A nation-state (or international union) rules Mars
A single nation-state (or, depending on how the planet is settled, an international union of nation-states) should govern Mars as a direct democracy.
According to the Outer Space Treaty of 1967, any scientific investigation or exploration in space should be conducted in the spirit of international cooperation and understanding in the event that people from multiple nations are on the same celestial body. Therefore, if multiple Earth countries establish settlements on Mars, each of these is required to work with one another, making an international union perhaps the most logical option for a government. The treaty also states that any country who establishes a settlement or agency on any celestial body is responsible for the activities of that group. This means that a Mars settlement would still have to have some contact, and likely negotiations, with its nation of origin on Earth.
Since an Earth government would be too out of touch to understand the needs of Mars settlers, a separate Martian government is necessary to maintain order, create and enforce laws, and coordinate the distribution of resources. The best option for a Martian government is either a nation-state or international union of nation-states because this is the level necessary for managing the settlers that come to Mars as well as the demands of governments back on Earth. A central government would be better able to unite all of the diverse motivations and interests of Mars colonists, and having a single governing body would make it easier for its corresponding Earth nation to coordinate with them. In addition, each nation-state should have a direct democracy so that every citizen has a voice and the likelihood of corruption is reduced. At least for the first years of a Martian settlement, there will likely be a small enough number of citizens, meaning that direct democracy would be the most feasible way of governing. It would also allow every member of society to have input. This argument rests on the assumption that settlements on Mars develop into nation-states eventually rather than, say, a network of cities or city-states, for example.
One main problem with a direct democracy is the possibility for minority ideas to be squashed under majority rule, which means that a group or even region could have their suggestions ignored or denied. It is incredibly crucial for a Mars colony, as far from earth as it would be, to maintain peace, collaboration, and equal opportunity, so unless the settlers have a solution for this fundamental flaw in this type of government, direct democracy may not be the best choice.
Rejecting the premises
More on a direct democracy on Mars: https://nationalinterest.org/feature/how-colonize-mars-25200?page=0%2C1