This question is inspired by the discussion about lobbyism and free speech.
There are two fundamental ideas in modern democracies that seem to contradict each other, while both being so fundamental that none could be severely restricted without burying the concept of a capitalistic democracy.
The first one is "one man, one vote". Each citizen in a democracy should have the same influence on electing the government. Giving some people more than one vote (for example, on the base of taxes paid or educational level) is considered undemocratic.
The second one is the freedom to accumulate wealth. While of course progressive tax rates exist, there is no upper limit as to how much money a single person may possess. It is considered a basic freedom to make as much money as one is able too (while, of course, adhering to the law).
In principle, I am okay with both. But now there is a severe conflict between the two, given by lobbyism and the influence of money on the outcome of elections. (Note that while inspired by current events, this is not a Donald Trump thing, the phenomenon can be seen far beyond this case and the political stance of the respective candidates is irrelevant to the question.)
If I have so much money that I can put pressure on the candidates running for election - by funding TV ads or political campaigns or by threatening not to do so - I exercise a power far beyond my own voting power. I am also not just representing a number of voters with the same goals. So, effectively my vote is worth much more than the vote of others, because giving my vote (and money) to another candidate is a much more powerful threat than some ordinary guy giving the vote to someone else.
So through the backdoor, I have introduced a sort of census suffrage. Now what are the options?
Accepting the situation as is. But in this case, I have a system where the rich effectively have much more voting power than the rest. Assuming (as a rough estimation) that wealth is proportional to voting power, this can lead to a situation where 1% of the population have 40% of the voting power. And this seems more like an aristocracy than a democracy.
Severely restricting the accumulation of wealth. The communist solution, and not very effective in the past. Moreover, this has not prevented (and maybe even supported) the emergence of small powerful undemocratic groups.
Putting restrictions to the usage of wealth in political situations. This solution is used in many western states, but is of course a violation of free speech and the possibility to exercise political influence at will.
Are there any more options? None of them seem very appealing and none of them will support a truly free and democratic system. How can personal freedom to acquire wealth and having the same voting power for everyone coexist without one undermining the other?
Edit for clarification: Voting power is not only about what I actually vote at the ballot box. When I go to my congressman and demand a certain behavior or else I will not vote for him the next time, I am also exerting voting power. The question mainly is about the strong correlation between wealth and this type of voting power.