Assume that we have a way of quantifying happiness, and assume that all the people mentioned are equally well-off (not that the second point matters, I don't think). I know what the answer would be if "happiness" was replaced with "money" in my question. Because of diminishing marginal returns, we would give 100 dollars each to 10 people to maximize total utility(happiness). But happiness itself surely doesn't have such diminishing marginal returns (because it is the end goal, and doesn't "return" anything). So would a pure utilitarianism say that the two decisions are morally equivalent?
To add onto this, given the choice between giving 10000 units of happiness to 1 person and distributing 9999 units equally amongst 10 people, would a utilitarian choose the former?
I consider myself a utilitarian, and personally believe it is far "better" than other ethical systems, but this is a question which somewhat troubles me as it goes against my intuition (which I know isn't really important).