I wish I knew the answer. I am likewise totally flummoxed by the ministers. I try to choose people whose special-interest groups are happiest, but that doesn’t work. Maybe they only care about improvement in their groups’ ratings, so we’re supposed to choose ministers whose groups are unhappy but about to get what they want.
I just wish that things like strong GDP and rising incomes would buoy political capital no matter what any groups or ministers thought of my individual policies. At the very least, a big election victory should boost political capital (because my party just elected a bunch of my cronies to support me in the legislature), but it has no effect. I’ve won over 90% of the vote before and found myself still with only 11 pol-cap per turn.
In D3, each successful election should spawn a new batch of available ministers whose support groups and political capital reflect the composition and margin of victory.