时序选举：福利、防策略性与比例性
Temporal Elections: Welfare, Strategyproofness, and Proportionality
AI总结：
本文研究了每轮选择单一备选项的序贯决策模型，探讨了最大化功利主义和平等主义福利的计算复杂性，及其与防策略性和比例性的兼容性，并提出了相应的算法与复杂性边界。
摘要：
我们研究了一种序贯决策模型，其中每一轮选择一个备选项。我们关注两个目标——功利主义福利（Util）和平等主义福利（Egal）——并考虑最大化这些目标的计算复杂性，以及它们与防策略性和比例性的兼容性。我们观察到最大化 Util 是容易的，但即使在受限情况下，Egal 对应的决策问题也是 NP 完全的。我们通过参数化复杂性分析和近似算法补充了 Egal 的这一硬度结果。此外，我们表明，虽然输出最大化 Util 结果的机制是防策略的，但所有用于计算最大化 Egal 结果的确定性机制都未能通过一种非常弱的防策略性变体，称为非显然可操纵性（NOM）。然而，我们证明当智能体在每个时间步具有非空批准集时，在按字典序打破平局的同时选择最大化 Egal 的结果满足 NOM。关于比例性，我们证明比例（PROP）结果可以被高效计算，但在保证 PROP 的同时寻找最大化 Util 的结果是 NP 困难的。我们还推导了关于 Util 和 Egal 的比例性（强）代价的上下界。我们的部分结果可推广至 Egal 和 Util 之外的 p-均值福利度量。
英文摘要：
We investigate a model of sequential decision-making where a single alternative is chosen at each round. We focus on two objectives -- utilitarian welfare (Util) and egalitarian welfare (Egal) -- and consider the computational complexity of maximizing these objectives, as well as their compatibility with strategyproofness and proportionality. We observe that maximizing Util is easy, but the corresponding decision problem for Egal is NP-complete even in restricted cases. We complement this hardness result for Egal with parameterized complexity analysis and an approximation algorithm. Additionally, we show that, while a mechanism that outputs an outcome that maximizes Util is strategyproof, all deterministic mechanisms for computing outcomes that maximize Egal fail a very weak variant of strategyproofness, called non-obvious manipulability (NOM). However, we show that when agents have non-empty approval sets at each timestep, choosing an Egal-maximizing outcome while breaking ties lexicographically satisfies NOM. Regarding proportionality, we prove that a proportional (PROP) outcome can be computed efficiently, but finding an outcome that maximizes Util while guaranteeing PROP is NP-hard. We also derive upper and lower bounds on the (strong) price of proportionality with respect to Util and Egal. Some of our results extend to $p$-mean welfare measures other than Egal and Util.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
