The biggest issue is the modern Nation-State was born out of the 30 years war and the outline was set by the Peace of Westphalia in 1648. The Nation State improved and expanded its ability to survive through developing more efficient systems of taxation, bureaucratic control of manpower and resources and the ability to field military forces and sustain them in the field batter than any competing system of organization or government. Historians like Niall Ferguson have written about this process at length.
So the short answer is you are not going to do this because the armed power of established States will simply overwhelm you. This explains the lack of "microstates", the impossibility of "sea steading" and a multitude of other schemes to diminish or delete the power of the State over individuals or groups. You could set up the "People's Democratic Meritocracy of Smithsville", but the second you fail to pay taxes or otherwise defy the power of the State your polity is in, the Police or Armed Forces will arrive, arrest the ringleaders, execute warrants to collect taxes owed and otherwise remind you who is really in charge. (Current events in Spain as of the time of writing should make that point abundantly clear).
There are really only two alternatives.
For all practical purposes, if you feel a private corporation can execute the job of managing a town better than an elected government, then the town can incorporate into a condominium or something similar. This solution ignores the fact that cities actually are "incorporated", the condo board replicated the city council and corporations are just as rife with internal politics as any city, county or other political division.
Call Elon Musk and arrange to get off the Earth altogether. This has the singular advantage of removing yourself from the armed power of any Earthly State (unless they choose to follow you), but the Mars colony will need to have an organization to manage the various resources needed to live and survive; probably an elected board of directors or elected councillors.
The real issue here isn't that elected officials are stupid, but rather there are a multitude of biological and institutional incentives for people to behave the way they do once in elected office. The real challenge is to devise a system of incentives which is both reasonable (many theoretical political systems fail because they go against human nature) and enforceable. Since we haven't seemed to have had much luck, the fall back is to use what has worked in the past, and so far a Republican form of government, backed by a fairly distinct set of cultural preferences (long time horizons, deferred gratification, balance between individual and group and cooperation at the lowest level using a multitude of voluntary associations, free markets and the unfettered use of personal property) seems to have worked the best.
Your Martian colonists may avoid a lot of what passes for government these days because they will be too busy trying to survive in a hostile wilderness that they won't have a lot of time for "politics" in the usual sense.