First you’d have to set up a general budget. The budget doesn’t necessarily mean “money”, you could also set a certain percentage of total-production to be used for public purposes. Then you distribute your budget on the ministries. The Infrastructure-Ministry needs production but no money, the Foreign Affairs the other way around, some need both. After distributing the resources, you can specify how they shall be used in the ministries.
Certain settings in Social Engineering would be bound to give a certain percentage of the budget to special ministries. Communists e.g. would have to spend at least let’s say 35% of the total-budget on the Social Ministry. A low setting in “Military”=not more than x percent may flow to the Military budget.
To illustrate what I have in mind some examples:
Infrastructure: With a higher budget, the AI would set more “Public Works” around your cities, like roads, mines etc.
You can specify the AI to focus more on “Transport” (roads), Production or Agriculture or concentrate in a certain area.
Foreign Affairs: This would replace units like spies and diplomats. It’s even weird that modern units need years to cross a continent, but the fact that diplomats/spies even after the invention of advanced flight still need years to get to a certain city is simply pathetic.
You may set priorities: Scouting (City Information)
Industrial Espionage (to steal plans=Techs and Maps)
Sabotage (sabotage like in Civ2 + sabotage of research
facilities=enemy invents slower)
a checkbox for: “Allow Atrocities” like poisoning a well
I never liked the “bribe city”-thing. It’s too simple to buy off a city. I’d include it somehow to the “Propaganda” Ministry.
Maybe you could even order your spies more specifically like “Set Action x in city y”.
Military: This is a good example for the difference between Social Engineering and Ministries I have in mind.
In Social Engineering a high degree on Military could mean the “Police Function” your Military has in you civ (like in many Latin American where the police is even part of the military) to lower Unhappiness and reduce crime. It could also mean how many units you can have at a certain population (using the “National Recruitment Pool” system).
The Ministry provides the upkeep for units (I’d suggest resources AND money to upkeep units, especially modern units) and the funds for drilling units

The Ministry system could also be used to change the Research-Paradigm of Civ, the “Listen everybody: Tomorrow we will invent the wheel”-paradigm how I like to call it.
In my version a high Military budget would then, if you already met the prerequisites, increase the chance of a military advance to be the next breakthrough.
In a more radical consequence, the Ministries could also serve to automatically build city improvements, although this would eliminate maybe even too much of micromanagement.

I won’t write more now (it’s long enough) and wait for your reactions. If it’s “boo” or “what’s your point anyway?” or “Too complicated” I safe time, if it’s “go on” I’ll do that soon.

Many people in other thread wanted to abolish different things and put in into a screen- trade and caravans, spies/sabotage. It's good to sees someone now try to design an overall system for the management of these "screens". But I don't think the ministries should be as powerful as specified above - eg auto-build roads or move improvements. When it gets to that stage, it's just the computer playing. I think instead that the minteries should be a front end for the user to govern efficiently, not a super-governor (the SMAC auto-build governor).

I hope the nice people here at apolyton will help you develop this.

-Group all a percentage of all production from all cities into
Ministries. Say for every 3 production points in a city 1 goes
into ministries.

-Group all trade production from all cities into ministries.
1 ministry point per 3 trade points

-Group all luxury and tax points from all cities into ministries.
1 ministry point per 2 tax and/or luxury points

Part II.

Say that you now have:
-4 Production Points
-7 Trade Points
-2 Tax Points
-5 Luxury Points

They translate into
-The 4 Production Points become Labor Points
-The 7 Trade Points become 1/2 Coin Points and 1/2 Labor Points if uneven the higher
number goes to Labor.
-The 2 Tax Points become Coin Points
-The 5 Luxury Points become 10 Coin Points

TOTAL:
-8 Labor Points
-15 Coin Points

You allocate them into:

Public Works- Allows your settlers to build Farmland, Railroads, Fortresses.
(Settlers can still build Roads, Irrigation without any public works.)

Foreign Affairs Allows your units to accumulate "diplomacy" points that
allow them to have all the options of a spy/diplomat and can use them against
your enemies/allies to set up embassies etc.

Police Force Lower Crime rate, elliminates need for temples. Most early
civs will allocate all resources here due to the high crime rates.

Part III.

Public Works
1 Railroad,Farm,Fortress costs 1 Labor Point and 1 Coin Point

Foreign Affairs
-each early diplomatic action costs 1 Labor Point and 3 Coin Points
-each later spy action costs 2 Labor Points and 5 Coin Points

Police Force
-1 content citizen costs 1 Labor Point and 3 Coin Points
-1 happy citizen costs 2 Labor Points and 5 Coin Points

You will specify how you want the content/happy citizens distributed if
you wish for both. However if you do not wish for both the computer will
allocate it so at most you should only have 1 unhappy citizen in each city.

If happy citizens are possible then your largest cities will have them.

Part IV.

Advantages:

-No need for Diplomats, Spys, Temples, Coloseums, etc.

Disadvantages: