I think that politicians tend to be very pro-social people who attempt to increase the welfare of the groups they belong to, usually quite rationally.
Their groups will be numerous, and of varying importance - including their nation, the voters in their district, the members of their class, race and religion, their colleagues, their own family... and then some.
Lobbyists attempt to be part of the politicians' groups, preferably as many of them as possible. They also bring in money, but they style themselves as brokers, or people who know people and carry favors, because they need to be liked and nobody likes a briber. Non-politicians mostly see the money, and think it is all about that, much like they mostly see what a politician is against, while most politicians chiefly see themselves as people who are for something.
It seems that politicians make a lot of decisions that aren't socially optimal because they want money from lobbyists and other campaign contributors. Presumably, the purpose this money serves is to keep them in office by allowing them to advertise a lot the next time they're up for reelection.
So the question then becomes, "why do they want to remain in office?". I could think of two reasons: money and power. From what I know, politicians have a pretty high salary (congressmen make ~$175k), so that's an understandable motivator. But power is the one I don't understand.
Supposedly they want to remain in office so they could use their power to have an influence. I don't know too much about politics, but it seems that politicians spend most of their time catering to lobbyists and voters rather than pushing the things they actually believe in. So much so that they aren't actually exerting that much power. And it seems that most of this catering is to special interests and is socially suboptimal. (I may very well be wrong on these points. I really don't know but it's the impression I get.)
Why are congressmen so motivated to stay in office, make $175k a year, exert a minimal amount of real power, and spend their time catering to lobbyists and making socially suboptimal decisions? I'm sure they could make twice as much in the private sector. I feel like there's something obvious that I'm missing here, but I'm genuinely confused.