We can imagine any group of human beings getting together and self organising a power structure. Teams have captains, committees have chairmen, clubs have presidents, armies have generals etc.
The reason humans choose unequal power distribution is very logical. Even social species in the animal kingdom have social hierarchy.
1. For an equal power group to work, there has to be consensus.
2. Larger groups cannot obtain consensus.
C. Large equal power groups cannot work.
Three friends can agree which pub to go to, but with four friends it can be harder. Each added person adds another layer of potential disagreement. As groups get larger, social dynamics challenge the group to become more structured.
We prefer that because a group that cooperates in the wrong direction is better than a group in chaos, or everyone going it alone. This is why so many humans are tolerant of even the worst leaders. Stable power distribution in a social group is preferable to anarchy.
MonarchiesIt's important to mention monarchies, because they represented a dominant power distribution model before modernity. Monarchies use lines of succession to distribute near absolute power.
The problem with monarchies are that they are completely arbitrary. There is no indication that the first born son of a monarch would be a good king.
They are also famous for succession battles, which destabilize societies.
Representative DemocraciesDemocracies try to divide power by giving every citizen a vote. In practice power distribution in democracies is more complex.
In no way does electing a president of a group tell us that there is equal distribution of power. That kind of power is representative. If we only choose the leader of a group once year, then each member only has one unit of power to use per year, whereas the chosen leader can make many different decisions on behalf of the group during their year in power.
Direct DemocraciesThese democracies have an electorate voting on specific issues. A good example application is the British Election to decide whether they should leave the EU (Brexit).
Direct democracies distribute power fairly evenly among the electorate, but suffer many deficiencies. Direct democracies can result in voter fatigue, high costs, and voters voting on issues they don't understand. The Brexit referendum was an excellent example of people voting on things they lacked expertise about, with some voters being interviewed after voting, but not even knowing what the EU really was.
The Highlander EffectDemocracies all suffer from a highlander effect. If someone dies, everyone else gains a little bit of power, but with each person reaching voting age, power is diluted because it is distributed.
This means that social progress can lag considerably in large democracies, and especially those with aging populations. The worst scenario for a large democracy is slowing population growth and a growing aging population. If a majority of voters were educated 60 years ago, the outcome of any election will not be progressive, because humans are naturally averse to learning as they age.
We may see dictatorships as always being bad, but not everyone agrees. China does especially well with a one party state (in some measures). The Chinese economy is set to overtake the U.S. as the largest economy in the world by 2028.
Besides that, the downsides of dictatorships are well known. Without the minuscule power of a single vote, the poorest citizen is at the mercy of their government.
How do we distribute power?
If political philosophy and discourse is based on this single question, we can relate practical and philosophical viewpoints without focusing squarely on current affairs and disagreements.
If we redistribute wealth, what we are really doing is redistributing power, because wealth is a proxy for power. The statement "Money is power" holds true. With enough of it, almost anything is possible. However we should consider that money is not the only currency of power. "power is power" is a tautology, but it can serve as a reminder that power is always what is at stake. Too often proxies are used in political discourse, like money, instead of facing the power issue directly. A new tax is really a decision to distribute power differently.
If a libertarian says: "tax is theft", they are really saying that taxes is a immoral power grab, but they are often unaware of what they are even saying. We can ask the question whether the tax is immoral if we can determine whether the loss of power is fair, if we take justice to be fairness for example.
If a socialist minded person says that "a living wage is a right" they are really saying that "businesses must distribute enough power to their employees for them to care for themselves".
In both cases, human beings can find a more fundamental discussion when it comes to power distribution, instead of having an emotionally charged proxy like money. In some cases, power can be distributed more fairly without any money even being involved. Giving prisoners the right to vote increases power distribution within a society. If we ask the question of whether it is fair, then we can answer it without falling back on partisan tropes in politics.