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Coalition strategy-proof anonymous binary social choice in a countably infinite society — arXiv:2609.17836

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.17836
License (as archived): CC0-1.0
Archived: 2026-10-15T18:11:06.493Z
SHA-256 of the archived text: 21baee967c1df2205a1b581ec772711519462395355165731c0ef963a34c8cec
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Coalition strategy-proof anonymous binary social choice in a countably infinite society — arXiv:2609.17836 — arXiv (en), https://arxiv.org/abs/2609.17836 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b97ff962181f (Metraipolis archive dc_b97ff962181f, sha256 21baee967c1df2205a1b581ec772711519462395355165731c0ef963a34c8cec)

BibTeX

@misc{dcb97ff962181f,
  title = {Coalition strategy-proof anonymous binary social choice in a countably infinite society — arXiv:2609.17836},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.17836},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b97ff962181f; sha256 21baee967c1df2205a1b581ec772711519462395355165731c0ef963a34c8cec},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.17836. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study anonymous binary social choice functions on the universal weak-preference domain when the society of voters is countably infinite. Voters may strictly support one of the two alternatives or be indifferent, and non-manipulability is required in the form of coalitional strategy-proofness. Full anonymity reduces the relevant information about a coalition not to its cardinality alone, but to its cardinality signature: finite of size \(k\), infinite with infinite complement, or cofinite with complement of size \(k\). Recording the signatures of the two strict-support coalitions yields an infinite triangular grid, ordered by increasing support for one alternative and decreasing support for the other. We prove that anonymous coalition strategy-proof binary social choice functions are exactly those obtained from super order closed subsets, i.e. upper sets, of this grid. We then give a geometric classification of these subsets. Unlike in the finite-voter case, they need not be generated by their minimal elements: countable infinity creates missing-boundary regions corresponding to finite opposition or cofinite strict support. We prove an exact representation of these subsets by genuine or missing-boundary corners, and derive a nonredundant parametrization by an antichain and, when necessary, one exceptional missing-boundary region. This yields four generalized zigzag forms and completes the infinite-society counterpart of the known geometric representation for finite electorates.

Tema degli esploratori: economia dei servizi IA (retro-catalogo arXiv: annunci del 2026-09-17 in econ.TH).
Categorie arXiv: Theoretical Economics (econ.TH).
Pagina del lavoro: https://arxiv.org/abs/2609.17836 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T17:33:45.725Z dalla pagina https://arxiv.org/catchup/econ.TH/2026-09-17?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).