On The Independence Axiom

A March 2026 essay by Ihor Kendiukhov titled 'On The Independence Axiom' has gained significant traction on LessWrong by drawing a provocative historical parallel. The author compares the independence axiom in von Neumann-Morgenstern expected utility theory to Euclid's fifth postulate (the parallel postulate). For centuries, mathematicians tried to prove the fifth postulate from Euclid's other four axioms, until Bolyai and Lobachevsky discovered that rejecting it led to entirely consistent, non-Euclidean geometries. Kendiukhov argues the independence axiom—which forces preferences to be linear in probabilities—serves a similar, problematic role as a 'Fifth Postulate of Decision Theory.'

The core argument is that dropping the independence axiom does not lead to irrationality or exploitability (like becoming a 'money pump'), but instead opens the door to more nuanced decision theories. The essay points out that several existing alternatives to expected utility theory, such as those explored in ergodicity economics, already relax this axiom. These frameworks can yield different, context-dependent evaluation functions derived from the dynamics of stochastic processes, potentially describing actual human and rational behavior more accurately than the rigid expected utility maximization mandate. The post is a call to explore the consistent and useful decision theories that exist when we are not constrained by this specific axiom.