时间投票中具有排序偏好的比例代表制

中文摘要 AI 辅助

我们研究时间投票中的比例代表制，其中每轮选出一名候选人。虽然先前的工作集中于批准投票，但我们考虑排序偏好，这种偏好可能随时间变化。一种自然的方法是将每位选民的最优候选人视为被批准，但正确的截止点可能因选民和轮次而异。因此，我们要求比例性对每个可接受的截止点选择都成立，无论截止点是固定且共同的、共同但随轮次变化，还是为每位选民在每轮中单独设定。将这些解释与正当代表制（JR）、比例正当代表制（PJR）、扩展正当代表制（EJR）以及固体联盟的比例性（PSC）的时间版本相结合，我们得到一组公理层级。我们询问这些公理中哪些可以被保证，以及需要多少未来知识。与批准投票不同，任何版本的EJR都无法被保证，而对于其他公理，截止点的灵活性是有代价的。在固定共同截止点下，JR、PJR和PSC可以被保证，但只能通过预先看到所有偏好的规则来实现。一旦截止点可能随轮次变化，即使这样的规则也无法为仅在部分轮次中达成一致的群体保证JR或PSC。然而，对于在每轮中都达成一致的群体，仅知道轮次数就足以在多项式时间内实现PJR，而PSC则完全不需要未来知识。在个体截止点下，任何版本的JR或PJR都无法被保证，但像串行独裁这样简单的规则可以实现PJR，其加性损失是任何规则都无法改善的，无论它知道多少。自然的偏好限制恢复了精确保证。最后，我们表明检查我们的公理通常是coNP完全的；但也许令人惊讶的是，更强的公理可能更容易检查。

英文摘要

We study proportional representation in temporal voting, where one candidate is selected in each round. While prior work has focused on approval ballots, we consider ranked preferences, which may change over time. A natural approach treats each voter's top candidates as approved, but the right cutoff may differ across voters and rounds. We therefore require proportionality to hold for every admissible choice of cutoffs, whether fixed and common, common but varying across rounds, or set individually for each voter in each round. Combining these interpretations with temporal versions of justified representation (JR), proportional JR (PJR), extended JR (EJR), and proportionality for solid coalitions (PSC) gives us a hierarchy of axioms. We ask which of these axioms can be guaranteed, and with how much knowledge of the future. Unlike with approval ballots, no version of EJR can be guaranteed, and for the other axioms, flexibility in the cutoffs comes at a price. With a fixed common cutoff, JR, PJR, and PSC can be guaranteed, but only by rules that see all preferences in advance. Once the cutoff may vary across rounds, even such rules cannot guarantee JR or PSC for groups that agree in only some rounds. For groups that agree in every round, however, knowing only the number of rounds suffices for PJR in polynomial time, and PSC needs no knowledge of the future at all. Under individual cutoffs, no version of JR or PJR can be guaranteed, yet a rule as simple as serial dictatorship achieves PJR up to an additive loss that no rule can improve on, however much it knows. Natural preference restrictions restore exact guarantees. Finally, we show that checking our axioms is often coNP-complete; but perhaps surprisingly, a stronger axiom can be easier to check.

发表机构

• Ariel University（阿里埃勒大学）
• University of Oxford（牛津大学）

机构由 AI 辅助整理，请以论文原文为准。