Option order stops steering the answer: iterated cyclic reordering drives flip rate to zero across five benchmarks and five models
System One decision models answer a choice question in one forward pass, but the answer shifts with the order in which options are listed, and the probabilities carry a prior over answer labels. IJev starts from an order that ignores the input order, repeatedly reorders options by a prior-corrected cyclic average, and averages the round distributions instead of returning the last round. Across five benchmarks and five models, every cell has flip rate zero; the default uniform round average lowers negative log-likelihood in 24 of 25 cells while accuracy stays comparable to a single cyclic average.