Oskar Morgenstern, Some Reflections on Utility (1976)

Oskar Morgenstern’s essay defends the axiomatic achievement of von Neumann–Morgenstern expected utility theory while identifying limits to its account of preferences. It distinguishes the mathematical validity of a representation from its empirical scope: anomalous choices may reveal neglected phenomena, but do not themselves supply a coherent alternative theory.

It is natural that the “expected utility hypothesis” as presented in Chapter I of Theory of Games and Economic Behavior [7] would be challenged.

Morgenstern presents criticism as an expected consequence of theoretical innovation. He recalls the advance beyond ordinal utility: introducing uncertain prospects with numerical probabilities permits a utility representation determined up to a linear transformation, leaving its zero and unit unspecified. He regards the underlying axiomatic construction as secure.

For these axioms we have carefully shown that they are free of contradictions and have all the properties a true axiomatic system has to exhibit.

Later authors’ weaker axioms and simpler proofs reinforce the result without making the original formulation exhaustive. Morgenstern therefore separates questions about proof from questions about phenomena excluded by the assumptions.

The next question is whether there are phenomena relating to our intuition which neither the original von Neumann-Morgenstern axioms nor later ones capture. There are so far two possibilities to be considered (perhaps later on additional ones may appear).

The two possibilities are subjective probability and a distinct utility of gambling. The original system assumes numerical probabilities; Morgenstern credits Pfanzagl with rigorously addressing their derivation from subjective judgments. Pleasure in gambling remains a different, unresolved problem. He accepts its intuitive plausibility but requires an axiomatic account showing how it can be integrated with utility generally.

This requirement organizes his response to Allais and other critics. A counterexample to a universal empirical statement differs, in his account, from an objection to an axiomatic construction. Critics must specify revised assumptions and establish what utility representation follows—or demonstrate why none can exist. His comparisons with physical theories emphasize that a theory can retain value within a bounded domain while approximating a more complicated reality.

Morgenstern questions whether familiar experiments place respondents within conditions they can meaningfully assess. Extremely small probabilities may exceed ordinary intuitive discrimination, while hypothetical fortunes may be remote from participants’ experience. Without evidence of comprehension, calculation, and familiarity with the stakes, he doubts that reported choices constitute decisive tests. His extreme examples involving hypothetical execution or torture sharpen the objection: imagined answers need not reveal determinate preferences for situations respondents have never approached.

The discussion also challenges treating rationality as a label independently attached to observed choices. In game theory, rational behavior must follow from specified assumptions about preferred payoffs. Yet Morgenstern gives expected utility an educational role, suggesting that understanding the theory can lead people to revise inconsistent choices. He cites theory-trained students at New York University whose responses conformed to expected utility, while acknowledging alternative explanations involving calculation, attitudes toward uncertainty, and the absence of actual monetary consequences. This leaves a tension between confidence in the theory’s normative authority and caution about experimental interpretation.

The historical account limits any claim to finality. Von Neumann and Morgenstern needed numerical payoffs for game theory and chose to derive them through uncertainty rather than simply postulate them. Their construction answered that problem; it did not settle every question about preferences.

The conclusion broadens the research agenda beyond gambling. Time may require explicit treatment, and preferences may be only partially ordered. Some subsets might possess the Archimedean property while others do not. Morgenstern’s comparison between an observatory outside the atmosphere and any number of terrestrial observatories suggests qualitative differences that resist ordinary substitution. Such cases trouble familiar assumptions about optimal allocation. More fundamentally, decisions may impose an order that underlying preferences did not previously possess.

The essay combines confidence in formal demonstration with dissatisfaction about the reach of existing preference theory. Its methodological demand is that criticism distinguish mathematical achievement, experimental intelligibility, and neglected experience—and turn the latter into an articulated theoretical extension.