Measurable triples and cardinal measurement

An axiom system is presented for a measurement structure incorporating homothetic and “Gorman polar form” weak orders as special cases. Representation theorems establish: (1) an operational method of constructing a numerical representation of such structures, and (2) that cardinal, rather than ordinal, measurement is obtained in that: (a) a class of elements is identified in the domain of the weak order which can play the same role as a yardstick in the measurement of length, and (b) the representation obtained is generally a ratio scale. Some simple special cases are also developed as are some implications for the theory of demand.