The Society (or Social System) of your settlement matters a great deal. This is how the people prefer to have things done. It represents the kind of freedom the people expect and who they will tolerate in positions of power.
Each system has 4 basic categories based on power-distribution: Autocratic, Elitist, Egalitarian and Populist.
Each of these categories has 6 options within. The options with a player-class bias give special class-associated bonuses, like Prosperity bonuses for Trader-type systems.
By setting the society, or having it forcibly set for you, you decide several key factors in the proceedings of your Settlement.
In most cases, Anarchy (caster:populist) is an exception, as (whether or not desks are sat in) the people don't recognize any authority at all.
What Societies Effect
Anarchy: Is Illegal.
Elitist arrangements allow for player citizens and/or groups of Ministers to decide your fate, with Sovereign/Minister judge to break ties.
In Egalitarian and Populist societies, NPCs decide!
Anarchy: No trials ever