More experienced ministers are more effective, so to the greatest possible extent, you want to keep the same ministers around forever.
However, you also want to consolidate your constituency. You cannot make everyone happy, so you want to consolidate the interests of your cabinet around target populations which you can make happy.
The effectiveness of ministers is most important in ministries with significant income, or expenses. Therefore, Tax is the most important, and at the start of America, Public Services, Welfare and Foreign policy are more important, while Law and Order, Economy and Transportation are less important.
Chain Reaction Resignations, Reshuffle and Firing
The resignation (or firing) of one minister reduces the loyalty of all other ministers. This can cause a chain reaction in resignation, and destroy your ability to maintain an experienced cabinet consolidated around your target constituencies. The firing of individual ministers through “reshuffle” does not have this effect, so it is less damaging to political capital to fire one minister by reshuffling the whole cabinet, than to directly fire the minister.
The constituencies which you plan to make happy, are not always the constituencies which are happy at the start of the game. For example, in America, the starting minister selection has a wide availability of capitalists. However, capitalists are not very happy at the start of the game. Therefore, even if you plan on eventually placating the capitalists and forming a constituency around them, the loyalty of any capitalists you appoint immediately will leak.
On max difficulty, this effect is significant, and you will find that ministers with low starting loyalty will become disloyal enough to begin the resignation chain-reaction before you can improve the opinion of their originally unsatisfied constituency. Ministers with higher starting loyalty will simply fade to orange, damaging political capital. Ministers respond to the happiness of their constituencies, not changes in their happiness.
Therefore, I find that it makes sense to identify your “A-Team” out of the seven start-available ministers best consolidated around your desired constituencies. However, if these desired constituencies are not immediately happy, it makes sense to appoint a “B-Team” of ministers whose constituencies start out happy, or who have high starting loyalty, and then work on pandering to your desired constituencies for the “A-Team”. Once your “B-Team” is near resignation because of your conscious neglect of their constituencies, you can reshuffle and put in the “A-Team”, who will be more loyal.
Fired ministers disappear forever - if I understand correctly, that means that when you fire a minister, a new minister will eventually be populated to fill the gap.
For this reason, it may be convenient to get rid of your “B-Team” by mass firing, and not through a reshuffle. New ministers are not populated on the same term, but their eventual repopulation will give you more options to further trim down your “A-Team” into a narrower constituency.
Using this strategy (except for the mass firing) I was able to enter the second term with a ministry consolidated around “Conservative, Parent, Commuter, Capitalist, Poor, Environmentalist” which had been reshuffled in just before re-election, and then further trim away “Environmentalist” with the free, post-election reshuffle.
This is much less of a headache than earlier playthroughs, in which I employed less effective strategies and found myself additionally attempting to pander to “Religious” and “Patriot”.
Ignore Campaigning, Starting Experience and Loyalty
You can win re-election by gross margins even without effective campaigners, experience will eventually hit 100%, and whatever starting loyalty a minister has will be adjusted by the happiness of their constituencies and by re-election until it stabilizes at the maximum. The only thing about your ministry which greatly matters, and will not fix itself over time, is the degree to which it is consolidated around your target constituencies.
Loyalty, Repopulation and Re-Election
Ministers become more loyal after re-election. So, the worst possible time to reshuffle is right after re-election, and the best possible time is just before re-election, so that the new ministers gain the re-election bonus to loyalty on the next turn.
More re-election means more loyalty, so the best strategy for political capital is for “term length” to be set to a minimum.
It seems that re-election is the event which repopulates or causes turnover in the list of available ministers. If that is the case, then more frequent elections are also a benefit to trimming down your constituency.
Free re-shuffle at game start, please
You always want to re-shuffle your ministry at the start of the game. It would be nice if you got a political capital-free reshuffle available on the first turn, or if you started with no ministers and had to appoint them.
Unclear Variable for "Minister Effectiveness"
I note that, even with full “Experience” and even when appointed to one of their desired jobs, some ministers do not achieve as high “Effectiveness” as others. It is not clear why this is, or if they desire some jobs more than others. Even fully-experienced ministers are variably effective. Whatever it is that affects their maximum effectiveness is not displayed, and their effectiveness itself is not displayed for available ministers.