Multi-Evaluator Quality Assessment Score

In modern AI evaluation pipelines, particularly when assessing the quality of generative model outputs, a common and robust approach is to aggregate ratings from multiple evaluators across weighted quality dimensions. This technique, often employed in LLM-as-a-judge frameworks, provides a more reliable assessment than single evaluator ratings by capturing consensus and measuring agreement.

Consider a scenario where you have N evaluators (which could be human annotators, different AI models, or specialized evaluation modules) each rating a response across K distinct quality criteria. Each criterion might represent dimensions such as accuracy, coherence, relevance, style, or safety. Since not all criteria are equally important for a given use case, each dimension is assigned a weight that reflects its relative significance.

The Evaluation Model:

Given:

• A matrix of scores where judge_scores[i][j] represents the score (0 to max_score) given by evaluator i for criterion j
• A weight vector criteria_weights where criteria_weights[j] is the importance weight for criterion j (all weights sum to 1)
• A passing_threshold representing the minimum normalized score required for approval
• A max_score representing the maximum achievable score per criterion

Your function should compute:

1. Criterion Scores: For each criterion j, compute the average score across all evaluators: $$\text{criterion_score}j = \frac{1}{N} \sum{i=1}^{N} \text{judge_scores}[i][j]$$

2. Weighted Score: Combine the criterion scores using their weights: $$\text{weighted_score} = \sum_{j=1}^{K} \text{criteria_weights}[j] \times \text{criterion_score}_j$$

3. Normalized Score: Scale the weighted score to a 0-1 range: $$\text{normalized_score} = \frac{\text{weighted_score}}{\text{max_score}}$$

4. Pass Status: Determine if the normalized score meets or exceeds the passing threshold.

5. Evaluator Agreement: Calculate a metric (0 to 1) indicating how much evaluators agree with each other. Use a standard deviation-based approach: compute the standard deviation for each criterion, average these values, and compare against the maximum possible standard deviation. Higher agreement (lower variance) yields values closer to 1.

$$\text{agreement} = 1 - \frac{\text{mean_std}}{\text{max_possible_std}}$$

Where max_possible_std is the standard deviation when scores are maximally dispersed (half at 0, half at max_score).

Your Task: Implement a function that takes the evaluator scores, criteria weights, passing threshold, and maximum score, then returns a comprehensive evaluation dictionary with all computed metrics.