OptimismBench: Directional Optimism Bias in LLM Probability Judgments

Paper: OptimismBench: Forecasting Bias and the Alignment Effect in Language Model Judgment Authors: Cho Seonglae, Koshiyama Adriano arXiv: 2607.26981

A Puzzling Piece of Arithmetic

Ask an LLM: "What is the probability this startup succeeds?" It answers 70%.

Then ask: "What is the probability it fails?" It answers 15%.

70 + 15 = 85. Where did the missing 15 points go?

Those 15 points are not a rounding error, nor "model uncertainty." They expose a directional bias that calibration metrics can never catch. Calibration metrics only measure the gap between predicted probabilities and true frequencies, and cancel out positive and negative errors — so a systematic tilt disappears from view. But the "vanishing" 15 points show the model systematically overestimates positive outcomes.

The paper proposes OptimismBench, using a method called inverted pairs to detect directional bias in LLM judgments — with no ground truth required.

Method: Inverted Pairs — Bias Detection Without Ground Truth

Traditional bias detection needs a "correct answer" — you must know the true success rate to judge whether a model is too optimistic or too pessimistic. But many real-world scenarios have no ground truth: whether a startup succeeds, whether a project ships on time, whether a negotiation concludes — the future is unknown.

OptimismBench's trick: it doesn't compare predictions against reality; it compares the model's answers to two phrasings of the same scenario.

For each scenario, two versions are constructed:

• Version A: ask for P(success)
• Version B: ask for P(failure)

If the model is unbiased, P(success) + P(failure) should equal 100% (the complementarity axiom). Any shortfall is the measure of directional bias. The authors define a Skew metric:

• Skew > 0 → optimism bias (overestimating positive outcomes)
• Skew < 0 → pessimism bias (overestimating negative outcomes)

Four Tracks

• Track A (calibration control): 15 calibration questions with true frequencies, confirming the bias is not mere miscalibration
• Track B (probability estimation): the main track, using inverted pairs
• Track C (recommendation): recommendations instead of probability judgments — does the bias persist?
• Track D (salience): varying scenario salience to amplify or suppress the bias

Factor Interventions

Four interventions were tested: narrative manipulation, perspective shifting, anchoring gradients, and self-debiasing. The bias survived all interventions — different prompts, temperatures, perspectives, and even self-correction left the directional bias intact.

Findings: 14/16 Optimistic, Only Anthropic Frontier Models Pessimistic

Across 16 models from 8 vendors:

• 14 models were optimistic — systematically overestimating positive outcomes
• 2 models were pessimistic — both from Anthropic's frontier (Claude) line

This is counterintuitive: alignment training is often assumed to make models more cautious, but here it appears to change bias *direction* — with different vendors pushing in different directions.

The Alignment Gradient

Comparing 11 base-vs-chat pairs across 4 model families:

• Post-training determines the sign of the bias — the same base model can end up with opposite biases after different vendors' post-training
• Qwen family: post-training moved models from pessimistic to optimistic
• Llama family: post-training moved models from optimistic to pessimistic

So optimism/pessimism is not inherent to architecture or pretraining data — it is shaped during post-training.

Model Identity > Language

A cross-language experiment (17 models, 6 languages) found between-model variance is 4.7x between-language variance. Swapping languages barely moves a model's bias; different models in the same language differ enormously.

Bias Can Reverse in Recommendation Tasks

In Track C, the bias sign can flip: a model optimistic in probability judgments may become pessimistic when giving recommendations. Bias is therefore not an intrinsic model property but a joint property of model × task framing.

Why This Matters

1. A structural blind spot in calibration metrics: ECE and Brier scores are unsigned — they cancel positive and negative errors. A model can be well-calibrated overall while systematically overestimating positive and underestimating negative outcomes, invisibly.

2. A side effect of alignment training: RLHF/DPO-style alignment shapes not only safety and helpfulness but also the direction of probability judgments. A model trained to be "more helpful" may systematically overestimate success rates — dangerous for risk assessment, medical decisions, and financial forecasting.

3. Downstream pipelines inherit the bias. As the paper's closing line puts it:

> "When alignment makes a model more helpful, it also tilts its probabilities; downstream pipelines inherit the tilt by default."

Any system using LLMs for probability judgments — prediction markets, risk assessment, project planning — should audit the directional bias of its models. You cannot assume "the model said 70%" means 70%: that number may be optimism-tilted.

A Cross-Domain Analogy: Human Optimism Bias

Human cognitive psychology has a well-known *optimism bias* — people systematically overestimate positive events and underestimate negative ones, first systematically documented by Weinstein (1980). LLMs plausibly inherit this pattern from human-generated training data. But there is a key difference: humans are universally optimistic, whereas LLM bias direction is determined by post-training — meaning alignment could counter-calibrate it, though different vendors have chosen different directions.

This raises a deeper question: should alignment calibrate models to be unbiased, or human-like and optimistic? Competing with humans in prediction markets might favor human-like optimism; risk assessment demands unbiasedness. The paper supplies the measurement tools, not the answer.

Limitations

1. Family-direction conclusions rest mainly on the Qwen and Llama pairs; Gemma-2-2b and Mistral-Small-24B were single-pair pilots with limited statistical power. 2. Cross-lingual evidence is unbalanced: 6 native-language prompts plus 4 English system prompts (DE/FR/HI/JA), a known confound. 3. Skew measures internal consistency, not deviation from human judgment — an "unbiased" model is not necessarily an "accurate" one. 4. No matched human-subject baseline, despite citing Weinstein (1980).

Closing Thoughts

The methodological contribution is elegant: inverted pairs turn ground-truth-free bias detection into an internal-consistency problem — a classic reframing that sidesteps the need for true outcomes.

The practical implication is more sobering: we increasingly use LLMs as probability-judgment engines, but they carry vendor-specific tilts. A risk-assessment system built on Claude may reach opposite conclusions from one built on Qwen.

Finally, there is a genuine tension between alignment and calibration: alignment makes models more helpful (users like optimistic answers) while tilting their probability judgments away from accuracy. There may be no perfect resolution — but now, at least, it can be measured.

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Paper: https://arxiv.org/abs/2607.26981 HTML version: https://arxiv.org/html/2607.26981v1 Dataset: 3,870 test items, 10 languages, open-sourced