Inequality in the Age of Pseudonymity
This addresses a critical issue for policymakers and researchers using inequality measures on digital platforms, revealing fundamental flaws in current methods when applied to pseudonymous data.
The paper tackles the problem of measuring inequality in pseudonymous settings where fake identities (Sybils) exist, showing that canonical inequality measures like the Gini coefficient cannot accurately assess inequality in such environments due to inherent limitations. It characterizes Sybil-proof measures and proves that popular measures fail this criterion, with concrete examples including the Gini coefficient.
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.