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On a functional equation related to Thurstone models
Abstract
If f and g are nonvanishing characteristic functions the functional equation g(s)g(t)g(-s - t) = f(as)f(at)f(-as - at) implies g(s) = eibsf(as), i.e., f and g corresponding to probability distributions of the same type. It is shown here that when f and g are allowed to vanish this equation also has solutions in which f and g correspond to distributions of different types. The practical implication is that there are nonequivalent. Thurstone models which cannot be discriminated by any choice experiment with three objects. © 1978.
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