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I can't end without mentioning that there has been some empirical work done on investigating which cognitive features make people libertarians. The main example that comes to mind is Philip Tetlock's investigation of taboo tradeoffs. Roughly, if you present subjects with a dilemma about a hospital administrator who has to choose whether to spend a million dollars on buying a six-year-old child a kidney, or spend the same million dollars on hospital equipment, doctor salaries, et cetera, what you discover is that most subjects, liberal or conservative, want to punish an administrator who even thinks about the question. People who identify as libertarian don't get angry at the administrator for thinking about it. And the first obvious interpretation of an experimental result isn't always the correct one, but sometimes, you know, it is.
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It suddenly occurs to me that Dumbledore has seen two interactions between Harry and a Dementor. In the first one, it almost destroys him. In the second, he casts a Patronus that destroys it. Neither would seem to provide the kind of evidence that you would need to confidently assume that other Dementors would run away from you if you said "Boo" to them.
So, is this enough evidence for Dumbledore to decide that he's wrong about who broke Bellatrix Black out of Azkaban?