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Besides productivity multiplier, loyality dropping to zero causes escape.
Everything that causes unhappyness seems to also drop loyality. So unfillfulled needs, crime, lack of water, heat, electricity.
Increase by being in range of monument, being educated by loyal teacher/profesor/caretaker/prisonguard, listening to radio/watching tv and driving a car. Formulas aren't public, so I doubt anyone can give trusty numbers, as it's ballance of dozen causes on both sides not listed in personal sheet for most cases.
Missing needs (there are a lot), traveling for too long (> "5 hours"), unemployment, crime, and ex-cons moving into their building all actively reduce loyalty. Loyalty also passively decreases to a steady level dependent on the number of loyalty rising effects the citizen has on them, the number of missed needs, and the "Unsatisfied citizens reaction" setting.
There are two types of loyalty buildings; the ones that (can) give a large temporary boost to loyalty (school, university, orphanage, prison) and those that raise the minimum steady level of loyalty that citizen's loyalty can decrease to (monuments, radio, TV, personal cars).
Children cannot own electronics and so cannot benefit from TV and Radio until they become adults. The point of schools/universities/orphanages is to give a boost to immigrant's and children's loyalty so that their loyalty is not limited to 30% to 40% when they enter the workforce (and can start getting radios and TVs); prisons are similar but for criminals. This means you can have a constant supply of high loyalty workers even if they cannot immediately consume radio/TV programming.
To increase the stable level of loyalty for a citizen, you need to invest in loyalty specific buildings, typically in this order:
Productivity is dependent mostly on happiness (attained by meeting most/all needs) and loyalty, with 100% happiness and around 40% loyalty resulting in 100% productivity. Productivity also has a minimum value of 30%, and foreign workers' loyalty scores seem to have a reduced impact on their productivity.
Low productivity reduces the output of a worker, and by extension, the production % of factories and heating/power plants, and the number of active service slots of service/leisure buildings. On the other hand, buildings' production percentages cannot exceed 100%, but you can achieve 100% production/service with fewer workers of a higher productivity.
The loyalty of workers at buildings which affect loyalty (schools, radio, prison, etc.) determine the effectiveness of the loyalty increases of students and radio/TV media consumers. Loyalty of secret police workers determines how long the loyalty of residents stays visible for (i.e. it determines the interval that the secret police must visit the building to update the surveillance equipment). There are settings to prevent low loyalty workers from working at certain buildings, but these settings appear to be mostly ignored. The top speed (and possibly other characteristics) of personal cars influence the loyalty gain from them.
If you enable cheats, the loyalty scores of residences and citizens will be revealed. The red star will be opaque if surveillance equipment is installed at their residence and transparent if not.
So, I'm working on a pretty mature Republic, and I decided to finally start my Uranium Town, by finding a way to get said uranium down off a "could be a cliff" mountainside. For no particular reason, I also decided that this new town would be a glorious home for only the most loyal of citizens. To make a point of it, I straight up set the town to only allow citizens with 75%+ Loyalty to move in. That last sentence is important, so take another look at it.
If you read the above comments, you might remember this:
"... ex-cons moving into their building [...] actively reduce[s] loyalty."
I had 80% average loyalty nationwide and a VERY effective prison system. People coming out of their 0.5-year stays in the slammer were hitting the streets with 100% loyalty and snapping up all the vacant flats that "below average loyal" citizens couldn't... in my "maximum loyalty only" nuclear town.
And that pissed off the residents. Now whole districts of that down are flirting with sub-60% loyalty rates, and until I came here, I had no idea what was happening.
TL;DR - I tried to make an exclusive town for the elite-tier loyal citizens of my Republic, and now all the brainwashed ex-cons are depressing the real estate market.
Don't do what I did, kids. Take your 80% nationwide loyalty and don't fly too close to the sun.
No there is no guides, no tutorial, although it has been some time since this mechanic was introduced.
We only rely on expert user advice and videos from Bballjo.