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.

Trust mechanisms diverge between centralized and decentralized exchanges, representing distinct sociotechnical governance paradigms. However, quantifying trust dynamics and their redistribution between these architectures remains empirically challenging, limiting understanding of how institutional shocks affect market behavior. The FTX collapse offers a natural experiment to bridge this gap. Through an interdisciplinary approach combining causal inference and computational text analysis, we find significant price declines and capital reallocation from centralized to decentralized exchanges following the event. While sentiment metrics showed no sharp discontinuities, topic modeling and network analysis of Discord communities reveal that seasonal holiday discourse obscured underlying trust concerns in centralized exchange forums. These findings underscore the fragility of institutional trust architectures and demonstrate how mixed methods can illuminate behavioral patterns during systemic crises, offering insights for exchange risk management and regulatory assessment.