Oh god this is embarrassing to be honest.
There is no one "interest of the people". There is no "people". There are different groups with different interests. Or are you proposing dictatorship of the proletariat? Because we know how that turned out, don't we?
If you want evidence of the above you need to look no further than a couple of weeks back to the Brexit vote. You have it there all.
- There is no disproportionate political influence by the rich. The majority of the rich said "don't do it! PLEASE FOR THE LOVE OF GOD DON'T DO IT!".
- There is no rich vs. poor. One of the richest, most influential people on Earth, Rupert Murdoch, used his media influence to sway the vote in favor of leaving.
- People unable or not interested in forming a balanced opinion. The decision was made because of demagoguery and blatantly false claims.
- Power-hungry, opportunistic politicians riding the wave, no matter what the wave is and then back tracking on their promises and claims.
Same thing happened in the Greek elections. A politician came, promised all sort of things, and in the end did exactly the opposite of what he promised.
So in the end people acted against their self-interest. Because they don't know what their interest is and because politicians tricked them. Story as old as mankind itself. There should be no need to "prove it". If it wasn't self-evident, then you are just out of touch with reality. But here you go, I spent 10 minutes explaining things that should be self-evident, to people who claim that they understand the politics and science of reconciling interests and opinions.