Dispersion Is Not Doubt: Rethinking LLM Confidence Estimation When Multiple Answers Are Valid

Confidence estimators often treat concentrated support as evidence of correctness, relying—explicitly or implicitly—on the assumption that concentrated support implies a correct answer. When several answers are valid, however, this assumption fails: support can spread across correct alternatives without indicating error. We call this mismatch the concentration–correctness gap, and propose two layered conjectures. (a) The inversion conjecture: as the number of valid answers $K$ grows, confidence falls even as the model answers better. (b) The dispersion-is-not-doubt conjecture: the decline stems from support being re-divided among valid answers, not from greater uncertainty about correctness. To test them, we introduce MACE (Multi-Answer Confidence Estimation), $12,000$ open-ended questions with controlled answer cardinalities ($K=1/2/4/6$) and exhaustive, expert-audited reference sets. Across 9 models and 15 training-free estimators, both conjectures are confirmed: a multi-answer confidence inversion is widespread; all 15 estimators lose AUROC under pooled cardinalities; and valid mass stays stable on correctly answered questions while support is unevenly re-divided—entropy decomposition, elicited confidence, and cross-model analysis ($r=0.93$) jointly attribute the decline to valid-answer diversity. These findings motivate CARE (CArdinality-Rescaled Evidence), which rescales sampled answer frequency by question-level cardinality to approximate the total support on valid answers. Using verified counts, CARE raises AUROC from $74.6$ to $78.9$ on the broadest mixture, recovering approximately $77\%$ of the loss and demonstrating the value of estimating the number of valid answers for more reliable confidence.