Below-Chance Blindness: Prompted Underperformance in Small LLMs Produces Positional Bias Rather than Answer Avoidance
Authors: Jon-Paul Cacioli
Organizations: Independent Researcher, Melbourne, Australia
Abstract
Detecting sandbagging--the deliberate underperformance on capability evaluations--is an open problem in AI safety. We tested whether symptom validity testing (SVT) logic from clinical malingering detection could identify sandbagging through below-chance performance (BCB) on forced-choice items. In a pre-registered pilot at the 7-9 billion parameter instruction-tuned scale (3 models, 4 MMLU-Pro domains, 4 conditions, 500 items per cell, 24,000 total trials), the plausibility gate failed. Zero of 12 model-domain cells showed significant below-chance performance under sandbagging instruction. Exploratory analyses revealed three qualitatively distinct failure modes. Qwen-2.5-7B and Phi-3.5-mini largely ignored the sandbagging instruction, with 62-88% response identity with the honest baseline. Llama-3-8B complied substantially but implemented underperformance as a positional heuristic, collapsing its response distribution onto middle-alphabet options (E at 31.8%, F at 26.1%) regardless of where the correct answer fell. This produced accuracy boosts of up to 33 percentage points when the correct answer coincidentally occupied the model's preferred position. An explicit anti-task instruction ("pick the least likely answer") drove two of three models below chance, with accuracy as low as 0.024. The capability for answer-aware avoidance therefore exists but is not activated by "deliberately underperform." BCB did not fail as a logical marker of answer-aware avoidance. It was not observed in this regime because the model showing the largest behavioural shift exhibited behaviour consistent with a position-dominant response policy rather than content-aware answer avoidance. We propose that positional-distribution shift may be a more effective behavioural signature than below-chance accuracy for detecting prompted underperformance at this model scale.
A predecessor pilot (Cacioli, 2026) found that Llama-3-8B implements prompted sandbagging as positional collapse rather than answer avoidance. However, fixed option ordering in MMLU-Pro left open whether this reflected a model-level position-dominant policy or dataset-level distractor structure. This pre-registered follow-up (3 models, 2,000 MMLU-Pro items, 4 conditions, 24,000 primary trials) added cyclic option-order randomisation as the critical control. The pre-registered item-level same-letter diagnostic did not confirm deterministic position-tracking (same-letter rate 37.3%, below the 50% threshold). However, pre-specified supporting analyses revealed that the response-position distribution under sandbagging was highly stable under complete content rotation (Pearson r = 0.9994; Jensen-Shannon divergence = 0.027, compared to 0.386 between honest and sandbagging conditions). Accuracy spiked to 72.1% when the correct answer coincidentally occupied the preferred position E, and fell to 4.3% at position A. The data provide strong evidence for a soft distributional attractor: under sandbagging instruction, the model enters a low-entropy response-position basin centred on E/F/G that is highly stable and largely content-invariant at the aggregate level. Qwen-2.5-7B served as a negative control (non-compliant, no distributional shift). These results provide evidence, at the 7-9 billion parameter scale, that response-position entropy is a promising black-box behavioural signature of this sandbagging mode.
When instructed to underperform on multiple-choice evaluations, do language models engage with question content or fall back on positional shortcuts? We map the boundary between these regimes using a six-condition adversarial instruction-specificity gradient administered to two instruction-tuned LLMs (Llama-3-8B and Llama-3.1-8B) on 2,000 MMLU-Pro items. Distributional screening (response-position entropy) and an independent content-engagement criterion (difficulty-accuracy correlation) jointly characterise each condition. The gradient reveals three regimes rather than a monotonic transition. Vague adversarial instructions produce moderate accuracy reduction with preserved content engagement. Standard sandbagging and capability-imitation instructions produce positional entropy collapse with partial content engagement. A two-step answer-aware avoidance instruction produces extreme positional collapse, with near-total concentration on a single response position (99.9% and 87.4%) and no measurable content sensitivity. This was the only multi-step instruction tested, and it produced the most extreme shortcut. The attractor position matches each model's content-absent null-prompt default. The effect replicates across both models and four academic domains. Distributional collapse and content engagement can co-occur (50% concordance between screening criteria), indicating that entropy-based screening and difficulty-based content assessment capture partially independent dimensions of response validity. Results suggest that instruction complexity can determine whether adversarial compliance uses content-aware or content-blind mechanisms in small instruction-tuned LLMs under greedy decoding.
A model should refuse two different things: answers it would get wrong, and questions it should not answer at all, such as unanswerable ones or ones resting on a false premise. The usual recipe thresholds a single confidence score, which cannot tell these apart. Across five instruction-tuned models from three families (2B to 14B), we find they are separate axes. Ordinary answer-confidence tracks whether an answer is right but is nearly blind to whether the question is answerable; a linear probe on hidden states does the reverse. The blind spot does not shrink with scale. It is worst on naturally occurring false-premise questions (CREPE). There, answer-confidence, P(IK), P(True), and even asking the model outright whether a premise is false all stay near chance, while a hidden-state probe reaches 0.69 to 0.77 AUROC: the model represents a problem it will not report. This turns out to be fixable. Instructing a model to check premises backfires, because it then disputes sound and false premises alike (57% false challenges), unable to tell them apart; routing the same instruction with the probe roughly triples challenge precision. We turn the two axes into a calibrated policy that answers only when an answerability score and a correctness score each clear a separately certifies behave differently: the unanswerable-answer rate is controllable at every scale, while the wrong-answer rate is capped by model accuracy, so the guarantee tightens as threshold policy certifies both budgets at 0.75 coverage of correct answers, against 0.31 for a single threshold; at 14B it is the only policy that certifies at all.