If I were a politician, my pleasure would probably partly depend on keeping my job and upon accomplishing policy that would bring me pleasure, otherwise I wouldn't have run for office -- and to do that, I would need to consider the pleasure needs of the voters, otherwise they might vote me out. So I don't see those processes as incompatible.
I would likely vote for an Epicurean before a utilitarian (depending on their specific policy positions), because a social utilitarian takes a quasi-religious view towards creating some kind of hypothetical "average happiness", and an Epicurean would be more likely to assess the actual pleasure requirements of real voters and not according to some sort of ideal. A person like that would be interested in what I need for pleasure, because I have friends and could influence the election, possibly. At least at the state level, I have been able to influence an occasional election by public speaking without making any financial contributions.
Plus, I could get to know that Epicurean as a friend, and then her happiness would include mine, lol.