Abstract
We study inequality measurement under socially constrained observability and introduce a local Gini coefficient computed on ego-centered comparison sets, rep- resented as fixed-width rank windows along Pen’s income parade. For a linear parade, the discrete sliding-window local Gini admits an exact closed form and is strictly below the population Gini, with rank monotonicity. For curved parades, the paper uses a first-order quantile approximation to derive explicit rank profiles for exponential and Pareto regimes and validates these profiles against finite-sample sliding-window Ginis in simulations. The framework implies systematic rank het- erogeneity in locally perceived inequality, inequality order reversals across societies relative to population Ginis (including majority misranking in the Pareto–linear comparison for 1 < α < 2 in the continuous-rank sense), and subunit-elastic local responses to changes in inequality within the Pareto family