Inflating Elo on Arena-Style Leaderboards with Sybil Votes

The model behind the leaderboard

Arena-style leaderboards fit a Bradley–Terry (or Elo) model to pairwise votes: models are matched, a voter picks a winner, and the ratings are updated so that the model's expected win probability approaches its observed win rate. The mathematics is a hundred years old, but it carries a hard assumption: votes are independent and sincere. Each ballot is supposed to be one human's honest preference between two outputs, uncorrelated with the other ballots and unmotivated by the standings.

Real leaderboards are traffic systems, and traffic systems are shaped by their friction. Voting requires an account, a captcha, a rate limit, a browser fingerprint; the operator throttles per-identity and per-IP. The friction is not decoration — it is the statistical assumption wearing clothes. Remove the friction and the model is fitting Elo to whatever bytes arrive, which is precisely the situation the rating math was never designed for.

The gap between "votes are sincere" and "votes are bytes" is where every manipulation lives, in principle. The rating system cannot distinguish one passionate user from five accounts controlled by one script; it can only see the vote stream and its statistics.