Godambe (1955) and Godambe and Joshi (1965) established the joint optimality of the Horvitz-Thompson estimates and the corresponding sampling designs with respect to a class of prior distributions which were "product measures." In the present paper the optimality is established replacing the "product measures" by prior distributions which are exchangeable in appropriately transformed variates. Furthermore, the optimality criterion is justified in terms of Chebychev's inequality.
"Estimation in Sampling Theory with Exchangeable Prior Distributions." Ann. Statist. 1 (6) 1212 - 1221, November, 1973. https://doi.org/10.1214/aos/1176342571