@Yell:
"if you think it necessary to be irrational you abandon rationality"
It is more complicated than that. As I have said, people hold things to be true irrationally all the time. This tendency for them to do so is a survival mechanism. And because it helps them survive, it is rational and justified then for them to hold such irrational beliefs.
"Truth
Main article: Truth
Whether someone's belief is true is not a prerequisite for (its) belief. On the other hand, if something is actually known, then it categorically cannot be false. For example, if a person believes that a bridge is safe enough to support him, and attempts to cross it, but the bridge then collapses under his weight, it could be said that he believed that the bridge was safe but that his belief was mistaken. It would not be accurate to say that he knew that the bridge was safe, because plainly it was not. By contrast, if the bridge actually supported his weight, then he might say that he had believed that the bridge was safe, whereas now, after proving it to himself (by crossing it), he knows that it was safe."
http://en.wikipedia.org/wiki/Epistemology
People cross the bridge every day believing it is safe because they have no choice. They are not privy to the information, facts, or knowledge that would prove it is safe. In almost every day-to-day decision, people believe something without knowing for sure whether or not it is actually true because they must believe it in order to function in society (cross the bridge).
In our world, people exploit this necessity for people to believe without knowing, politicians especially. The knowledge that the responsible citizen of a democracy needs to know in order to be a responsible voter politicians are in the business of manipulating, keeping it locked away. It is their currency: they release only portions of it (perhaps to give credence to their outright lies) and only insofar as to do so might manipulate public opinion in a way favorable to those the politician's interests.
The same is done by anyone, mainstream media tycoons, government agencies, institutions, or even individuals etc.. Those in control of the information maintain their control of it by not making it available to others or accessible to the public. In terms of legitimacy of democratic government, the key insights or analysis that would inform the voter sufficiently to provide legitimacy to the democratic process are inevitably lost amidst the foray misinformation and omissions.
Despite this, people naturally continue to believe in the democratic process, continue to vote based on the 'facts' available to them and their conscience, knowing full well that such has been manipulated. Politicians know this too, which is why they are able to get away with virtually anything they want.
It is perfectly rational and justifiable for people to maintain this irrational belief in the legitimacy of contemporary democracies' democratic processes, for holding on to such irrational belief furthers their chances of surviving and prospering. The very design of the system exploits this.