How do profile choices work.

[Keifre]

If you are a meritocracy will you get more meritocracy choices, is it random, is it situational (war, peace, building) or does it depend on leaders in power.

[Twotribes]

It doesn't seem to have anything to do with what you get.

[Soar_Slitherine]

If you pick Commerce at the start, you're basically guaranteed to get a corporation which comes with opportunities to boost Commerce further. Poor happiness or unrest in your cities provides repeated opportunities to boost Autocracy, Democracy or Meritocracy, and Fist and Mind are also easy to increase by starting wars or doing diplomacy, respectively.

In addition, factions will make demands related to their preferred profiles, which will boost the related profile if fulfilled. Refusing the demand will decrease the profile slightly, failing the demand will hit the profile hard. The game doesn't explicity state the affected profile before accepting a demand, but it's generally something that makes sense. Beware of demands to boost profiles that you can't already consistently boost - it's a bit stupid, but accepting those can be counterproductive, you may simply never get any opportunity to boost the profile enough to reach the demanded level.

EDIT: Clarity.