Intransitive Preferences Or Choice Errors? A Reply To Birnbaum

Birnbaum (2020) reanalyses the data from Butler and Pogrebna (2018) using his 'true and error' test of choice patterns. His results generally support the evidence we presented in that paper. Here we reiterate the reasons for our agnosticism as to the direction any cycles might take, even though the paradox that motivated our study takes a 'probable winner' direction. We conclude by returning to the potential significance of predictably intransitive preferences for decision theory generally.