We consider the problem of fairly reallocating the individual endowments of a perfectly divisible good among agents with single-peaked preferences. As agents may have different individual endowments in this problem, the standard concept of envy-freeness cannot be applied directly. Thus, we propose a new concept of fairness, which we call envy-freeness for similarities. It requires that each agent whose best amount is strictly greater (less) than his individual endowment should not envy another agent whose best amount and assignment are strictly greater (less) than her individual endowment. We then construct a rule satisfying envy-freeness for similarities and some other desirable properties. In doing so, we propose a new extension of the well-known uniform rule for the reallocation problem, which we call the gross uniform reallocation rule. Moreover, we show that the gross uniform reallocation rule is the only rule that satisfies efficiency, individual rationality, strategy-proofness, and envy-freeness for similarities.

我们考虑一个问题，即在具有单一语言偏好的代理商之间公平地重新分配完全可分割的商品的个人individual赋。由于代理人在此问题上可能具有不同的个人end赋，因此无法直接应用无羡慕的标准概念。因此，我们提出了一个新的公平概念，我们称其为相似性羡慕自由 。它要求每个最佳代理人的最佳金额严格大于（小于）其个人end赋的代理人不应羡慕另一个代理人，其最佳金额和工作分配严格大于（小于）其个人end赋。然后，我们为相似性构造一个满足嫉妒自由的规则 和其他一些理想的属性。在此过程中，我们提出了对重新分配问题的众所周知的统一规则的新扩展，我们称其为总统一重新分配规则。而且，我们表明，总的统一重新分配规则是满足相似性效率，个人理性，策略证明和嫉妒 自由的唯一规则。