We study organizational elections in which each group nominates one candidate and receives as payoff its members expected utility under a probabilistic winning rule. We empirically justify a standard monotonicity assumption by simulating two- and three-group elections, finding that a candidates aggregate voter utility correlates monotonically with win probability. For three or more groups, we show that pure-strategy Nash equilibria (PSNE) may fail to exist even under egoistic preferences, and that deciding PSNE existence is NP-complete in a succinct (general form) representation. For cross-monotone winning-probability functions, we give simple sufficient conditions for PSNE existence and an FPT algorithm to compute one, parameterized by the number of irresolute groups and nominating depth. Finally, for crossmonotone, order-preserving winning-probability functions, we bound the price of anarchy of egoistic games by the number of groups.

翻译：我们研究组织选举，其中每个团体提名一名候选人，并根据概率性获胜规则获得其成员期望效用作为收益。通过模拟两团体和三团体选举，我们实证验证了标准单调性假设，发现候选人的总选民效用与获胜概率呈单调相关。对于三个或更多团体，我们证明即使存在利己偏好，纯策略纳什均衡也可能不存在，且判定纯策略纳什均衡存在性在简洁（一般形式）表示下是NP完全问题。针对交叉单调获胜概率函数，我们给出纯策略纳什均衡存在的简单充分条件，并提出一种以无决议团体数量和提名深度为参数的FPT算法来计算均衡。最后，对于交叉单调且保序的获胜概率函数，我们通过团体数量界定了利己博弈的无政府代价。