The constrained equal welfare rule, $f^{CE}$, distributes the surplus according to the uniform gains method and, hence, equalizes the welfare of the agents subsequent to the allocation process, subject to making nobody worse off. We show that $f^{CE}$ is the unique rule on the domain of surplus-sharing problems that satisfies efficiency, welfare monotonicity, path independence, and weak less first imposing an egalitarian bound for allowing positive payoffs to particular players. We provide an additional axiomatization employing consistency, a classical invariance property with respect to changes of the population. Finally, we show that the set of efficient solutions for cooperative TU games that support constrained welfare egalitarianism, i.e., distribute increments in the worth of the grand coalition according to $f^{CE}$, is characterized by aggregate monotonicity and bounded pairwise fairness requiring that a player can only gain if his initial payoff does not exceed the initial payoff of any other player by the amount to be divided.

受约束的平等福利规则， $F^{CË}$，根据统一收益法分配盈余，因此，在分配过程之后，均衡了代理人的福利，这会使任何人的处境变得更糟。我们证明$F^{CË}$这是在满足效率，福利单调性，路径独立性和弱势性的盈余共享问题领域的唯一规则，首先要施加平等主义的界限，以允许特定参与者获得积极的回报。我们提供了使用一致性的另一种公理化方法，一致性是关于人口变化的经典不变性。最后，我们证明了针对合作社TU游戏的有效解决方案集，这些游戏支持受约束的福利平等主义，即根据$F^{CË}$的特征在于总的单调性和有界的成对公平性，要求玩家仅在其初始收益不超过任何其他玩家的初始收益除以要除的金额后才能获得收益。