As others have stated, obligation isn’t really part of utilitarianism. However, if you really wanted to use that term, one possible way to incorporate it is to ask what would the xth percentile of people do in this situation (where the people are ranked in terms of expected utility) given that everyone has the same information and use that as a boundary to the label “obligation.”
As an aside, there is a thought experiment called the “veil of ignorance.” Although it is not, strictly speaking, called utilitarianism, you can view it that way. It goes something like this: when deciding how a society should be set up, the designer should set it up as if they had no idea who they would become in the society. In this case “obligation” would probably loosely correspond to “what rules should that society have?” In this case, a utilitarian’s obligated giving rate would be something like
k*(Income—Poverty Line) where k is some number between 0 and 1 such that you maximize utility if everyone did the same.
As others have stated, obligation isn’t really part of utilitarianism. However, if you really wanted to use that term, one possible way to incorporate it is to ask what would the xth percentile of people do in this situation (where the people are ranked in terms of expected utility) given that everyone has the same information and use that as a boundary to the label “obligation.”
As an aside, there is a thought experiment called the “veil of ignorance.” Although it is not, strictly speaking, called utilitarianism, you can view it that way. It goes something like this: when deciding how a society should be set up, the designer should set it up as if they had no idea who they would become in the society. In this case “obligation” would probably loosely correspond to “what rules should that society have?” In this case, a utilitarian’s obligated giving rate would be something like
k*(Income—Poverty Line) where k is some number between 0 and 1 such that you maximize utility if everyone did the same.