Princeton just wasted money on a research...
Princeton highlighted a reality which many people don't like to acknowledge. Direct, Athenian, democracy simply doesn't scale beyond a certain level. That's why most countries have representational republics but, even there, influence will always be proportional to one's wealth and power. Everyone simply is not created equal.
This inequality manifests itself in many ways.
Organizing a special interest lobby takes time and resources, and rich people have more of both compared to poor people. Of course poor people can also organize themselves -- there are teachers' lobbies and government workers' lobbies -- but it takes lots of poor people to match the influence of fewer rich people. On a per-head basis, a rich person has more influence than does a poor person.
Also, poor people's votes can be bought, directly or indirectly, by the rich.
There is also a fine line between bribery of politicians, which is illegal, and political contributions, which are considered a form of free speech and a cornerstone of democracy. There can't be a direct contract (which would be bribery), but the unspoken
quid pro quo underlying political contributions is understood by both parties. You are helping a candidate get elected and, in return, you expect them to be responsive to your concerns.
The influence of money in the American political process is a subject of heated debate.
One final complication is that issues are prioritized by voters. So, a voter may have certain views on the issue of immigration (A), environment (B), gun control (C), and economy (D). But it is unlikely that there will be a candidate who has the exact same policy proposals on all these issues that match the voter's views. So the voter has to prioritize and vote for a candidate because of agreement on issue (D), even though their views on issue (C) may diverge. So, when Princeton says that issue (C) is not being represented, that's only because it wasn't a priority for enough voters compared to other issues.