Shannon Entropy for Quantifying Uncertainty and Risk in Economic Disparity

The rise in economic disparity presents significant risks to global social order and the resilience of local communities. However, existing measurement science for economic disparity (e.g., the Gini coefficient) does not explicitly consider a probability distribution with information, deficiencies, and uncertainties associated with the underlying income distribution. This article introduces the quantification of Shannon entropy for income inequality across scales, including national-, subnational-, and city-level data. The probabilistic principles of Shannon entropy provide a new interpretation for uncertainty and risk related to economic disparity. Entropy and information-based conflict rise as world incomes converge. High-entropy instances can resemble both happy and prosperous societies as well as a socialist-communist social structure. Low entropy signals high-risk tipping points for anomaly and conflict detection with higher confidence. Finally, spatial-temporal entropy maps for U.S. cities offer a city risk profiling framework. The results show polarization of household incomes within and across Baltimore, Washington, DC, and San Francisco. Entropy produces reliable results at significantly reduced computational costs than Gini coefficients.