Formal Power Series Representations in Probability and Expected Utility Theory
This provides a foundational framework for expected utility theory, addressing limitations in orthodox models for decision-making under uncertainty.
The paper tackles the problem of developing a general theory of coherent preference that relaxes traditional restrictions like transitivity and continuity, showing that any coherent preference system can be extended to a complete one and represented by utility in an ordered field extension of the reals.
We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it satisfies a certain coherence requirement analogous to the one de Finetti advanced for his foundations of probability. Unlike de Finetti's theory, the one we set forth requires neither transitivity nor Archimedeanness nor boundedness nor continuity of preference. This theory also enjoys the property that any complete preference system meeting the standard of coherence can be represented by utility in an ordered field extension of the reals. Representability by utility is a corollary of this paper's central result, which at once extends Hölder's Theorem and strengthens Hahn's Embedding Theorem.