What's that vulnerability/weakness of human psychology which is consciously/subconsciously utilized by politicians or people with authority/fame? Below is just an example:

I am from India and I remember that we were promised by our PM, Narendra Modi, that he would bring all the black money from Swiss banks and he will deposit around 15 lac INR into every Indian citizen's account. 

Like this, he made a lot of promises. He said "good days will come" in 2014 and most of these promises are have not yet been fulfilled, but still most of the people are highly impressed by him.

I know that he is a good orator, but what I don't know is, what is the weakness of "Being impressed and convinced and remain the same over the time" is called? And why sometimes the realization takes time to come?
I think that one of the reason people believe in those things is that they are those who prefer to give part of their lives into other people's hands rather than take care of it by themselves. In other words, they prefer to be given a fish instead of a rod so when they hear 'I will give you money' they just vote for them blindly believing this is going to happen. Other reasons might include the rule called 'birds of a feather flock together'. Some people are attracted to people who voice cenrtain opions to which they tend to incline. I would also agree with @user3169 who said that some people simply believe in people in positions of authorities and struggle to act against them. In order to dig into more details in this topic you might want to watch Milgram experiment on obedience to authority figures available on YouTube.