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机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究刻画了满足四项公理的索赔问题分配规则，证明其构成单参数对数指数族，包含CEA、CEL及比例规则等特例，且连续性可由其他公理导出。
AI 中文摘要
我们刻画了满足同等者同等对待、双边一致性、向下合成与向上合成的索赔问题分配规则。这些规则恰好是单参数对数指数族$\{r^θ\}_{θ\in[-\infty,+\infty]}$的成员，其端点为约束平均授予（CEA）和约束平均损失（CEL）。对于有限$θ$，$r^θ$是效用为$u_θ=\logφ_θ$的授予端等牺牲规则，其中$φ_θ(x):=\frac{e^{θx}-1}θ\quad(θ\ne0)$，$φ_0(x):=x$，同时也是对偶效用$u_{-θ}$的损失端等牺牲规则。比例规则为其中点，即$θ=0$。规则的连续性并非假设前提，而是其他公理的推论。
英文摘要
We characterise the division rules for claims problems that satisfy equal treatment of equals, bilateral consistency, composition down, and composition up. The rules are precisely the members of a one-parameter log-exponential family $\{r^θ\}_{θ\in[-\infty,+\infty]}$, with constrained equal awards (CEA) and constrained equal losses (CEL) as its endpoints. For finite $θ$, $r^θ$ is the equal-sacrifice rule in awards for $u_θ=\logφ_θ$, where \[ φ_θ(x):=\frac{e^{θx}-1}θ\quad(θ\ne0), \qquad φ_0(x):=x, \] and simultaneously the equal-sacrifice rule in losses for the dual utility $u_{-θ}$. The proportional rule is the midpoint, $θ=0$. Continuity of the rules are not assumed but a consequence of the other axioms.
