Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that each agent specifies a weak order on single alternatives, from which a preference relation over subsets is derived using some preference extension. We consider five prominent extensions (responsive, downward lexicographic, upward lexicographic, best, and worst). For each of them, we consider the corresponding Pareto optimality notion, and we study the complexity of computing and verifying Pareto optimal outcomes. For each of the preference extensions, we give a complete characterization of the complexity of testing Pareto optimality when preferences are dichotomous or linear. We also consider strategic issues: for four of the set extensions, we present a linear-time, Pareto optimal and strategyproof algorithm that even works for weak preferences.

中文翻译：

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计算和测试帕累托最优委员会

根据代理人的偏好选择一组备选方案是委员会选择及其他方面的重要问题。在提出委员会可取性的各种标准中，帕累托最优性是最低且重要的要求。由于要求代理商在指数选择的多个子集上指定其偏好实际上是不可行的，因此我们假设每个代理商在单个选择上指定一个弱顺序，使用某些偏好扩展从中推导出子集的偏好关系。我们考虑了五个突出的扩展（响应式，向下词典序，向上词典序，最佳和最差）。对于它们中的每一个，我们都考虑相应的帕累托最优概念，并且研究计算和验证帕累托最优结果的复杂性。对于每个首选项扩展，当偏好为二分或线性时，我们给出了检验帕累托最优性的复杂性的完整特征。我们还考虑战略问题：对于四个扩展集，我们提出了线性时间，帕累托最优和策略证明算法，该算法甚至适用于弱偏好。