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In contrast to some (or possibly all) of the other answers, I don't think it's to do with what particular traits the villian has so much as whether they embody a consistent set of ideals (however a...
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Source: https://writers.stackexchange.com/a/29022 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
In contrast to some (or possibly all) of the other answers, I don't think it's to do with what particular traits the villian has so much as whether they embody a consistent set of ideals (however appalling those ideals may be). We may not exactly _forgive_ a villian for their disregard for the other character's lives, but if they show the same disregard for their own we will more inclined to like them in spite of it. Similarly, a dishonest character willing to forgive others for their dishonesty is more likeable than one who fumes at them for lying. I even think you can go as far as actively giving your villian virtues, just as long as you also make them a hypocrite about these virtues. A brave character who despises and belittles the bravery of those around them will probably not be very likeable, regardless of what "badass" things they personally do. As for showing the damage the character does, this is just a matter of putting the heroes of the story (or the narrator, if nothing else) in the right place at the right time. Show what the villian does to other people's lives, while simultaniously making it clear that the villian isn't acting according to any reasonable or consistent set of values (and that the acts they perform are therefore motivated by a weakness, essentially, rather than a misguided application of strength), and I think it will be difficult for the reader to forgive or like them.