In the 1920 Supreme Court case Ex parte IN THE MATTER OF THE STATE OF NEW YORK et al., Petitioner, the State of New York and other petitioners sought a writ of prohibition to prevent Judge Julius M. Mayer from proceeding with a case in which he had been assigned as special master by the Supreme Court. The original dispute involved water rights between New Jersey and New York over shared bodies of water. The petitioners argued that Judge Mayer was biased due to his previous involvement in similar cases, thus compromising his ability to act impartially. The Supreme Court denied their request for a writ, stating that it did not have jurisdiction under federal law to issue such an order against a judge acting as special master on its behalf. Furthermore, they found no evidence supporting claims of bias or prejudice on part of Judge Mayer. This decision reinforced judicial discretion and independence while also emphasizing the importance of concrete proof when alleging judicial bias.

The dissenting opinion in the Ex parte IN THE MATTER OF THE STATE OF NEW YORK et al., 1920 case, argued that the Supreme Court did not have jurisdiction to issue a writ of mandamus against state officials. The dissenters believed that such an action was beyond the court's constitutional authority and infringed upon states' rights. They also contended that it was inappropriate for federal courts to intervene in matters pertaining to state taxation and finance, which they viewed as strictly within the purview of individual states. Furthermore, they expressed concern about setting a dangerous precedent by allowing federal courts to compel actions from state officials under threat of legal penalty. This could potentially undermine principles of federalism and disrupt delicate balances between different levels of government.