Bayesian Bradley-Terry Framework for Ranking Multi-Indicator Entities: Application to Indian States and Union Territories

Often, real-world entities are explained by multiple indicators, and ranking those is challenging, e.g., administrative units, sport teams, and machine learning models. Existing methodologies rely on single indicators or composite indices, leaving a gap for frameworks capable of handling multi-indicator scenarios. We present a ranking methodology motivated by the Bayesian Bradley-Terry (BT) model. We convert indicators to paired comparisons to utilize the BT framework. The prior covariance of the BT latent merit parameters is modeled as a function of a covariate to accommodate prior information. For parameter estimation, we use a Markov chain Monte Carlo (MCMC) algorithm that employs a hybrid Metropolis--Hastings scheme with a preconditioned Crank--Nicolson proposal and Gibbs sampling. We show that the proposed estimator converges. Furthermore, we propose a problem-specific stopping rule based on ranking stability. To demonstrate the methodology's practical utility, we apply it to rank the states and union territories (UTs) of India using multi-indicator data from the National Family Health Survey-5. By estimating and comparing rankings across various economic regimes, including low-income, mid-income, and outlier-excluded subsets, our application uncovers meaningful deviations between regional economic standing and overall developmental performance, illustrating the framework's broad value for resolving complex multidimensional ranking problems.