Different nations select their judges differently. I believe the more lawmaking power judges (particularly supreme court justices) have, the more appropriate for them to be selected in a democratic way. The United States is the "example par excellence" of judicial supremacy over the other branches, according to Judicial Supremacy: Explaining False Starts and Surprising Successes by University of Washington political scientists Victor Menaldo and Nora Williams. They write:
"The example par excellence of judicial supremacy is the United States system. For
example, in the 2000 case of Bush v Gore the judiciary ruled on the constitutionality of a case
that had an impact on both the executive and legislative branches. The Supreme Court ultimately
awarded the contested presidential election George W. Bush. While Al Gore’s party held the
executive, the losing branch abided by the decision of the judiciary instead of taking what could
have been dramatic action."