physics and Society arXiv:2401.00592 (physics) [Submitted on 31 Dec 2023 ( v1 ), last revised 14 Aug 2026 (this version, v6)] Title: Majority voting is not good for heaven or hell, with mirrored performance Authors: Pavel Chebotarev , Vadim Afonkin View a PDF of the paper titled Majority voting is not good for heaven or hell, with mirrored performance, by Pavel Chebotarev and Vadim Afonkin View PDF HTML (experimental) Abstract: The ViSE (Voting in Stochastic Environment) model studies voting strategies and social decision rules under a stochastic agenda of proposals with random gains. The pit-of-losses paradox established earlier shows that, in hostile ("hell") environments, majority voting can be worse than rejecting all proposals. We show a counterpart in favorable ("heaven") environments, where majority voting can be worse than accepting all proposals. A one-line identity underlies this symmetry: for an antisymmetric voting body, the expected capital gain of each agent under a gain generator of mean $\mu>0$ exceeds that under the opposite generator by exactly $\mu$. Complementary voting strategies together with a complementary social decision rule provide a broad sufficient, but not necessary, condition for antisymmetry. This includes symmetrized majority with individualistic, utilitarian-group, and majoritarian-group strategies. For symmetric location families, the result yields mirror symmetry of performance relative to the baseline that rejects all proposals in unfavorable environments and accepts all in favorable ones. We also strengthen the Gaussian pit-of-losses result: simple majority has a pit in every society of $n>2$ individualists, and every rule requiring at least $r$ of $n$ votes, $r<n$, has one as well, while unanimity avoids the pit. Finally, under complementary strategies, optimal voting thresholds inherit the mirror structure. For stochastic vote-count rules under the same condition, a complementary optimal rule can always be selected, and optimal total performance is even in $\mu$ in symmetric location families. In the two-plus-trio paradox, the optimal vote-count rule outperforms all threshold rules even in a neutral symmetric environment. Comments: 34 pages, 5 figures. Submitted to a journal. The manuscript has been extended Subjects: Physics and Society (physics.soc-ph) ; Computer Science and Game Theory (cs.GT); Optimization and Control (math.OC) MSC classes: 91B12, 91B14, 91B70, 91B15 Cite as: arXiv:2401.00592 [physics.soc-ph] (or arXiv:2401.00592v6 [physics.soc-ph] for this version) https://doi.org/10.48550/arXiv.2401.00592 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Pavel Chebotarev [ view email ] [v1] Sun, 31 Dec 2023 21:59:40 UTC (329 KB) [v2] Tue, 16 Jan 2024 13:55:19 UTC (328 KB) [v3] Wed, 11 Dec 2024 14:41:48 UTC (439 KB) [v4] Sun, 13 Apr 2025 10:53:35 UTC (467 KB) [v5] Sat, 20 Dec 2025 19:03:51 UTC (491 KB) [v6] Fri, 14 Aug 2026 19:09:43 UTC (976 KB) Full-text links: Access Paper: View a PDF of the paper titled Majority voting is not good for heaven or hell, with mirrored performance, by Pavel Chebotarev and Vadim Afonkin View PDF HTML (experimental) TeX Source view license Current browse context: physics.soc-ph < prev | next > new | recent | 2024-01 Change to browse by: cs cs.GT math math.OC physics References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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