One step beyond the anti-hero, there's the amoral or morally challenged main character. Sometimes, a protagonist is so dark, you can't even use the term "hero" to describe him or her. But how do you get your audience to root for a character who might throw an old lady under a bus? Here are 10 ways.
Top image: Death Note.
This is sort of the easiest way. We are willing to give someone a lot of slack for doing terrible things in the service of a goal that we can understand and maybe support. After all, most of us probably support politicians whose methods we don't entirely endorse, so this is no big leap.
Even someone who defies all known moral codes can still have personal limits and standards. Or at least one thing that he or she won't do — like maybe they won't kill nuns, because they were raised by nuns.
Similarly, a serial killer who loves cats might be more sympathetic than a serial killer who only loves knives. And a murderer who cares deeply about one or two people, in particular, is automatically more sympathetic.
It doesn't have to be a sob story — but if we can see how this character used to have a moral compass and then it went out the window, either due to tragedy or just an understandable series of steps that we could imagine ourselves taking, then we can picture ourselves becoming this questionable character.
To some extent, making us buy into your potentially hateful main character is a worldbuilding challenge. We have to understand the context in which this person makes sense — and if this person happens to be the least bad person in a terrible world, then we're more likely to be in his or her corner.
Most of us would rather follow a quotable fiend than a bromide-spouting paragon. The more entertaining and funny your main character is, the more likely we are to fall for (or at least find ourselves liking) him or her.
We always root for the underdog, it's just human nature. So if we see your morally challenged hero lose fight after fight — or only win by the skin of his/her teeth — then we can't help wanting to see him or her eke out a victory. (Although we also root for competent protagonists. So you can't push the "losing" thing to the point of idiocy.)
We always want to root for people who are convicted in the court of public opinion (or even an actual court) of crimes they didn't commit. And if your protagonist is accused of killing a busload of kids and we know for sure he or she didn't do it, then we're way more likely to forgive the fact that he/she actually did kill one or two grown-ups.
Likewise, it's hard not to pull for someone who's universally despised. Especially if there's an element of unfairness or cruelty about it.
Because audiences like to work hard, at least if we feel like it's going to be rewarded. And there's no harder work than forgiving someone for an unforgivable act. So if we see your protagonist doing something that absolutely crosses the line and makes us want to hate him/her — but at the same time, we can see that we're going to wind up finding a way to forgive this monster eventually — then we'll be inexorably drawn into an intense, if not entirely healthy, relationship with them.