Dokow and Holzman determined which predicates over $\{0, 1\}$ satisfy an analog of Arrow's theorem: all unanimous aggregators are dictatorial. Szegedy and Xu, extending earlier work of Dokow and Holzman, extended this to predicates over arbitrary finite alphabets. Mossel extended Arrow's theorem in an orthogonal direction, determining all aggregators without the assumption of unanimity. We bring together both threads of research by extending the results of Dokow-Holzman and Szegedy-Xu to the setting of Mossel. As an application, we determine, for each symmetric predicate over $\{0,1\}$, all of its aggregators.

翻译：Dokow与Holzman确定了在$\{0, 1\}$上满足阿罗定理类比性质的谓词：所有一致性聚合器均为独裁型。Szegedy与Xu在Dokow和Holzman早期工作的基础上，将该结论推广至任意有限字母表上的谓词。Mossel则从另一方向拓展了阿罗定理，在不假设一致性的条件下确定了所有聚合器的特征。本研究通过将Dokow-Holzman与Szegedy-Xu的结论推广至Mossel的研究框架，整合了这两条研究脉络。作为应用，我们针对$\{0,1\}$上的每个对称谓词，完整刻画了其所有可能的聚合器。