Calibrated Confidence Is Hard to Beat: A Negative Result on Evidence-Accumulation Buzzing for Zero-Shot Incremental Question Answering

A natural hypothesis for incremental question answering—motivated by the drift-diffusion model (DDM) of primate decision making—is that a frozen language model emits noisy per-clue evidence and that a training-free controller should accumulate that evidence to an optimal stopping boundary, beating a model that buzzes when its self-reported confidence is high. We test three forms of this hypothesis on 150 human-written adversarial QANTA tossups with a frozen GPT-4o: a self-consistency DDM, a reward-rate-optimal stopping rule, and a contradiction-aware accumulator. All three controllers lose decisively to a one-line baseline that buzzes when verbalized confidence exceeds a threshold (9.84 vs. 7.41, 6.87, and 6.32 mean points; non-overlapping 95% bootstrap CIs). The cause is measurable: verbalized confidence is well calibrated (ECE 0.051), whereas the accumulated self-consistency signal is not (ECE 0.142), because sample agreement saturates early on plausible-but-wrong entities. On frontier models, incremental QA collapses to a near-trivial stopping problem in which thresholding already sits at the reward-rate frontier, and added machinery buys nothing. We characterize the regime in which accumulation could still help.