Inequality in the Age of Pseudonymity

TL;DR

This paper investigates the challenges of measuring inequality in digital environments with pseudonymity and Sybil attacks, showing that popular measures like the Gini coefficient are vulnerable to manipulation and proposing the characteristics of Sybil-proof inequality measures.

Contribution

It characterizes the class of all Sybil-proof inequality measures and demonstrates that popular measures are not Sybil-proof, highlighting limitations in current inequality assessment methods.

Findings

Popular inequality measures are not Sybil-proof.

Sybil-proof measures must satisfy relaxed properties.

Creating Sybils hampers accurate inequality measurement.

Abstract

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.