Makes you wonder if its just easier to farm fire's and trash from rioters to gain points at a steady rate.
I'm still gathering info for uoguide but I *think* it goes like this:
Arresting Angry Rioters → 100 points towards positive loyalty
Helping Angry Protestors → 25 points towards positive loyalty
Putting out fires → 2 points towards positive loyalty
Killing Angry Rioters → 400 points towards negative loyalty
So you should put out 200 fires to reach "Commended" while arresting only 4 rioters takes you to the same loyalty. Killing only a single rioter will make you "Disfavored" and 5 will make you "Detested" ((?) : educated guess):
Level 1 ("Commended"

"Disfavored") : 400 points
Level 2 ("Respected"

"Detested") : 2,000 points
Level 3 ("Adored"

"Reviled") : 10,000 points
Level 4 ("Venerated"

"Abhorred(?)") : 50,000(?) points
Do not bother with the fires. I didn't test the garbage yet, but I guess it is the same as putting out fires.
I consider "Commended", "Respected", "Adored" and "Venerated" as "pure" positive ratings while "Disfavored", "Detested", "Reviled" and "Abhorred" (not sure about the last one) as "pure" negative ratings. If you both helped the city and killed rioters, you get mixed ratings like "Despised", "Disliked", "Doubted" and "Esteemed".
I'm still not sure how killing a rioter affects your positive loyalty or helping the city affects your negative loyalty.