What's the best way to get people to believe faulty logic is sound? Use that faulty logic to convince them of something that they already believe. People will tread any shoddy path if it gets them somewhere they already want to go.
This is why politically slanted media is so common. People will consume media that tells them they're correct in their views. Most of that media gets away with telling people they are right by appealing to particular example and pretending it's a general rule, or by citing confusing data, or by emphasizing one aspect of an issue over another. This provides a fudge factor, allowing people to feel right about their conclusions despite dubious data. It turns out that a fudge factor isn't needed. Even straightforward logic can be scrambled without people noticing it, as long as that scrambled logic reinforces their existing beliefs.
One of the oldest and most famous logical arguments is the syllogism. Two basic premises are put together to support a logical conclusion. The most famous syllogism is this:
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.
Mmmm. That's good logic. And it seems fairly simple. Still, it can be subverted. All it takes is a conclusion that people want to believe, or even a conclusion that really is true, and people throw logic out the window. One experiment had people evaluate the following syllogism.
All police dogs are vicious dogs.
No vicious dogs are highly trained.
Therefore all police dogs are highly trained.
Most likely, police dogs are highly trained, but the argument to support it — in this case — makes no sense. Still, people taking a look at the syllogism spared themselves the task of following the logic if they believed the conclusion was true. This is the essence of the belief bias.
Exactly why people accept faulty logic is up for debate. Possibly they don't bother following the argument because they know the conclusion is true. Possibly they don't think that anyone can get to a true conclusion with faulty logic. It's even possible that they believe that a bad argument disproves its own conclusion, and are reacting defensively. Whatever the reason, this is obviously the way to get people believe you're a genius. Tell them what they want to hear, and they'll believe whatever crazy logic you use to get there.
[Via The Nature of Reasoning]