So a politician is supposed to represent their constituents. Okay. But if they're absolutely supposed to represent their constituents, then you don't need elections, political parties, political platforms, or any of the other panoplies of modern democracy. Just pick a reasonably open minded lawyer from a given population, send him to Congress, and then periodically hold polls on specific issues as they come up. The "representative" would then have to get his "constituents" what they voted for however possible. That's really the only system in which politicians wouldn't be lying to either the supporters which campaigned for them or the moderates that swung the vote in their favour (where applicable).
Also, this only applies to systems in which the candidate actually represents the area in a meaningful sense. In Ontario, we recently had provincial elections that were contested between three parties, the Liberals (mildly left of centre), the Conservatives (right wing), and the NDP (usually far left, but a bit more populist recently). In Parliament, representatives basically have to vote for the party line, so they don't get the freedom American legislators get when it comes to "representing their constituents", so instead the parties basically support measures that help the areas that got them into parliament. In the case of the last election, the Liberals had a seat in Windsor held by a Cabinet Minister that they really wanted to keep, so they did a fair bit of campaigning talking about all the local improvements we could get from infrastructure spending, increased investment by the provincial government in the area's healthcare system, and so on. Well, the Liberals ended up losing the seat to the NDP, who dominated the north and southwest, while similarly not doing so well in most of the province. Yet they won overwhelmingly in Toronto, which basically gave them the election and a majority government, despite having lost basically everywhere else bar a few cities. Further, because of the Toronto seats, they won a majority government with about 37% of the vote, showing just how hard they were pummelled elsewhere. So obviously the talk of the area is that the Liberals aren't going to be sending much funding for hospitals or supporting policies that would benefit the southwest, and will instead be representing their "constituents" in Toronto. Does this at all seem like a good way for a democracy to function?