Some natural random variables have a normal distribution, some have Pareto distribution and some power law distribution. For example, height of humans is normally distributed, income has Pareto distribution and stock market returns follow some other power law distribution. Only some random processes have uniform distribution when the outcomes are equally likely, e.g. a coin toss.
Is then democracy a random process? I am a skeptic about this. When a (lurking) criminal mind has the same voting power with a law abiding citizen, this is a random process. When a lazy person has the same voting power with a hard working individual, then this is a random process that assumes equally likely outcomes. Possibly, voting power could be adjusted according to contribution to GDP but then a few people with control the outcome. You have to start from zero. Unfortunately, this cannot happen.
What is the alternative? There is possibly one we are not willing to see. Inequality and fat tailed distributions give rise to small groups in a democratic system that can appeal to a lot of people who otherwise do not share all their beliefs but support them because they want revenge from the system. This is the danger from democracy, i.e., a limiting process towards fascism, left or right.
Classical Greeks gave us many wonderful things but possibly their concept of democracy was flawed. It applied within a circle of elites with almost uniform purchasing power. But when one applies democracy to a system with inequalities, that can lead to tail risk: social unrest, war, terror, etc.
Does a worker in a factory have the same rights with the factory owner? In democracy equality of rights is given but income inequality shadows the rights equality. Should equal income become a right? Maybe that is an answer but then no one would like to take the risks of starting a factory. Is democracy a cul de sac? Possibly. As you see, I do not know the answers. The task of a true philosopher is to identify the right questions to ask that are compatible with empirical evidence. The empirical evidence is that democratic systems around the world continue to create inequality, crime and terror. It is time to rethink whether we do not understand what we are talking about when we speak of democracy.