Ah, but this wasn't the question. You've confused formal political input with the broader idea of power.
In this hypothetical perfectly fair democracy, the ones with power would be the ones best able to sway the populace. Popularity, rhetoric, and control over media would skew the true distribution of power away from the perfectly flat one you might be hoping for.
Instead of aiming for perfection, we should oppose the systems that result in power becoming more concentrated over time. Our goal is an equilibrium where power is spread broadly and the most powerful are the most deserving (e.g, a scientist's voice has power because their expertise is respected).
One person, one vote is a good place to start. But it isn't the whole solution.
In democracy, the maximum should be 1. One vote per person. That's it.
In practice, we can delegate stuff, but I don't see reason why should people (as adults) accept any sort of authoritarianism in their lives.