Inequality measures such as the Gini coefficient are used to inform and motivate policymaking, and are increasingly applied to digital platforms. We analyze how measures fare in pseudonymous settings that are common in the digital age. One key challenge of such environments is the ability of actors to create fake identities under fictitious false names, also known as ``Sybils.'' While some actors may do so to preserve their privacy, we show that this can hamper inequality measurements: it is impossible for measures satisfying the literature's canonical set of desired properties to assess the inequality of an economy that may harbor Sybils. We characterize the class of all Sybil-proof measures, and prove that they must satisfy relaxed version of the aforementioned properties. Furthermore, we show that the structure imposed restricts the ability to assess inequality at a fine-grained level. We then apply our results to prove that popular measures are not Sybil-proof, with the famous Gini coefficient being but one example out of many. Finally, we examine dynamics leading to the creation of Sybils in digital and traditional settings.

翻译：不平等度量指标（如基尼系数）常被用于指导政策制定并推动其动机，近年来也越来越多地应用于数字平台。我们分析了这些度量指标如何在数字时代常见的伪名环境中运作。此类环境的核心挑战在于，参与者能够以虚构假名创建虚假身份（即“女巫攻击”）。尽管部分参与者可能出于保护隐私的目的这样做，但我们发现这种行为会阻碍不平等度量——满足文献中经典公理化性质的度量指标无法评估可能存在女巫攻击的经济体的不平等程度。我们刻画了所有抗女巫攻击度量指标的类，并证明它们必须满足上述性质的松弛版本。进一步研究表明，这种结构限制会削弱对不平等进行细粒度评估的能力。最后，我们将上述结论应用于证明：包括著名的基尼系数在内，诸多流行度量指标均不具备抗女巫攻击性。我们同时探讨了数字与传统环境中导致女巫攻击产生的动态机制。