I don't think we should ask politicians to reflect or stand for something as complex and ethereal as the 'people's interest', which is something that I would claim that doesn't even exist. At most, politicians could get to reflect and stand for their voter's interests and the ideals that they resonate with.
If any, it would be the whole political system (meaning the totality of political institutions, from the Federal Government and Congress to the smallest Council, including far right and left political parties , anarchists and so on), rather than just the politicians, what could be able to reflect that hypothetical and utopian 'people's interest'.
In my view, a good politician, a good statesman (or woman) wouldn't be the one that eventually gets to connect with that dream 'people's interest'..., that is fantasy; but rather the one who's able to lead and converge the people's enthusiasm and energy around his own goals, interests, ideals and worldwiew, which by the way, does not necessarily mean, watch out, that those goals, ideals and worldview have to be selfish or bad for the people. I mean, they could, but nor as a matter of course.
Kind regards from South Europe.