Monthar
Deity
On the councils part, couldn't we just remove them as a civic choice and add in two world wonders for them similar to the Apostolic Palace in the vanilla game? Then the membership in them be based on having the required religions. If you want to ensure only belonging to one the other or neither base said membership on how many of your cities have each of the two religions. To belong to neither you either have to not have either religion or have an equal number of cities having each. Thus if all your cities have both you'd belong to neither.
Also, while on the subject of the councils, the voting needs a serious overhaul. After all it's rather ridiculous that there can be three members and it only takes one of them to vote yes for the resolution to pass. While such a vote could happen in vanilla it was based on a weighted system involving, iirc, the population and/or number of cities of each member. So perhaps giving each vote a similar weight and show this on the pop-up window would solve this problem. In fact if it was a straight up total population of your cities is how many votes you got them the results would make more sense. So if I had 10 cities and they all had a population of 20 then my vote would be counted as 200 votes. Thus the powerful civs would have more control over what does and doesn't pass than the weak civs. Then if you choose the defy option that effectively doubles your vote count for that voting cycle and makes you immune to the resolution's effects even if it passes, at least until the next voting cycle. With, of course, the unhappiness problem if you defy the resolution. This unhappiness amount could be based on your current alignment and what resolution is defied and in some cases it's a happiness boost to defy instead of an unhappiness penalty. for instance if my alignment is evil and I defy the resolution to band death magic, then my population is happy about that defiance since they want the death magic.
As for the other civics and their categories.
Religion sounds to me like a modification of the "Free Religion" civic from vanilla. So perhaps rename it to that Most of these cultural values are really about happiness and not culture so move them to a new Happiness Values section. In this category is only the civics that modify happiness. Each that boosts happiness should have some smaller unhappy aspect to it. Such that what boosts happiness under one might cause unhappiness in another, or some other cause for unhappiness that's fitting.
Happiness Values
Consumption has plus happiness and unhappiness as others suggested as well as the added happiness from the current settings of it, but adding unhappiness for each non-state religion temple (thus negating the happy bonus of having those extra temple). Remove the gold bonus. Since a gold bonus really goes into the labor civics where you're either boosting production, income or both at some other expense.
Pacifism add +1 happiness per specialist then it'd fit with the idea of boosting happiness in this category.
Free Religion it keeps the happiness bonus it has now, but adds an unhappiness for each building that increases the unhealthiness (such as forges). After all, in the medieval times you also went to the church for your health care needs. This also fits into the fantasy realm where the priests and clerics practiced healing magics. This civic could also change your alignment to neutral (it reverts to your default alignment when you change to a different civic). Of course, with these changes, all civs would need start with Nationhood selected instead of religion. Also, have no state religion when running this civic, since the whole point is the populace can worship whomever they want.
Social Order could be renamed to Justice. Add happiness bonus from the 3 types of palace as was suggested for the nationhood here instead, since those palaces are more about reducing maintenance (anti-corruption) and reducing the crime rate. It could be something like +3 happiness in the city they are built in, +2 happiness in adjacent cities and +1 in all other cities. Or even just a flat +1 happiness in this city and +1 happiness in all cities on this continent. So having all 3 on one continent would give +3 happiness to all cities (+4 in the city that built it since the +1 this city would stack with the all cities).
Nationhood Add +1 happiness for archery range, siege workshop, stables, palisade and walls to go with the one for training yard. Because these offer the populace a sense of pride in their nation and a sense of security from its governing body, thus making them happy.
Government
Crusade move to the Government section adding these two to its current settings +25% military building production (siege workshop, archery range, etc), and -25% non-military building production. After all when you're on a crusade so the whole point is to be at war and building troops to support the war effort. No other aspect of government matters right now.
Economy
Sacrifice the Weak move it over to this section because it's really more about money, food and healthiness/unhealthiness.
Guardian of Nature remove the happiness bonus to the grove and increase what it is on the grove itself. Having it from the grove and the civic when it requires running this civic to gain any happiness from the grove is redundant. Instead add a +1 health, +1 food and +1 commerce from forests, jungles and ancient forests. After all you're teaching the people how to live off the natural environment, thus they can find more food and sell off some of the new-found excess food. This would make this civic a better fit to this category.
On the grove itself make it +1 happiness just from having it (so it's worth building even if you don't run the civic), but +3 if you are also running this civic. After all the grove is basically like a park in the real world. That is a place where people go to relax and have fun.
Cultural Values
After moving several to a different category, we're left just two, Scholarship and Liberty. So let's add a couple more to flesh it out a little better and boost the culture bonuses so a cultural win is as easy as other types of wins.
Scholarship Remove the happiness and unhappiness effects. Add +1 culture per specialist.
Liberty to go with the Arcane Knowledge idea, boost the culture bonus to +180% or leave it at 100% and +1 culture to monument, theater and temples.
Arcane Knowledge +10% culture and +10% science for each type of mana you have. So if you manage to have at least one of each type that would give a total of +180% to culture and Science. The likelihood of actually getting all 18 types at once is rather low on all but huge maps and possibly large maps. In all likelihood you'd be close to a domination win if you owned enough nodes to max out this civic.
On a related, though off topic, note, I feel arcane units should all have a +1 affinity for the 2-3 mana types that civ's palace gives. Thus giving them all the first level spell of those magics for free. In the case of Shamans that can't be upgraded, they could also use a promotion to get the 2nd level of the magics they have an affinity for.
I can't think of a 4th for the cultural values. I haven't spent a lot of time on these ideas, so they might need some adjustment for balance.
Also, while on the subject of the councils, the voting needs a serious overhaul. After all it's rather ridiculous that there can be three members and it only takes one of them to vote yes for the resolution to pass. While such a vote could happen in vanilla it was based on a weighted system involving, iirc, the population and/or number of cities of each member. So perhaps giving each vote a similar weight and show this on the pop-up window would solve this problem. In fact if it was a straight up total population of your cities is how many votes you got them the results would make more sense. So if I had 10 cities and they all had a population of 20 then my vote would be counted as 200 votes. Thus the powerful civs would have more control over what does and doesn't pass than the weak civs. Then if you choose the defy option that effectively doubles your vote count for that voting cycle and makes you immune to the resolution's effects even if it passes, at least until the next voting cycle. With, of course, the unhappiness problem if you defy the resolution. This unhappiness amount could be based on your current alignment and what resolution is defied and in some cases it's a happiness boost to defy instead of an unhappiness penalty. for instance if my alignment is evil and I defy the resolution to band death magic, then my population is happy about that defiance since they want the death magic.
As for the other civics and their categories.
Religion sounds to me like a modification of the "Free Religion" civic from vanilla. So perhaps rename it to that Most of these cultural values are really about happiness and not culture so move them to a new Happiness Values section. In this category is only the civics that modify happiness. Each that boosts happiness should have some smaller unhappy aspect to it. Such that what boosts happiness under one might cause unhappiness in another, or some other cause for unhappiness that's fitting.
Happiness Values
Consumption has plus happiness and unhappiness as others suggested as well as the added happiness from the current settings of it, but adding unhappiness for each non-state religion temple (thus negating the happy bonus of having those extra temple). Remove the gold bonus. Since a gold bonus really goes into the labor civics where you're either boosting production, income or both at some other expense.
Pacifism add +1 happiness per specialist then it'd fit with the idea of boosting happiness in this category.
Free Religion it keeps the happiness bonus it has now, but adds an unhappiness for each building that increases the unhealthiness (such as forges). After all, in the medieval times you also went to the church for your health care needs. This also fits into the fantasy realm where the priests and clerics practiced healing magics. This civic could also change your alignment to neutral (it reverts to your default alignment when you change to a different civic). Of course, with these changes, all civs would need start with Nationhood selected instead of religion. Also, have no state religion when running this civic, since the whole point is the populace can worship whomever they want.
Social Order could be renamed to Justice. Add happiness bonus from the 3 types of palace as was suggested for the nationhood here instead, since those palaces are more about reducing maintenance (anti-corruption) and reducing the crime rate. It could be something like +3 happiness in the city they are built in, +2 happiness in adjacent cities and +1 in all other cities. Or even just a flat +1 happiness in this city and +1 happiness in all cities on this continent. So having all 3 on one continent would give +3 happiness to all cities (+4 in the city that built it since the +1 this city would stack with the all cities).
Nationhood Add +1 happiness for archery range, siege workshop, stables, palisade and walls to go with the one for training yard. Because these offer the populace a sense of pride in their nation and a sense of security from its governing body, thus making them happy.
Government
Crusade move to the Government section adding these two to its current settings +25% military building production (siege workshop, archery range, etc), and -25% non-military building production. After all when you're on a crusade so the whole point is to be at war and building troops to support the war effort. No other aspect of government matters right now.
Economy
Sacrifice the Weak move it over to this section because it's really more about money, food and healthiness/unhealthiness.
Guardian of Nature remove the happiness bonus to the grove and increase what it is on the grove itself. Having it from the grove and the civic when it requires running this civic to gain any happiness from the grove is redundant. Instead add a +1 health, +1 food and +1 commerce from forests, jungles and ancient forests. After all you're teaching the people how to live off the natural environment, thus they can find more food and sell off some of the new-found excess food. This would make this civic a better fit to this category.
On the grove itself make it +1 happiness just from having it (so it's worth building even if you don't run the civic), but +3 if you are also running this civic. After all the grove is basically like a park in the real world. That is a place where people go to relax and have fun.
Cultural Values
After moving several to a different category, we're left just two, Scholarship and Liberty. So let's add a couple more to flesh it out a little better and boost the culture bonuses so a cultural win is as easy as other types of wins.
Scholarship Remove the happiness and unhappiness effects. Add +1 culture per specialist.
Liberty to go with the Arcane Knowledge idea, boost the culture bonus to +180% or leave it at 100% and +1 culture to monument, theater and temples.
Arcane Knowledge +10% culture and +10% science for each type of mana you have. So if you manage to have at least one of each type that would give a total of +180% to culture and Science. The likelihood of actually getting all 18 types at once is rather low on all but huge maps and possibly large maps. In all likelihood you'd be close to a domination win if you owned enough nodes to max out this civic.
On a related, though off topic, note, I feel arcane units should all have a +1 affinity for the 2-3 mana types that civ's palace gives. Thus giving them all the first level spell of those magics for free. In the case of Shamans that can't be upgraded, they could also use a promotion to get the 2nd level of the magics they have an affinity for.
I can't think of a 4th for the cultural values. I haven't spent a lot of time on these ideas, so they might need some adjustment for balance.