Relative utilitarianism

Let ${\displaystyle X}$ be a set of possible `states of the world' or `alternatives'; society wishes to choose some state from ${\displaystyle X}$. Let ${\displaystyle I}$ be a finite set, representing a collection of people. For each ${\displaystyle i\in I}$, let ${\displaystyle u_{i}:X\longrightarrow \mathbb {R} }$ be a utility function. A social choice rule (or voting system) is a mechanism which uses the data ${\displaystyle (u_{i})_{i\in I}}$ to select some element(s) from ${\displaystyle X}$ which are `best' for society. (The basic problem of social choice theory is to disambiguate the word `best'.)

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