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Is the Grand Inquisitor appointed because of power and/or skill, or is there other reasons? (Tactical or analytical abilities, perhaps?)

Probably a mix of all those things. I still think he was a total waste of a character and I hope that there becomes material of him during his days as an Inquisitor, how he rose through the ranks to be the GI.

He was probably the best tactician/leader. Because I doubt it's decided the Sith Way of "if 7th sister kills GI then she becomes the new GI."

End of the day they all answer to Vader/Palpatine and one of them will decide whose in charge. Same reason why GI would take orders from Tarkin.

Maybe it was whoever had the most prolific Jedi kills and/or accomplishments. Which, technically, doesn't necessarily mean they'd be the most skilled or powerful.