The best replacement for elected is appointed judges.

The best alternatives to elected are rated as following:
★★★★★  appointed judges
★★★  appointed school boards
★★★  appointed
★★  selected
★  nominated
★  appointed house of lords
★  reelected
★  appointed senate
★  appointed school board members
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Your alternative for elected is not listed? Suggest!
Speaking about elected, one probably shouldn't forget about president.

Other search terms related to elected and their ratings are:
★★★★★ president
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elected
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appointed school boards