Abstract
The purpose of the present paper is to demonstrate and briefly comment on three essential theorems on the theory of cardinal utility and random choice. According to the first theorem the invariance of cardinal utility in any linear transformation implies a particular invariant form for the preference function of random choice. According to the second theorem the Postulate of cardinal isovariation 1 is a necessary consequence of the invariance of cardinal utility in any linear transformation. According to the third theorem the neo-Bernoullian index B(x), if it exists, is identical to cardinal utility u(x).
Science strives to render identical things which at once appeared to be different.
Emile Meyerson
Science moves towards unity and simplicity
Henri Poincaré
When one has presented a theory in science, our purpose should never be to keep it by searching all that can justified it and by ruling out all that can invalidate it, since real progress always consists of replacing an old theory which contains fewer facts by a new one which embodies more…
The ideas and theories of our predecessors must be preserved only as far as they present the state of science, but evidently they are destined to change, unless we admit that science is not to progress any more, which is impossible.
Claude Bernard
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Allais, M. (1988). Three Theorems on the Theory of Cardinal Utility and Random Choice. In: Eberlein, G.L., Berghel, H. (eds) Theory and Decision. Theory and Decision Library, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3895-3_10
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DOI: https://doi.org/10.1007/978-94-009-3895-3_10
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