An uncountable number of scenarios exist where a perfectly rational person is mathematically blocked from making the right choice.
Finite probability spaces contain infinite situations where subjective beliefs prevent an agent from reaching an objectively good decision. Even when provided with all relevant information, a person's internal probability model can create a permanent barrier to the correct path. Standard economic theory assumes that rational actors will eventually find the optimal solution if they have enough data. This proof demonstrates that rationality itself can be a cage that keeps people from seeing the truth. Human decision-making is fundamentally limited by the mathematical structure of our own perspectives.
Uncountably many conditionally inaccessible decisions exist in every finite probability space
arXiv · 2605.02865
In a recent paper \cite{Redei-Jing2026} the notion of conditional $p$-inaccessibility of a decision based on utility maximization was defined and examples of conditionally $p$-inaccessible decisions were given. The conditional inaccessibility of a decision based on maximizing utility calculated by a probability measure $p^*$ expresses that the decision cannot be obtained if the expectation values of the utility functions are calculated using the (Jeffrey) conditional probability measure obtained