Suppose a finite population is stratified such that the variate values, appropriately scaled, are exchangeable within strata and independent from stratum to stratum. Consider designs with fixed sample sizes within strata, and unbiased estimators of the population total. Minimum expected variance is achieved with a stratified $\pi ps$ design and the usual (Horvitz-Thompson) unbiased estimator.
"Stratified Sampling with Exchangeable Prior Distributions." Ann. Statist. 6 (5) 1168 - 1169, September, 1978. https://doi.org/10.1214/aos/1176344320