A thought experiment on reconsidering ordinal utility theory

Abstract: I design a thought experiment with the control variable method and reduction to absurdity to show that there is at least one problem making the internal logic of ordinal utility theory inconsistent, that is, under the condition that only ordinal utility information of articles is obtained, many fundamental axioms of ordinal utility theory cannot be established, which can explain why ordinal utility theory cannot be established. More importantly, this experimental method shows the form and properties of the real ordinal ranking, thus illustrating the perspective of this paper from both positive and negative angles, that is, ordinal utility theory cannot be established, and utility is essentially cardinal in nature.