发表机构
Dipartimento di Scienze Economiche e Statistiche, Università Federico II; Department of Computer Information Systems, Indiana University Northwest; School of Business and Economics, Indiana University Northwest（那不勒斯费德里科二世大学; 印第安纳大学西北分校; 印第安纳大学西北分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画可数无限社会中匿名联盟策略性防操纵的二元社会选择函数，证明其等价于三角网格上的超序闭子集，并给出含缺失边界角点的几何分类与四种广义锯齿参数化形式。
AI 中文摘要
我们研究当选民社会为可数无限时，在普遍弱偏好域上的匿名二元社会选择函数。选民可能严格支持两个备选方案之一，或持无所谓态度，并且非可操纵性以联盟策略性防操纵的形式被要求。完全匿名性将关于联盟的相关信息不仅缩减为其基数，而且缩减为其基数特征：大小为\(k\)的有限集、具有无限补集的无限集、或补集大小为\(k\)的余有限集。记录两个严格支持联盟的特征产生一个无限三角网格，按对一个备选方案支持增加而对另一个支持减少排序。我们证明匿名联盟策略性防操纵二元社会选择函数恰好是由该网格的超序闭子集（即上集）所获得的那些函数。然后我们给出这些子集的几何分类。与有限选民情形不同，它们不必由其极小元素生成：可数无限性产生了对应于有限反对或余有限严格支持的缺失边界区域。我们证明这些子集由真实或缺失边界角点精确表示，并导出一个由反链以及（必要时）一个例外缺失边界区域组成的非冗余参数化。这产生了四种广义锯齿形式，并完成了有限选民已知几何表示在无限社会中的对应物。
英文摘要
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.
