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