moonsorter

Browser-based ranking system using the Plackett-Luce model with uncertainty quantification. Built in MoonBit, compiled to WebAssembly.

What it does

Ranks items through pairwise comparisons or full ranking inputs. Uses the Plackett-Luce (PL) statistical model to estimate relative strengths and compute confidence intervals via bootstrap resampling.

Algorithm

Plackett-Luce Model (Luce 1959, Plackett 1975): Extends Bradley-Terry to full rankings. For a ranking where item i is placed above item j:

P(i > j | remaining items) = exp(strength_i) / sum_k(exp(strength_k))

For pairwise comparisons (Bradley-Terry special case):

P(i beats j) = 1 / (1 + exp(-(strength_i - strength_j)))

MM Algorithm (Hunter 2004): Iterative majorization-minimization for MLE. Update rule:

gamma_i^new = (W_i + prior) / (denominator_i + prior)

where gamma_i = exp(strength_i), W_i = wins at position i, and denominator aggregates over ranking positions.

MAP Regularization: Uses prior = 1.0 by default to prevent degenerate solutions with sparse data.

Converges to MLE without gradient computation or line search. Constraint: sum(strengths) = 0 for identifiability.

Build

Requires MoonBit toolchain.

# Build WASM
moon build --target wasm-gc

# Copy output to site
cp target/wasm-gc/release/build/src/src.wasm site/public/moonsorter.wasm

Run

cd site
bun install
bun run dev

Visit http://localhost:4321 and start ranking items.

Development

# Typecheck + format
moon check && moon fmt

# Generate interface files (always run after changes)
moon info

# Run tests
moon test

# Update test snapshots after behavior changes
moon test --update

# Coverage report
moon coverage analyze > uncovered.log

Project Structure

src/
  types.mbt           # Core PL model, MM fitting
  indexed_ranker.mbt  # Main API with uncertainty quantification
  clustering.mbt      # K-means tier clustering
site/
  src/                # Astro site source
  public/
    moonsorter.wasm   # Compiled WASM binary

Features

• Full rankings: Input complete orderings, not just pairwise
• Uncertainty quantification: Bootstrap confidence intervals for ranks
• Pair selection policies: Random, uncertainty-based, coverage-based
• Tier clustering: Group similarly-ranked items via k-means
• Undo: Revert last comparison

Code Style

• Block-style organization with ///| separators
• Snapshot testing with inspect (prefer over assert_eq)
• *_wbtest.mbt for whitebox tests

References

• Luce (1959): Individual Choice Behavior
• Plackett (1975): The Analysis of Permutations
• Hunter (2004): MM Algorithms for Generalized Bradley-Terry Models
• Bradley & Terry (1952): Rank Analysis of Incomplete Block Designs