  The idea of a representation theorem for expected utility dates back to Ramsey (1926).  (His sketch of a representation theorem is subsequently filled in by Bradley (2004) and Elliott (2017).) Ramsey assumes that preferences are defined over a domain of gambles, which yield one prize on the condition that a proposition \(P\) is true, and a different prize on the condition that \(P\) is false.  (Examples of gambles: you receive a onesie if you’re having a baby and a bottle of scotch otherwise; you receive twenty dollars if Bojack wins the Kentucky Derby and lose a dollar otherwise.) 