You do a couple missions for him. I only managed to get up to 76% for the voting tho. Dunno if it can be higher.
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When you first get back from defeating the warlord, you get 2 quests. The first one is getting your hands on an some kind of resource that gives free power to poorer folk for Garth. Succeeding in that helps a lot.
After that there is a quest to get police officers to do what they said they would. I beat them up because they were jerks, but you can convince them without violence.
Even when you do that quest tho, there are officers who do not do what they are supposed to and harass one of those of Garth's race. So I beat the crap out of them too.
You get that scene by wandering around downtown and it is repetitive. Tho doesn't increase the votes further.
Having high Akra respect also helps. So make sure you work on that. The best way is before you overthrow Galiano and work at the bar. A dominant character gains respect by forcing a gang member to do the hazing instead.