Like it says on the tin, what are the thresholds for different ratings and what effects do they have on production? I have had no luck on finding any documentation for this game. Two underdeveloped wikis and an informative but brief manual that doesn't have all the information I want.

(City) Approval affects the relevant city's Food and Industry production. (Empire) Approval affects all of your cities' Science and Dust production - and (Empire) Approval is the average of all (City) Approval, weighted by population.



0-10% Rebellion

(City) Food -50%

(City) Industry -50%

(Empire) Dust -50%

(Empire) Science -50%



11-39% Unhappy

(City) Food -20%

(City) Industry -20%

(Empire) Dust -20%

(Empire) Science -20%



40-60% Content

No change.



61-89% Happy

(City) Food +15%

(City) Industry +15%

(Empire) Dust +15%

(Empire) Science +15%



90-100% Fervent

(City) Food +30%

(City) Industry +30%

(Empire) Dust +30%

(Empire) Science +30%

Wow, okay, that is some really serious stuff. And even the outliers can bring down the empire, it's not all localized. Thanks, very good to know.

In theory, you're better off grabbing as many cities as you can afford to settle or take and hold though, regardless of approval rating effects. ALMOST. I'll explain why:



For example, imagine you had only basic cities, no districts - each city starts out with 60% base approval rating. For each additional city, you have -10% approval rating (expansion disapproval). (Explanation of this graphic and the numbers below.)





Then let's say you got Sewer System on all of your cities (+20% approval) - so each city starts out with 80% base approval rating.





Then let's say you got Central Market on all of your cities (+25% approval) - so each city starts out with 105% base approval rating (visually 100%).





Level 1 districts will affect approval by -10% each, but level 2 districts will affect approval by +5% each. Then there are some anomalies which give you approval as well. You've also got luxury resource boosters, Wine giving you +30% approval, others giving you maybe +5% each. And there's the empire plan, economy, tier 3 which gives +25% approval rating.



Explanation:

So imagine that all of your cities (whether you have one or more) were cookie cutter six-tile triangles - 3 level 2 districts (+15%), 3 level 1 districts (-30%), Sewer System (+20%), Central Market (+25%). Your "basic" approval (the approval that you would have with just one city) is what really determines the benefit you gain from all of your cities. The "basic" approval here is 60+15-30+20+25 = 90%. With one city you would have 90% approval (1 city x 1.3 production modifier = 1.3 effective cities), with two cities you would have 80% approval (2 cities x 1.15 modifier = 2.3 effective cities), with three cities you would have 70% approval (3 cities x 1.15 modifier = 3.45 effective cities), and so on.





You take a hit for every approval level you fall from, but within each approval level your empire's overall production (effective cities) rises.



For argument's sake, let's say late game you're absolutely rolling in the dough, your cities are all net-positive approval (say, 10-tile triangles: 7 level 2 districts, 3 level 1 districts = +35%, -30%). You've got wine activated all the time (+30%). You've got empire plan economy tier 3 activated all the time (+25% approval). You've got Sewer System and Central Market (+20%, +25%). You've got 4 other miscellaneous boosters activated all the time (+5%, +5%, +5%, +5%). Your total approval is 60+35-30+30+25+20+25+5+5+5+5 = 185% approval.





Obviously, the above is a simplification (assuming that all cities have the same basic approval), but it's a good illustration.



In conclusion, the more approval you can have, the more cities you should have to make use of it. On the other hand, if you have very bad approval, the same applies: you should have more cities to make up for it. Perhaps the best advice, then, is if you're going to take an approval level hit, you need to manage the transition: you need to rush a whole bunch of cities out at once (whether by taking them or settling them) in order to overcome the loss in effective cities.

Realistically, your cities will not all have exactly the same approval, which will cause those curves to smooth out a bit.

I think it would be nice to be given a 'free' city depending on map size. So normal you get one city before the -10 comes into play. Large would give you two cities, and huge would give you three. Perhaps something similar could be done with smaller maps and districts.

Stealing another factions capital gives you a free city as it retains the palace bonus for being a capitol city.