Police State is certainly not a top-tier civic, but with the right playstyle this civic isn't on the lower end either.
I've been considering this civic in the context of an authoritarian/stratified economy playstyle. It's entirely possible to run a more egalitarian empire with Police State, and I'm sure more thought will yield more ideas on the synergy of that situation. But this discussion is assuming you're focused on worker output, slavery, and/or disenfranchising the lower class.
First off, there's the +5 Stability. Everyone agrees it's useful, but one can argue Aristocratic Elite can provide more, up to +15 Stability (correct?) at the cost of one building slot and three population workers (two of which could instead be producing unity as administrators). However, hidden in the decisions menu of each planet is the ability to strike a deal with crime lords, earning an additional +10 Stability at the cost of +50% crime. (There needs to be a fair amount of existing crime before it appears, ~10% I believe. Disable enforcer jobs until it appears at around 10 pop.) Any empire can do it, but with Police State enforcers are a little more useful and not so much of a wasted job. Police State is more willing (and usually more able) to counteract the crime cost. So Aristocratic Elite can get more in the late game, when capitol building upgrades are unlocked and building slots are less valuable, but Police State can access the benefit earlier.
Those who care about unity know that the only sources come from enforcers, cultural workers or priests (planet-unique building), administrators and other ruler jobs (limited in number), trade value and the correct policy, and entertainers. Enforcers and entertainers are the only unity jobs that can scale with population.
Enforcers now produce 2 unity and reduce 30 crime (and produce defensive armies). Entertainers produce 2 unity and 10 amenities at the price of 1 consumer good. Unless you need the amenities, enforcers can essentially replace entertainers under Police State.
You usually won't need the amenities, or at least you'll need much less than an egalitarian empire.
Amenities affect happiness, happiness affects approval rating, and approval rating affects stability. Under stratified economy's political power weightings, the happiness of the upper class have an outsized effect on approval rating than the happiness of workers or slaves. Low amenities affect everyone equally, but because the majority of your population will be in the lower classes, the penalty to approval rating will be dampened by the political power modifier. The upper class is easier to keep happy with the hefty +15% happiness. Stratified economy living conditions are the most suited for at-par or below-par amenities.
However, happiness also affects crime, and crime isn't modified by political power. Each population produces 2*(1-happiness) crime. The happy rulers will generate less, but the majority of your population are unhappy workers and will cause more crime per pop.
Essentially, a planet can have high amenities and high happiness by employing entertainers, or have low amenities, unhappiness and high crime, which can be countered with enforcers. Police state puts enforcers on equal footing with entertainers (and less consumer goods usage), making the latter option more attractive.
One implication of this synergy is that authoritarian empires will have an easier time settling low-habitability, raw-resource-producing planets. Low habitability means higher amenity and consumer goods usage. Authoritarians can use stratified economy or slavery to counteract the consumer goods toll, and simply ignore the amenity problem.
Police state grants +15% Stability (5% from base, 10% from crime lord deals), and can use more enforcers instead of entertainers.
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