A risky challenge for intransitive preferences

Philosophers have spent a great deal of time debating whether intransitive preferences can be rational. I present risky decision that poses challenge for the defender intransitivity. The intransitivity faces trilemma and must either: (i) reject rationality preferences, (ii) deny State-wise Dominance, or (iii) accept bizarre verdict you required to pay relabel tickets fair lottery. If we take first horn, then synchronic refutation intransitivity, an improvement on widely criticized diachronic arguments. sketch possible responses may rescue argue each response is but generates explanatory debt. conclude by showing how here clarifies foundations theory without transitivity, conditional some debt being payable.