Ranking geographical or administrative units, such as countries or states, is a well-known approach for comparing developmental progress and informing evidence-based policymaking. Existing ranking methodologies typically rely on a single indicator, such as Gross Domestic Product (GDP), or a limited subset of indicators, e.g., the Human Development Index (HDI). However, to the best of our knowledge, a ranking methodology based on a large set of indicator variables is not available in the literature. To address this gap, we present an inclusive ranking methodology. We utilize the Bayesian Bradley-Terry (BT) model, which allows us to incorporate relevant prior information. We model the prior covariance of the BT merit parameters using an independent covariate, such that units with similar covariate values exhibit higher covariance, which decays as differences in the covariate increase. A hybrid of Metropolis-Hastings with preconditioned Crank-Nicolson proposal and Gibbs sampling scheme is used to estimate the merit parameters. The proposed methodology has been shown to converge, and a ranking-based stopping rule is proposed. We apply this methodology to rank the states and union territories (UTs) of India using data from the National Family Health Survey-5. We estimate and compare rankings under different regimes, e.g., all states/UTs, low-income states/UTs, mid-income states/UTs, and states/UTs by removing high-income states/UTs. Our results reveal meaningful deviations between economic standing and overall performance.

翻译：对地理或行政单元（如国家或邦）进行排名，是比较发展进展并为循证决策提供依据的常用方法。现有排名方法论通常依赖于单一指标（如国内生产总值）或有限子集的指标（如人类发展指数）。然而，据我们所知，文献中尚不存在基于大量指标变量的排名方法。为填补这一空白，我们提出了一种包容性排名方法论。我们采用贝叶斯Bradley-Terry模型，该模型允许纳入相关先验信息。我们利用独立协变量对BT优势参数的先验协方差进行建模，使得协变量取值相似的单元之间协方差更高，并随协变量差异增大而衰减。采用预条件Crank-Nicolson提议的Metropolis-Hastings与吉布斯采样混合方案来估计优势参数。所提方法已被证明收敛，并提出了基于排名的停止规则。我们将此方法应用于印度国家家庭健康调查-5的数据，对印度各邦与中央直辖区进行排名。我们估计并比较了不同情境下的排名，例如所有邦/中央直辖区、低收入邦/中央直辖区、中等收入邦/中央直辖区，以及移除高收入邦/中央直辖区后的邦/中央直辖区。结果揭示了经济地位与整体表现之间的显著偏差。