Part of the assumption of the problem was that hitting with a stick has some constant negative utility for all the people.

It's always hard to think about this sort of thing. I read that in the original problem, but then I ended up thinking about actual hitting people with sticks when deciding what was best. Is there anything in the archives like The True Prisoner's Dilemma but for giving an intuitive version of problems with adding utility?

Then it depends. If you're a utilitarian, it is still better to hit the guy nine times than to hit ten people ten times.

If you allow some ideas about the utility of equality, then things get more complicated. That's why I think most people reject the simple math that 9 < 10.