Technical Summary: OptimismBench

Problem Statement

Large language models (LLMs) are increasingly deployed as decision aids where their probability judgments directly influence downstream choices. However, existing evaluation frameworks fail to detect a specific type of systematic error: directional bias. Standard calibration metrics (e.g., Expected Calibration Error) aggregate unsigned errors, meaning a model that is uniformly optimistic (overestimating positive outcomes) and one that is uniformly pessimistic (underestimating them) can yield identical calibration scores. Furthermore, naturalistic forecasting tasks often lack ground-truth probabilities, making it difficult to distinguish between a model that is simply inaccurate and one that possesses a systematic "tilt" toward positive or negative valences.

The paper posits that LLMs may exhibit a valence-dependent distortion similar to human optimism bias (Weinstein, 1980; Sharot, 2011), where models systematically overestimate the probability of positive outcomes and underestimate negative ones, or vice versa. This bias has not been directly measured because prior work on probability coherence (e.g., Zhu and Griffiths, 2025) reported only unsigned violations without decomposing the direction of the error.

Methodology: OptimismBench

To address this gap, the authors introduce OptimismBench, a benchmark designed to detect directional bias using inverted pairs.

Core Mechanism: Inverted Pairs

For every scenario, the model is asked to estimate two complementary probabilities:

1. $P(\text{success})$ (Positive framing)
2. $P(\text{failure})$ (Negative framing)

A perfectly consistent model should produce estimates that sum to 100. The benchmark defines a Skew metric to quantify directional asymmetry:
$$\text{Skew}_i = s^+_i - (100 - s^-_i)$$
Where $s^+_i$ and $s^-_i$ are the model's integer responses (0–100) to the positive and negative versions of scenario $i$.

• Positive Skew: Indicates optimistic bias (overestimating success relative to failure).
• Negative Skew: Indicates pessimistic bias.
• Zero Skew: Indicates internal consistency.

The metric is decomposed into valence components ($\delta^+$ and $\delta^-$) to distinguish between "compound overclaim" (inflating both outcomes) and classical directional optimism/pessimism.

Experimental Design

• Dataset: 60 controlled inverted-pair scenarios across 6 domains (everyday, academic, project, business, policy, health). Scenarios are culturally neutral and lack stated base rates to force probabilistic judgment rather than retrieval.
• Scale: The released dataset includes 3,870 items across 10 languages.
• Models Evaluated: 16 models from 8 providers (OpenAI, Anthropic, Google, Alibaba, DeepSeek, Mistral, Meta, Zhipu), ranging from small to frontier tiers.
• Tracks:
  • Track A (Calibration Control): Scenarios with explicit base rates to verify models can report known probabilities (expecting Skew $\approx$ 0).
  • Track B (Primary): Naturalistic scenarios without stated base rates.
  • Tracks C & D: Recommendation and Salience tracks to test if bias persists across different elicitation frames.
• Interventions: The study employs factorial interventions including narrative manipulation (adding positive/negative context), perspective shifts (first/second/third person), temperature variations, and explicit self-debiasing warnings.

Key Results

1. Universal Directional Bias

All 16 evaluated models exhibit significant directional bias ($p < 0.002$).

• Optimism: 14 models are optimistic, with Skew values ranging from +4.2 to +16.6.
• Pessimism: Only Anthropic's frontier-tier models (Opus 4.6: -5.1, Sonnet 4.6: -7.7) exhibit pessimistic bias.
• Provider Agnostic: The bias spans commercial APIs, Chinese providers, and European models, indicating it is not specific to a single provider's training data.

2. The Role of Post-Training (Alignment)

The direction of bias is determined by post-training (alignment) rather than pre-training or architecture alone.

• Controlled Probes: Comparing matched base-versus-chat pairs across four families (Qwen, Llama, Gemma, Mistral) reveals family-specific shifts:
  • Qwen: Alignment shifts bias toward less optimism (negative shift in all 5 pairs).
  • Llama: Alignment amplifies optimism (positive shift in all 4 pairs).
  • Gemma/Mistral: Show single-pair pilots consistent with these trends.
• Anthropic Gradient: Within Anthropic, the lightweight Haiku 4.5 is optimistic (+6.1), while the larger Opus and Sonnet are pessimistic. This non-monotonicity rules out a simple "larger models are less biased" hypothesis, suggesting alignment recipes vary by tier.

3. Robustness and Stability

• Prompt & Temperature: Bias direction is preserved across prompt variations, temperatures (0.7 vs. 1.0), and perspective shifts (ruling out sycophancy as the primary cause).
• Self-Debiasing: Explicit warnings about optimism bias reduce the magnitude slightly but do not eliminate the direction, suggesting the bias is a deep property of the model's learned representations.
• Narrative Susceptibility: While adding positive/negative context shifts estimates by ~20 percentage points, the direction of the underlying bias (optimistic vs. pessimistic) remains unchanged.

4. Cross-Lingual and Domain Variance

• Model Identity Dominates: Inter-model variance is 4.7× larger than inter-language variance. The specific model used matters far more than the language it is speaking.
• Domain Modulation: While bias magnitude varies by domain (e.g., health habits show the largest spread), the direction of bias is stable across domains.

5. Probability Coherence

• Conjunction vs. Dose-Response: Models show high coherence on simple conjunction axioms ($P(A) \ge P(A \cap B)$) but high violation rates (27–47%) on dose-response monotonicity (consistent updating across evidence ladders). Alignment improves single-step coherence but does not fix multi-step monotonic reasoning.

Significance and Claims

The paper claims that directional probability bias is a universal, measurable, and stable property of current LLMs, distinct from calibration error.

1. Alignment Side-Effect: The study identifies valence-dependent probability distortion as a previously unmeasured side-effect of alignment. The direction of this bias (optimism vs. pessimism) is set by family-specific post-training stacks.
2. Auditability: OptimismBench provides a signed metric (Skew) that allows practitioners to audit models for directional bias without requiring ground-truth probabilities.
3. Task-Framing Dependence: Crucially, the paper notes that bias is not a single latent tilt. While probability framing (Track B) yields consistent directional bias, recommendation framing (Track C) can reverse the sign (eliciting caution), and salience framing (Track D) elicits uniform optimism. This implies that downstream pipelines inheriting these models will inherit the specific tilt of the framing used.
4. Practical Implication: For forecasting and advisory systems, the model's identity and its specific alignment history are the primary determinants of bias, not the language or the specific domain. Practitioners must profile models per task type rather than assuming a uniform bias direction.

The authors conclude that while alignment makes models more helpful, it simultaneously tilts their probability judgments, and this tilt is inherited by default in downstream applications. The benchmark and dataset are released to enable per-model directional-bias auditing.