I think, for me, there is a difference between characters who have a lot of negative traits, but the author wishes to portray as positive or heroic and a character who has acknowledged negative traits who manages to be engaging. To use popular examples, Edward Cullen is an example of someone who we're supposed to root for in the Bella/Edward relationship, but who many (including myself) would argue is such an overwhelmingly negative influence on the book that he (among other things) makes the book impossible to enjoy. On the other hand, Harry from Harry Potter has many negative traits which are acknowledged but is still an enjoyable character to read and empathise with. As an example which could go either way, Humbert Humbert is possible to read about because the author expects you acknowledge that he is a vile person who is delusional in his treatment of Lolita. But on the other hand, many people find the entire subject matter (understandably) far too upsetting to read about, and that Humbert Humbert's negative qualities undermine anything the book has to offer them.
Of course, your mileage may vary on pretty much any example - I hopefully managed to illustrate my point without being rude in any way!
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