I haven't played C3C Communist yet, so my thoughts are based on theory. I have been thinking about it a fair bit though because I'm considering going to Communism soon in my current game. Based on theory:
Don't build cities very densely if you do plan to take over the world. At a certain point (but a very high one) too many cities will have a significant negative effect. (See table below and compare having 200 small cities vs. 100 large ones for example.)
The SPHQ should greatly increase the effective number of cities. Assuming there's no bug in its implementation. So, the fact that SPHQ made little difference in your game suggests to me that you are currently very far from having too many cities.
The number of cities depends on map size and difficutly level. You need to check OCN for them in the editor. Theoretically it should also be influenced by the commercial trait which would give it a boost - unknown whether that works in combination with communism.
As an example, suppose your Monarch game (.85) is on a standard map (OCN=20) and you are not a commercial Civ, and you have both an FP and SPHQ. And suppose we're looking at cities which do not have a courthouse nor a police station.
Using
Alexman's formulas
Code:
Nopt = max(OCN * (L/100 + c + Gr + Gp*Nwe + 0.25*Ni), 1)
= 20 * (0.85 + 0 + 2 + 3* 2 + 0
= 136
Now suppose you have 200 cities. Then:
Cr = R / (2 * Nopt), if R < Nopt
(2 * R Nopt) / (2 * Nopt) otherwise
= (200 / 2) / (2 * 136)
= 0.37
I.e. rank corruption will be 37% in the city.
Doing the same calculation for a series of numbers:
#cities corrupt
50 9%
100 18%
200 37%
272 50%
400 97%
The progression is linear up to 272 cities in this case and begins to increase more rapidly after that.
The presence of a courthouse and/or police station in a city will further reduce its rank corruption, but only by a very small amount so I haven't included this factor here.
That accounts for rank corruption only. Distance corruption must be added. It is a constant in Communism:
Code:
MaxD = (MapW+MapH)/4
= (100+100)/4
= 50
d = (MaxD) / 4
= 12 (assuming truncation to integer)
da = 0.5^Ni * min(Gd * t * d, MaxD)
= 0.5^Ni * 1 * 1 * 12
Cd = da /MaxD
Depending on the number of courthouse/policestation in each city the result is:
0 c/p Cd = 12/50 = 24%
1 c/p Cd = 6/50 = 12%
2 c/p Cd = 3/50 = 6%
So, for each city we must add 6, 12, or 24 percent to the rank corruption depending on whether it has a courthouse and/or police station.
From all that I conclude that:
1) It isn't necessary to worry about the total number of cities unless you are packing them tight. Very tight (ICS) packing will be counter-productive in Communism because the rank corruption of all cities will start to become significant, and because it is desirable to have a courthouse in most cities.
2) Most cities should have a courthouse. It will reduce corruption by about 1/8th.
3) Very high output cities (those with scientific wonders, or lots of shields and factories) should also have a Police Station to gain another 1/16th.
4) Communism can be VERY powerful now. An empire of 200 cities each at 50% corruption can be built on a standard map in Monarchy.
One more thought about Communism: A downside to this government is the forced-labor rushing. After being in Communism for a while and growing I'd expect to be running a high gold surplus. But with nothing to spend it on! One possible use for it: each turn, pillage a critical resource for building a particular unit, keep all cities building an earlier unit in the upgrade path, next turn start by reconnecting, use the gold to upgrade units, then disconnect again.