algo-rank-wilsonlisted

# Wilson Score Ranking ## Overview Wilson Score interval provides a lower confidence bound on the true proportion of positive ratings. Unlike simple averages, it penalizes items with few ratings, preventing a 5/5 review item (1 review) from outranking a 4.8/5 item (1000 reviews). Computes in O(1) per item. ## When to Use **Trigger conditions:** - Ranking items by user ratings when review counts vary widely - Building "top rated" or "best of" lists that are fair to well-reviewed items - Sorting binary feedback (upvote/downvote) with confidence **When NOT to use:** - For continuous scores (use Bayesian average instead) - When comparing items with similar sample sizes (simple average suffices) ## Algorithm ``` IRON LAW: Never Rank by Simple Average When Sample Sizes Differ A 5.0 average from 1 review is NOT better than 4.8 from 1000 reviews. Wilson Score lower bound accounts for sample uncertainty: Items with few ratings get a LOWER bound, properly reflecting our uncertainty about their true quality. ``` ### Phase 1: Input Validation Collect per item: number of positive ratings (p), total ratings (n). For star ratings, convert to binary (e.g., 4-5 stars = positive). **Gate:** n > 0 for all items, confidence level chosen (typically 95%, z=1.96). ### Phase 2: Core Algorithm 1. Compute observed proportion: p̂ = positive / total 2. Wilson lower bound: (p̂ + z²/2n - z × √(p̂(1-p̂)/n + z²/4n²)) / (1 + z²/n) 3. Rank by Wilson lower bound descending (conservative estimate of tr