LessWrong (Curated & Popular) "On Independence Axiom" by Ihor Kendiukhov
Mar 10, 2026
A dive into whether the independence axiom is decision theory’s shaky fifth postulate. Two meanings of utility are contrasted and argued to be frequently conflated. Alternatives like resolute choice, ergodicity economics, prospect-style models, and ranked-dependent utilities are surveyed. Classic puzzles such as Allais and Ellsberg are reframed through long-run growth and holistic exposure.
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Independence Is The Structural Leap To Expected Utility
- The independence axiom forces preferences to be linear in probabilities, making VNM utility cardinal and risk attitudes meaningful.
- Dropping independence still yields coherent preference orderings (via Debreu) and opens alternative decision geometries that better fit some real-world dynamics.
Two Different Utilities Are Often Conflated
- 'Utility' hides two different objects: ordinal preference utility (F1) and cardinal VNM utility (F2) with real curvature information about risk attitudes.
- F2 is defined up to affine transforms and determines gamble acceptance, while F1 only ranks certain bundles.
Hammond Shows Independence Follows From Two Sequential Principles
- Hammond's 1988 result shows dynamic consistency plus consequentialism logically implies independence, which justifies independence in sequential settings.
- But that only proves sufficiency; other coherence strategies can also block exploitation without independence.