Variance Regulation in Joint Inference of the Hubble Constant

We examine how statistical tension between local and early-universe measurements of the Hubble constant affects parameter inference. Defining a composite parameter �, we find that while the mean value of � remains stable across tension regimes, its variance is strongly and systematically suppressed as inter-dataset tension increases. Using variance-ratio tests, robust non-parametric statistics, correlation analysis, and permutation tests, we show that this tension-dependent variance suppression is statistically significant and unlikely to arise from random fluctuations. The result is consistent with regularization effects in joint cosmological inference under dataset conflict, rather than measurement error or new physical mechanisms. This work reframes aspects of the Hubble tension as a property of inference behavior under disagreement and provides a diagnostic framework for assessing stability and uncertainty in composite cosmological parameters.