Seeing many discussions about republic vs. monarchy and so on, I have some thoughts about comparing different governments, especially their financial incomes.
The most relevant factors are number of cities (C), population (P), and units (U). More precisely, C = C1 (pop <= 6) + C2 (pop from 7 to 12) + C3 (pop >=13).
Despotism: unit support S = 4*C = 4*(C1+C2+C3).
Republic: S = C1 + 3*C2 + 4*C3. Each unit more than that costs 2 gpt.
Monarchy: S = 2*C1 + 4*C2 + 8*C3.
Feudalism: S = 5*C1 + 2*C2 + C3. Above this each unit needs 3 gpt.
Communism: S = 6*C = 6*(C1+C2+C3).
Fascism: S = 4*C1 + 7*C2 + 10*C3.
Democrazy
has no unit support at all.
Republic and democrazy have less corruption than monarchy and feudalism: both have more Nopt by 0.1*OCN, and democrazy reduces rank corruption by 1/4. But these effects are generally quite small.
Republic and democrazy have commerce bonus, which is roughly 1 (base) gpt per citizen. After considering corruption (make it less) and multipliers (market, library, etc., make it more), the net increase in commerce is M*P, where M varies usually from 1 to 1.5, depending on corruption and multipliers.
When we are comparing republic and monarchy, that's usually in late AA or early MA, so metropolis doesn't exist, C3=0. Therefore, monarchy's unit support is bigger than that of republic simply by the number of all the cities C=C1+C2. In typical situations, the total number of units U is larger than support limit of monarchy, therefore the unit maintenance under monarchy is U-2*C1-4*C2 gpt, and that under republic is 2*(U-C1-3*C2) gpt. So monarchy saves U-2*C2 gpt comparing to republic.
It may seem confusing at first sight: why the number of towns C1 doesn't affect it? The reason is: adding a town, under monarchy you gain 2 more unit support and drop 2 gpt for maintenance, under republic you gain 1 more support and drop 2 gpt too.
So the basic lesson is: the more units, the better monarchy is; the more pop 7-12 cities, the better republic is. Note that if there are metros, 8*C3 and 2*4*C3 will still cancel, so what makes difference is just the number of middle size cities.
Now the question is, does this U-2*C2 advantage of monarchy offset the M*P advantage of republic? Certainly it depends on concrete situation. Let's say you have 10 towns and 2 cities, 50 units, 40 citizens. Then U-2*C2=50-4=46, M*P=40-60. They are actually quite close, aren't they? After considering war weariness and military police (bothing favoring monarchy), they are even closer.
Of course, under monarchy you want to maintain a large army to take advantage of U, while under republic you want to grow as much as possible to increase P and C2, build infrastructures to increase M, and maintain a small force to decrease U. Needless to say, under republic every worked tile must be roaded to make commerce bonus possible, but that is necessary for any government.
Feudalism is a funny government in that it strongly favors small towns. In the above example, 10 towns and 2 cities will give free support to 54 units! So don't worry about the 3 gpt maintenance, it just won't happen (unless you are extremely devoted to war). OTOH, in that example, monarchy and republic support 28 and 16 units, respectively. Feudalism saves 22 gpt than monarchy when there are 50 units.
Typically unit upkeep under feudalism is 0. So mathematically what feudalism gains is just the U-2*C1-4*C2 gpt upkeep fee of monarchy, or 2*U-2*C1-6*C2 gpt of republic.
Somebody could object to feudalism because it discourages growth. But that's unfair, what you need to do under feudalism is just some ICS in front or highly corrupt area, and your core cities can still happily grow. This ICS trick is applicable to any government, but it's the most useful for feudalism.
Another benefit of feudalism is that it's an necessary tech, so you can skip an optional tech. This could be important when the difficulty level is so high that you can hardly keep up with tech pace.
Certainly, war weariness is a drawback of feudalism vs. monarchy. But you have many tricks to deal with WW (oscillating war, artillery, army ...), while the U-2*C1-4*C2 gpt advantage is there every turn. From my experience, as long as you pay less than 30% (or even 40%) lux for WW, feudalism is more profitable than monarchy. Of course, if you don't go to war, it's a huge waste to keep so many units. So feudalism is really for hard core warmongers and difficult situations.
Communism is THE super power government in C3C, because of its amazingly low corruption. When you see every city has < 20% corruption, you will hate other governments. What's more, communism supports 6*C units, which is simply huge. And even if you exceed that limit, each unit only costs 1 gpt. Truly nothing to complain.
Fascism could be useful if it comes earlier. But since it's as late as communism, it becomes plainly the worst government (good coincidence with history
). Not to mention pop loss in revolution and no culture until assimilation. It's just too bad.
Democrazy is awkward for the same reason (coming too late). I can only think of one scenario where it could be worth a 2nd anarchy: when you have way too many units (otherwise why not stick on republic), and you are religious. But even so, the high WW still makes people think twice before revolution.
Conclusion: For your 1st revolution, republic is the choice for peaceful development, and feudalism is the choice for war and "pointy stick research". Monarchy is in general ok for every thing but great for nothing, except one field: always war (or the war is so hard and long that it's close to AW). Communism is usually the only government worth a 2nd revolution, and you won't be disappointed to it.
The most relevant factors are number of cities (C), population (P), and units (U). More precisely, C = C1 (pop <= 6) + C2 (pop from 7 to 12) + C3 (pop >=13).
Despotism: unit support S = 4*C = 4*(C1+C2+C3).
Republic: S = C1 + 3*C2 + 4*C3. Each unit more than that costs 2 gpt.
Monarchy: S = 2*C1 + 4*C2 + 8*C3.
Feudalism: S = 5*C1 + 2*C2 + C3. Above this each unit needs 3 gpt.
Communism: S = 6*C = 6*(C1+C2+C3).
Fascism: S = 4*C1 + 7*C2 + 10*C3.
Democrazy
has no unit support at all.Republic and democrazy have less corruption than monarchy and feudalism: both have more Nopt by 0.1*OCN, and democrazy reduces rank corruption by 1/4. But these effects are generally quite small.
Republic and democrazy have commerce bonus, which is roughly 1 (base) gpt per citizen. After considering corruption (make it less) and multipliers (market, library, etc., make it more), the net increase in commerce is M*P, where M varies usually from 1 to 1.5, depending on corruption and multipliers.
When we are comparing republic and monarchy, that's usually in late AA or early MA, so metropolis doesn't exist, C3=0. Therefore, monarchy's unit support is bigger than that of republic simply by the number of all the cities C=C1+C2. In typical situations, the total number of units U is larger than support limit of monarchy, therefore the unit maintenance under monarchy is U-2*C1-4*C2 gpt, and that under republic is 2*(U-C1-3*C2) gpt. So monarchy saves U-2*C2 gpt comparing to republic.
It may seem confusing at first sight: why the number of towns C1 doesn't affect it? The reason is: adding a town, under monarchy you gain 2 more unit support and drop 2 gpt for maintenance, under republic you gain 1 more support and drop 2 gpt too.
So the basic lesson is: the more units, the better monarchy is; the more pop 7-12 cities, the better republic is. Note that if there are metros, 8*C3 and 2*4*C3 will still cancel, so what makes difference is just the number of middle size cities.
Now the question is, does this U-2*C2 advantage of monarchy offset the M*P advantage of republic? Certainly it depends on concrete situation. Let's say you have 10 towns and 2 cities, 50 units, 40 citizens. Then U-2*C2=50-4=46, M*P=40-60. They are actually quite close, aren't they? After considering war weariness and military police (bothing favoring monarchy), they are even closer.
Of course, under monarchy you want to maintain a large army to take advantage of U, while under republic you want to grow as much as possible to increase P and C2, build infrastructures to increase M, and maintain a small force to decrease U. Needless to say, under republic every worked tile must be roaded to make commerce bonus possible, but that is necessary for any government.
Feudalism is a funny government in that it strongly favors small towns. In the above example, 10 towns and 2 cities will give free support to 54 units! So don't worry about the 3 gpt maintenance, it just won't happen (unless you are extremely devoted to war). OTOH, in that example, monarchy and republic support 28 and 16 units, respectively. Feudalism saves 22 gpt than monarchy when there are 50 units.
Typically unit upkeep under feudalism is 0. So mathematically what feudalism gains is just the U-2*C1-4*C2 gpt upkeep fee of monarchy, or 2*U-2*C1-6*C2 gpt of republic.
Somebody could object to feudalism because it discourages growth. But that's unfair, what you need to do under feudalism is just some ICS in front or highly corrupt area, and your core cities can still happily grow. This ICS trick is applicable to any government, but it's the most useful for feudalism.
Another benefit of feudalism is that it's an necessary tech, so you can skip an optional tech. This could be important when the difficulty level is so high that you can hardly keep up with tech pace.
Certainly, war weariness is a drawback of feudalism vs. monarchy. But you have many tricks to deal with WW (oscillating war, artillery, army ...), while the U-2*C1-4*C2 gpt advantage is there every turn. From my experience, as long as you pay less than 30% (or even 40%) lux for WW, feudalism is more profitable than monarchy. Of course, if you don't go to war, it's a huge waste to keep so many units. So feudalism is really for hard core warmongers and difficult situations.
Communism is THE super power government in C3C, because of its amazingly low corruption. When you see every city has < 20% corruption, you will hate other governments. What's more, communism supports 6*C units, which is simply huge. And even if you exceed that limit, each unit only costs 1 gpt. Truly nothing to complain.
Fascism could be useful if it comes earlier. But since it's as late as communism, it becomes plainly the worst government (good coincidence with history
). Not to mention pop loss in revolution and no culture until assimilation. It's just too bad.Democrazy is awkward for the same reason (coming too late). I can only think of one scenario where it could be worth a 2nd anarchy: when you have way too many units (otherwise why not stick on republic), and you are religious. But even so, the high WW still makes people think twice before revolution.
Conclusion: For your 1st revolution, republic is the choice for peaceful development, and feudalism is the choice for war and "pointy stick research". Monarchy is in general ok for every thing but great for nothing, except one field: always war (or the war is so hard and long that it's close to AW). Communism is usually the only government worth a 2nd revolution, and you won't be disappointed to it.
Actually, I don't think milkers want to go through another anarchy to go to democracy. The reduced corruption doesn't really help much, anyways.
YUCK! 
). The combination of no tile penalties (as in Despo), and whipping, means that Temples/Libs/Caths can be whipped very very quickly.
