有害决策的比例公平性
Proportional Fairness for Harmful Decisions
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中文总结 AI 辅助
研究公共坏品分配问题，引入针对公共坏品的核心形式化定义，在特定条件下零尊重林达尔均衡满足定义且有公平保证、推广CEEI，无此条件时有不良行为及不可能性结果，还给出归约规则，为该领域研究奠定基础。
中文摘要 AI 辅助
我们研究（可分割的）公共坏品的分配问题，即参与者为不同选择承担成本，目标是从这些选择中挑选一个概率分布。我们表明，公共物品、私人物品和私人坏品（杂务）分配中比例代表制的核心标准——传统的核心定义，在公共坏品分配中并不适用。我们引入了两种针对公共坏品量身定制的核心形式化定义。在一个包含私人坏品分配的结构条件下，我们证明零尊重林达尔均衡满足这两种形式化定义，具有额外的公平保证，并且严格推广了私人坏品分配中的等收入竞争均衡（CEEI）。没有这个结构条件时，我们表明林达尔均衡表现出不良行为，证明了区分公共坏品和公共物品的尖锐不可能性结果，但表明一种使用向公共物品归约的规则恢复了我们的一种核心形式化定义。我们的结果为研究公共坏品的公平分配奠定了基础，这是一个被忽视但基本的问题，并突出了几个仍未解决的结构和算法方向。
英文摘要
We study allocation of (divisible) public bads, where agents incur costs for alternatives and the goal is to pick a lottery over the alternatives. We show that the traditional definitions of the core, a central criterion of proportional representation for allocation of public goods, private goods, and private bads (chores), do not make sense for allocation of public bads. We introduce two formalizations of the core tailored to public bads. Under a structural condition which subsumes allocation of private bads, we show that zero-respecting Lindahl equilibria satisfy both formalizations, exhibit additional fairness guarantees, and strictly generalize competitive equilibria from equal incomes (CEEI) for allocation of private bads. Without this structural condition, we show that Lindahl equilibria exhibit undesirable behaviors, prove sharp impossibility results separating public bads from public goods, but show that a rule using a reduction to public goods recovers one of our formalizations of the core. Our results lay the groundwork for studying fair allocation of public bads, an overlooked yet fundamental problem, and highlight several structural and algorithmic directions that remain open.
