I believe the answer has been known for 23 centuries, and I believe most politicians don't know this at all. But some will object to the following as reading between the lines too much, and maybe I am wrong about the ignorance. So I am posting here before submitting to a journal. I appreciate your views.

While teaching Alexander the Great, Aristotle wrote one of the most powerful observations on the dynamics of a voting group established on the basis of equality for everyone. In a system where everyone has equal voting power, the rich APPEAR to have less power than the poor, because there are less rich people. But what Aristotle observed is an arithmetic progression that results in the rich having disproportionate power, even though they have less votes.

Start by imagining you have 2 rich and 4 poor. One of the poor quickly realizes he can be more powerful by voting with the rich, creating a stalemate.

Now, extrapolate!

If there 2 rich and 6 poor, the poor realize they can split in two (2:3:3), and each poor group can partner either with the rich group or the other poor group to win (6:2 or 5:3). And the latter example can collapse into the first, because 1 guy realizes, again, he can switch groups to make a 4:4 split.

As you may know, Aristotle was also the founder of logic and mathematics as we know it today. He was far more intelligent than his writings reveal on the surface. If you understand the way Aristotle thinks, you can see what he leaves unsaid.

Further extrapolation, mathematically, makes the splits work up to about 100 people, after which it starts to break down. This is why, in fact, the US senate is purposefully small, so the splits work; whereas the congress is purposefully much larger, so they don't work so well. However, clever politicians can still exploit larger groups in the same way, by playing to the different interests of different groups of constituents, as often happens in USA's Presidential elections.

With the splits, a system naturally evolves where the rich have disproportionally more power There are more poor, but being a larger group, they split into smaller groups each vieing for more power. However, the rich always vote in their own interests (Aristotle clearly knew that, but it was one of the things he did not directly say, because he did not want to alienate the rich patrons who were supporting him. There are many examples like that in Aristotle).

So the rich have disproportionately more power, and there naturally evolves a tiny swing group, or even a single person, deciding most issues. And that's what's been happening in democracies since 600 BCE. It still happens, but these days, almost no one understands why. They just see it happening and take it for granted.

People who play to the middle are often known as centrists. and they become more powerful individually, while diminishing the power of the party (Aristotle is a cynical realist, not an idealist). While those who are good at centrism become far more powerful than their constituents would warrant, it is a dangerous game playing to the center for personal benefit, because it lose support from the left base. Very few people have been really successful at it. Centrists have to know when to flip sides and play their cards very artfully, because as I say, the base has no idea what they are doing.

Do you think all politicians should be required to read Aristotle? Maybe it would be a good idea. But Aristotle himself did not think so. He thought it better that people not know too much about how politics work, because otherwise they don't just act in the interests of their constituents and become too manipulative.

It was one of the few beliefs Aristotle held which could really be wrong, because the opposite now happens so much. Aristotle did not know the power of modern propaganda techniques, which have continually advanced as media propagation technologies, such as the printing press, radio, TV, and Internet, have improved. Modern propaganda makes the opposite come true, where the ignorant are too easily manipulated by the knowledgeable.

With the increase of propaganda's power in the last 30 years, centrists are now frequently Presidential candidates in the USA, including McCain, Lieberman, and the Libertarian party's Ron Paul; as well as Presidents now, like President Clinton.