My seven-year-old son asked me why politicians lie, and the best answer I could give him was the following:
Imagine a town needs a new school. There is a politician called Mr White who wants to become the boss of the town in the next election. There is also a politician called Mr Black who also wants to become the boss. Mr White now says that a modern school for the expected number of kids will cost 5 million euros. This is a lot of money. Mr Black, however, says that Mr White does not know what he is talking about, and the truth is that the school will only cost 4 million euros. This is much less money. Mr Black is also planning tax reductions. To build a school is a difficult thing to do and few people can estimate the costs themselves. Therefore, they are not sure who is right. People, however, know for sure that paying less taxes is nice, because they have more money to spend on other things, like holidays, toys, or so. Therefore, at the end more people vote for Mr Black than Mr White in the elections.
After the elections some time passes by for the planning of the school. After a year Mr Black says that the school will be smaller than planned because market prices have increased. Many voters do not remember what Mr Black said before the elections a year ago, others do not know exactly how much market prices have actually changed, and since Mr Black is now in power, there is not much the voters can do over the next years till the next elections. Only few parents with kids and their kids, who will not be able to go to school in a few years, will probably protest in the future, and accuse Mr Black of lying, maybe even those parents who voted for him initially. However, many people are happy with Mr Black, because they have to pay lower taxes. When school actually will be opened in several years, and some kids actually cannot go to school, Mr Black’s time of being boss is over anyway. The next boss will have to tell people that some kids will not be able to go to school and he will have to face the anger and has to solve the problem.
So at the end, Mr Black, who lied, is happy because he got into power and does not have to face the anger of the voters. The voters are happy because because they pay lower taxes and can blame Mr Black (or his follower) for lying (so they don’t have to feel guilty). Only those kids who will not be able to go to school (and maybe their parents) will not be happy.
Therefore, policitians lie and adults, who vote, “want to believe their lies”. However, this just means that these adult lie that they belief politicians lies.
Note: Hanna Arendt argued in a similar way in her essays on “Truth and Politics”  .
see also my previous blog 
 Hanna Arendt (1972). Wahrheit und Politik. In: Wahrheit und Lüge in der Politik. Zwei Essays. München: Piper.
Original in English: Hannah Arendt (1976-02-25). TRUTH AND POLITICS. The New Yorker.