Why do you say it can't lower the political power of unhappy slave?
The game files have a rule stating if an Unhappy Pop has a political power lower than 0.5, it is increased TO 0.5.
A pop's political power starts at 1. Being enslaved modifies this by -75%, bringing it down to 0.25. Building the Slave Facility supposedly adds another -25%, bringing it to 0 political power.
Except the game has a defined value where if a pop is unhappy, it's political power is always at least 0.5, no matter what it is after modifiers. BUT this only happens if it's unhappy.
If the slave is happy, it's political power is still reduced to 0 by this facility. Why that is a good thing, I don't know since happy pops increase stability. Maybe it's good because despite being happy they're not "as happy" as the free pops.
This has been known since 2.2.0 apparently, and they still haven't changed it. Little ticked by it, honestly. Either fix the game rule or update the descriptions.
Sources:
https://forum.paradoxplaza.com/foru...-must-have-because-the-game-is-lying.1149634/
https://forum.paradoxplaza.com/foru...roval-political-power-weighting-math.1138232/
https://forum.paradoxplaza.com/foru...tic-elite-is-not-strong-in-late-game.1148163/
Btw, there is an inverse: happy pops can never have a political power higher than 2. This means unhappy rulers will use all 5-10 of their political power if they're unhappy, but then only 2 if they are happy. This creates some stupid situations, where making a happy ruler unhappy will INCREASE stability.
EDIT: Actually the facility may not make it completely 0 PP, since it could be a rare multiplicative modifier. Meaning it'd be -25% of 0.25, which could put slave political power at 0.1875 before being incrased to 0.5.
