From choices to comparisons#

Every choice becomes one comparison and a tie becomes two half-weight comparisons. A qualified comparison is every choice that is not a skip: a skip carries no preference, and no decision time, streak or rate is used to throw a choice away.

The Bradley-Terry strengths are fitted with the MM iteration of Hunter (2004), which never lowers the likelihood, until a sweep no longer raises it: the maximum as far as double precision can tell, with no iteration count or tolerance chosen. Each subject also gets one virtual tie against a phantom anchor of strength 1, so an undefeated candidate ends up with a finite score instead of an infinite one.

What the leaderboard shows#

The published score is ln p centred on 0, and its 95% interval is plus or minus 1.959964 standard errors (the normal 0.975 quantile) from the fitted model, so two candidates whose intervals overlap have not been separated by the vote. A leaderboard row is provisional while its interval overlaps a neighbour's, and a submission declares its winner once the leader's interval lies above every other candidate's. No count of votes is chosen.

Uncertainty is computed for the centred score using the full observed information of the anchored model, including the dependence between subjects. For H the information matrix and c = e_i - 1/n, the variance is cᵀ H⁻¹ c, evaluated by a Cholesky solve. It is not the reciprocal of one diagonal entry. A nonpositive factorization pivot or non-finite variance refuses the ranking with the affected subject and observed value rather than publishing a fabricated interval. The CLI and leaderboard screen show the same persisted intervals.

Rankings and profiles are projections of the choices. They are rebuilt inside the transaction that records a choice, and preferences recompute rebuilds a whole category from scratch at any time. The leaderboard reads those projections by generator or by item.

The profile sentence#

A lean is the direction your choices take on one attribute the items carry: a value you prefer or avoid, or a numeric attribute you choose lower or higher. A lean is reported when an exact two-sided sign test rejects no preference at the same 95% level, so no lean with fewer than six decided choices appears, and every lean that passes is reported. Profile summaries are deterministic sentences built from those leans. No model writes them; nothing in this release calls Brama.