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Inequality measures such as the Gini coefficient are used to inform and motivate public policymaking, and are increasingly applied to digital platforms.
We analyze how measures fare in pseudonymous settings, as common to internet-based or blockchain-based platforms.
One key challenge that arises is the ability of actors to create multiple 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 inadvertently distort inequality metrics.
We prove a set of impossibilities for Sybil-proof measures that simultaneously satisfy subsets of the literature's canonical set of desired properties, and show that a wide range of commonly used measures are indeed sensitive to Sybil manipulations, including the famous Gini coefficient.
We present several classes of Sybil-proof measures, and, by fully characterizing them, we prove that the structure imposed restricts their ability to assess inequality at a fine-grained level.
In addition, we examine which popular inequality metrics are vulnerable to Sybil manipulations and the dynamics that result in the creation of Sybils, whether in pseudonymous settings or traditional ones.
