I remember reading somewhere that the Federation was intended to be similar to the United Nations.
Each world has it's sovereignty.
Kirk: Your world is yours.
That being the case, then each world would have it's own political systems for electing or choosing representatives for the Federation Council.
This means one Government/Planet/Member, one vote, with founding members possibly having veto power.
Starfleet would then take on the roles of both exploration and peacekeeping, similar to the peacekeeping forces the UN currently has.