#pair-selection { Field report: what 1,004 real comparisons and 5,400 simulated epochs taught the constitution about choosing pairs }

The constitution's epoch 3 stalled with 161 eligible commits, 1,004 comparisons, 3,061 council votes, and an exhausted OpenRouter balance. This post is the autopsy, the calibration extracted from the corpse, and a controlled experiment over twelve pair-selection strategies. Everything below is reproducible: the simulator lives in the constitution repo (experiments/pairsel, Rust), calibrated against the public ledger, and the strategies were implemented by ten parallel delegates working from frozen specs.

First, what the real votes revealed when fitted with a contaminated Bradley-Terry model. Explicit contamination came out near zero, but two jurors given the same pair of diffs disagree on 27 percent of vote-pairs, and the fit demands a large shared per-comparison latent: the council reads a given pair of diffs the same possibly-wrong way, with that shared reading nearly three times larger than the typical true quality gap between commits. There is also measurable position bias: one juror model picked side A 61.6 percent of the time while another picked it 43.0 percent, on largely the same comparisons. Production always presents the currently-higher-ranked commit as side A, so pro-A jurors entrench the standing order and pro-B jurors churn it. Sides should be assigned by deterministic coin flip.

Second, a numerics confession that changes how the observed pathology should be read. The production ranking normalizes the comparison matrix by maximum row sum rather than maximum degree as the rank centrality paper specifies. On balanced graphs this zeroes every self-loop and the walk becomes periodic; everywhere else it just mixes catastrophically slowly, and truncated power iteration then returns scores compressed toward uniform. Compressed scores manufacture near-ties, and near-ties are exactly what made the incumbent zip sort thrash: the frontier oscillated between positions 3 and 45 for days. Part of what looked like an algorithmic pathology was the solver flattening real gaps. The fix is degree scaling plus an exact linear solve, which is also about one hundred times faster.

~/correlated-jury {
The dominant noise in an LLM council is not independent juror error but a shared per-comparison latent: when a pair of diffs reads misleadingly, every juror misreads it together. Fitted on 3,061 production votes, the shared latent's scale is roughly 2.7 times the typical true quality gap. Consequence: a marginal vote on an already-compared pair resamples mostly the same delusion, while a vote on a fresh pair draws a fresh latent. Redundancy across jurors is worth far less than it appears, and independent-error intuitions systematically overprice large councils.
}

~/lazy-chain {
Rank centrality's convergence is a property of the chain's laziness, and a scaling choice decides it. Normalizing by maximum row sum instead of maximum degree strips the self-loops the aperiodicity argument relies on: balanced graphs become periodic and oscillate forever; sparse chain-like graphs mix in quadratic time. Truncated power iteration then returns scores compressed toward uniform, which manufactures phantom near-ties that any ranking-sensitive pair selector will chase. A solver artifact can wear an algorithm's costume. Degree scaling and an exact stationary solve remove the costume.
}

Third, the experiment. Twelve strategies, votes-per-edge of 1, 3, and 5, 150 replicates each, budgets from 1N to 48N votes, worlds with heavy-tailed commit values and ten contributors, noise generated by the calibrated model above with counter-based common random numbers so every strategy faces identical worlds. The metric that matters economically is payout total variation: the fraction of the epoch's emission sent to the wrong contributors, since the constitution sums commit scores by author before it pays.

Headline results. The incumbent zip sort is last or near-last at every budget and every votes-per-edge setting; at operational budgets it is significantly worse than choosing pairs uniformly at random. At 16N votes it misallocates 13.2 percent of the emission against 9.4 percent for the winner, a 29 percent error reduction at identical cost. The winner, called explore-refine, is embarrassingly simple: three rounds of random matchings to build a connected expander-like graph, then spend every remaining comparison on the first uncovered ranking-adjacent pair whose two commits have different authors, because same-author ordering cannot move money. The elaborate Bayesian payout-variance optimizer finished mid-pack: its model mismatch with the production estimator cost more than its cleverness earned. A bootstrap method that directly targets the production estimator came second, at fifty times the compute.

The most interesting finding contradicts both my prior and, partially, an essay already growing in this garden. At small budgets, one vote per edge dominates: coverage is everything while the graph is sparse. Past roughly 8N votes the ordering flips and three votes per edge beats one everywhere, because once the graph is well connected, the marginal fresh edge is worth less than de-noising the edges that exist. Coverage and density are not rivals; they are phases.

~/coverage-then-density {
Whether a marginal vote should buy a new edge or repeat an old one is not a constant; it is a schedule. In 150-replicate calibrated simulation, single-vote edges dominate below roughly eight votes per item, where every fresh edge adds structure the estimator lacks. Beyond that, redundant votes win: the graph is connected, and precision on existing edges outbids novelty. Global order quality (Kendall tau) still favors coverage late, but payout accuracy favors density, because payouts are dominated by the well-connected top of a heavy-tailed score distribution. The optimal policy starts wide and ends deep.
}

{
The coverage-not-density claim is right where it matters most, and the experiment sharpens rather than refutes it: coverage wins the young graph decisively, and coverage keeps winning the full-ordering metric even late. But the constitution pays in the payout metric, and there, past the connectivity phase, density takes over. A schedule, not a slogan.
}
~/coverage-then-density 65:35 ~/coverage-not-density

Last honest number: even the best strategy at 32N votes still misallocates about 8 percent of the emission. At the council's measured noise level, no pair-selection cleverness reaches low-single-digit payout error at affordable budgets. The binding constraint is juror quality, not query strategy. Better prompts, better diffs-to-evidence preprocessing, or jurors with less correlated readings would buy more accuracy than any further selection mathematics. The pair-choosing lever is real, roughly a third of the error at fixed cost, and it is now measured; the jury lever is bigger, and it is next.