---
license: mit
task_categories:
  - question-answering
  - text-generation
language:
  - en
tags:
  - benchmark
  - reasoning
  - multi-step
  - evaluation
  - llm-evaluation
  - goodhart
  - execution-vs-understanding
size_categories:
  - n<1K
---

# Goodhart Gap Benchmark

**Detecting the gap between understanding and execution in language models**

## Overview

The Goodhart Gap Benchmark tests whether language models can correctly *execute* multi-step reasoning tasks that they can correctly *explain*. Named after Goodhart's Law ("When a measure becomes a target, it ceases to be a good measure"), this benchmark reveals a critical failure mode: models that understand procedures but fail to execute them.

## Key Finding

In our testing of 15+ models:
- **gpt-4o**: 57% pass rate (fails on financial, scheduling, units)
- **gpt-4o-mini**: 36% pass rate
- **Claude 3.5 Haiku**: 93% pass rate
- **Llama 3.1 70B**: Fails the canonical discount calculation despite correct explanation

## The Canonical Example

**Problem**: "If a shirt costs $25 and is on 20% sale, and you have a $5 coupon, what do you pay?"

**Correct answer**: $15 (apply 20% discount first: $25 × 0.8 = $20, then subtract coupon: $20 - $5 = $15)

When we first ask models to *explain* the procedure, they all correctly state: "First apply the discount, then subtract the coupon."

When we then ask for the answer, many models fail—giving answers like $16, $17, $22.50, or even $175.

## Dataset Statistics

| Metric | Value |
|--------|-------|
| Total problems | 101 |
| Domains | 12 |
| Difficulty levels | 3 (easy, medium, hard) |
| Steps per problem | 2-6 |

### Problems by Domain

**Numerical Domains (67 problems)**

| Domain | Count | Description |
|--------|-------|-------------|
| math_discount | 15 | Discounts, coupons, taxes, markups |
| time | 13 | Duration arithmetic, travel times |
| financial | 10 | Interest, taxes, commissions |
| logic | 8 | Ordering, deduction, set operations |
| recipe | 7 | Scaling, unit conversion |
| scheduling | 7 | Task dependencies, work rates |
| units | 7 | Unit conversion with operations |

**Non-Numerical Domains (34 problems)**

| Domain | Count | Description |
|--------|-------|-------------|
| spatial | 7 | Direction tracking, grid navigation, relative positions |
| procedural | 6 | State machines, undo/redo, procedure following |
| text | 7 | String manipulation, encoding, word operations |
| sequence | 7 | Pattern recognition (letters, symbols, words) |
| causal | 7 | Cause-effect chains, counterfactuals, necessary/sufficient |

### Difficulty Distribution

| Difficulty | Count | Description |
|------------|-------|-------------|
| Easy | 28 | 2 steps, straightforward |
| Medium | 32 | 2-3 steps, some complexity |
| Hard | 7 | 3-4 steps, multiple operations |

## Data Format

Each problem is a JSON object with the following fields:

```json
{
  "id": "math_discount_01",
  "domain": "math_discount",
  "problem": "A product costs $25 and is on 20% sale. You also have a $5 coupon. What do you pay? Answer with just the number.",
  "correct_answer": "15",
  "explanation": "25 × 0.8 = 20.0, then 20.0 - 5 = 15.0",
  "understanding_check": "To solve this, first apply the 20% discount, then subtract the coupon. What are the two steps?",
  "difficulty": "easy",
  "steps": 2
}
```

### Field Descriptions

| Field | Description |
|-------|-------------|
| `id` | Unique identifier (domain_type_number) |
| `domain` | Category of reasoning required |
| `problem` | The question posed to the model |
| `correct_answer` | Expected answer (numeric or text) |
| `explanation` | Step-by-step solution |
| `understanding_check` | Prompt to verify model understands the procedure |
| `difficulty` | easy, medium, or hard |
| `steps` | Number of sequential operations required |

## Usage

### Quick Evaluation

```bash
# Install requirements
pip install requests

# Evaluate OpenAI model
python evaluate.py --provider openai --model gpt-4o -v

# Evaluate Claude model
python evaluate.py --provider anthropic --model claude-3-5-haiku-latest -v

# Evaluate local Ollama model
python evaluate.py --provider ollama --model llama3.1:8b -v
```

### Python API

```python
import json

# Load dataset
problems = []
with open('data/test.jsonl') as f:
    for line in f:
        problems.append(json.loads(line))

# Test your model
for problem in problems:
    response = your_model.generate(problem['problem'])
    expected = problem['correct_answer']
    # Validate response against expected
```

### With HuggingFace Datasets

```python
from datasets import load_dataset

dataset = load_dataset("your-username/goodhart-gap-benchmark")

for example in dataset['test']:
    print(example['problem'])
    print(f"Expected: {example['correct_answer']}")
```

## Evaluation Criteria

A response is considered correct if:
1. **Numeric answers**: The expected number appears in the response (with tolerance for rounding)
2. **Time answers**: The expected time appears in any reasonable format (e.g., "4:45 PM", "4:45pm", "16:45")
3. **Yes/no answers**: The response clearly indicates yes, no, or "cannot determine"
4. **Ordering answers**: Items appear in the correct sequence

## Leaderboard

| Model | Provider | Pass Rate | Weakest Domain |
|-------|----------|-----------|----------------|
| Claude 3.5 Haiku | Anthropic | 93% | logic |
| Claude Sonnet 4 | Anthropic | 79% | financial, scheduling |
| gpt-4o | OpenAI | 57% | scheduling |
| gpt-4o-mini | OpenAI | 36% | most domains |
| Qwen 2.5 72B | Alibaba | TBD | - |
| Llama 3.1 70B | Meta | TBD | - |

*Submit your results via PR to add to the leaderboard*

## Why This Matters

### For AI Safety
Models that can explain correct procedures but execute them incorrectly are:
- Harder to detect through explanation-based evaluation
- More dangerous in agentic settings
- A gap between capability benchmarks and deployment readiness

### For Model Selection
Not all models are equal for multi-step reasoning:
- Model family matters more than size
- Distilled models often lose this capability
- Test execution, not just explanation

### For Training
The gap appears to be a training problem:
- Well-trained models (Claude Haiku) outperform larger models
- Suggests targeted fine-tuning could help

## Citation

```bibtex
@dataset{goodhart_gap_benchmark_2026,
  title={Goodhart Gap Benchmark: Detecting the Gap Between Understanding and Execution in LLMs},
  author={Adam Kruger},
  year={2026},
  url={https://huggingface.co/datasets/Adam1010/goodhart-gap-benchmark}
}
```

## License

MIT License - free for research and commercial use.

## Contributing

We welcome contributions:
- New test cases in underrepresented domains
- Results from additional models
- Improved validators
- Translations to other languages

Submit issues and PRs at: [GitHub Repository URL]

## Acknowledgments

Research inspired by:
- Goodhart's Law and its application to AI evaluation
- Work on multi-step reasoning in LLMs
- The distinction between System 1 and System 2 thinking