According to H. R. Haldeman, his chief of staff, Richard Nixon subscribed to "the madman theory of the presidency." The idea is that, in adversarial negotiations, you benefit if the other side has to consider the possibility that you are just crazy enough to make good on threats that would be dismissed if made by a manifestly rational actor. The threat to use nuclear weapons, for instance, is a bit too much like a gun with two barrels, one conventional and the other curved around so that it points straight back. One may threaten an intruder with such a weapon but it can never make sense to shoot. A smart burglar understands this and is undeterred.
If, on the other hand, you appear unstable and reckless, then your adversary will be more inclined to credit the threat, and will conform his behavior to your will.
One problem is that your cultivation of madness has to be thoroughgoing to be believed. Thus the madman theory commits you to act recklessly at all times, on all matters, lest your adversary see through the ruse. Riding this logic to the end of the line, you can see how it is best actually to be crazy, and why President Obama is at somewhat of a disadvantage when negotiating with the Republicans on such issues as the debt ceiling. It's possible that they really would shut down the government and default on the national debt. By the logic of the madman theory, the tea-party brigade is well-positioned to take advantage of Obama's sanity, his seriousness about governing and natural reluctance to do whatever is necessary to avert a catastrophe.