Selective Preference Feedback Changes the Information Order

Can deleting a tie category make preference learning impossible? Under selective response, yes. We study fixed-confidence identification from complete response/nonresponse laws. Binary one-protocol feedback can be nonidentifying; retaining a scored tie yields quartic information and a ${\Delta }^{-4}\log (1/\delta )$ lower bound, while valid protocols yield quadratic information and a ${\Delta }^{-2}\log (1/\delta )$ lower bound. After profiling an analytic nuisance manifold, the first normal likelihood jet not reproduced by nuisance or model uncertainty determines the profiled KL order. In a degree-$r$ scored model, we derive a sharp support threshold, coefficient, and finite-gap alias radius at scale ${\Delta }^{r+1}$. Under imperfect exclusion, arbitrary compact joint validity uncertainty yields a product-space coefficient; when the joint set is convex, maximin protocol design becomes a weighted Chebyshev-center problem, while rectangular budgets alone admit a closed-form pair design. A compact deployment-reference family gives positive, negative, and ambiguous decisions, with separate radii for losing a unique sign and attaining an opposite sign. An exchange-symmetric two-protocol product class exhibits a robust quadratic–quartic crossover; correlated response errors with equal marginals can differ. All sample-complexity statements are lower bounds; we do not claim an attaining same-sample algorithm.