On Independence Axiom

A viral essay titled 'On Independence Axiom' by Ihor Kendiukhov, published on the rationality forum LessWrong, makes a provocative historical analogy to challenge a cornerstone of modern decision theory. The author compares the 'Independence Axiom'—one of four axioms in the von Neumann-Morgenstern (VNM) theorem that forces preferences to be linear in probabilities—to Euclid's problematic fifth postulate about parallel lines. For centuries, mathematicians tried to prove the 5th postulate from Euclid's other four, until Bolyai and Lobachevsky created consistent non-Euclidean geometries by simply rejecting it. Kendiukhov argues we are in a similar moment with the Independence Axiom.

The essay contends that dropping the Independence Axiom does not lead to irrationality or exploitability via 'money pumps,' as is often claimed. Instead, it opens the door to alternative, coherent decision theories that may better model actual human and agent behavior. The piece points to existing frameworks like ergodicity economics, which derives evaluation functions from the dynamics of stochastic processes rather than expected utility maximization, as examples of viable paths forward. The core claim is that the axiom is not a necessary truth of rationality, but one choice among several, and that exploring alternatives could be as fruitful for decision theory as non-Euclidean geometry was for physics.