A Geometric Welfare-Sensitive Development Index for Indian States and Union Territories: Reassessing Spatial Inequality through Multidimensional Distributional Diagnostics

Spatial inequality in India is frequently assessed using composite indices that conflate welfare achievements with settlement characteristics, thereby blurring the sources of inter-territorial disparity. This study constructs a three-dimensional Welfare-sensitive Development Index for all 36 Indian states and Union Territories using literacy rate, per capita Gross State Domestic Product, and sex ratio for 2011 and a modeled 2021 scenario. Population density is excluded on theoretical grounds because its welfare polarity is indeterminate without corroborating evidence on service quality and environmental burden. Each indicator is transformed into a ratio-to-mean coefficient and aggregated using a geometric mean to reduce perfect compensability across dimensions. Distributional structure is evaluated using the coefficient of variation, Gini coefficient, Theil index, and Atkinson index, complemented by dimensional balance and binding-constraint diagnostics and rank stability tests. Results show that per capita GSDP is the dominant source of inter-state inequality, with a 2021 coefficient of variation of 55.51 percent, Gini of 0.293, and Theil index of 0.137, whereas literacy and sex ratio display substantially lower dispersion. The composite index shows moderate inequality with a coefficient of variation of 19.72 percent, Gini of 0.110 and Theil index of 0.019. Goa, Delhi and Sikkim emerge as the top three in the 2021 ranking, whereas Bihar, Uttar Pradesh and Jharkhand are the bottom three. Per capita GSDP is the binding constraint for 19 of 36 units. The findings imply that addressing spatial inequality in India requires strengthening productive regional economies along with human capability formation rather than isolated improvements in social indicators.