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For story purposes, using a multi-tiered variant of utilitarianism based on social distance could lead to some interesting results. If the character were to calculate his utility function for a given being by something Calculated Utility = Utility / (Degrees of Separation from me)^2, it would be really easy to calculate, yet come close to what people really use. The interesting part from a fictional standpoint could be if your character rigidly adheres to this function, such that you can manipulate your utility in their eyes by becoming friends with their friends. (e.g. The utility for me to give a random stranger $10 is 0 (assuming infinite degrees of separation), but if they told me they were my sister's friend, it may have a utility of $10/(2)^2, or $2.50) It could be fun to play around with the hero's mind by manipulating the social web.
I think I once heard of a variant of this, only using degrees of kinship instead of social connections. Eg, direct offspring and full siblings are discounted to 50%, grandchildren to 25%, and so forth.