Given that that little minigame ends when you get to 100+ authority, you might be better to do away with the randomization altogether and either add enough new scenes to hit 100 or simply buff the existing scenes to hit it since once you've seen them all it's just pure grinding to hit 100. Don't even know if hitting 100 will have an effect later though i presume it would and repeating scenes might make a new player think it doesn't matter, negatively affecting outcomes that depend on getting to 100, later.
There are plans to have authority effecting tax revenue, once I add in the government management mechanics.
Narratively the whole idea is that each time you go out on patrol, the crimes that occur are just part in parcel of life in Themis, that it is in its nature, generic and common place. You stepping in to do something being the exception to everyone's lives, until that intervention becomes the new normal.
When adding in the patrols I knew that this was just the first step to a series of story events, culminating in the first ever "competent" and "Lawful Evil" drow city of the Underneath. Setting the stage for the takeover of all of the other "less competent" and "Chaotic Evil" drow cities.
TLDR: Player woos the Neath by being the only source of stability and harsh justice, and then using this reputation as a launchpad for conquest.
(That's actually how the Taliban conquered Afghanistan from the Mujahideen).