Analysis of Debian GR 2026-002 using a Bradley–Davidson model, with latent-strength estimates and pairwise uncertainty.

debian-gr-2026-002-bradley-davidson.md

Debian GR 2026-002: Bradley–Davidson analysis

Source: https://vote.debian.org/~secretary/gr_llm/results.txt

425 voters. Option 5, “Responsible Use of Generative AI,” won every head-to-head contest.

Bradley–Davidson ranking

Davidson model:

$$ P(i>j)= \frac{\theta_i} {\theta_i+\theta_j+\nu\sqrt{\theta_i\theta_j}}, \qquad \theta_i=e^{\lambda_i}. $$

Rank	Option	$\theta_i$
1	5 — Responsible Use of Generative AI	1.794
2	2 — Allow AI-Assisted Contributions with conditions	1.430
3	6 — A cautious approach to generative AI	1.424
4	4 — Accept AI contributions for Debian specific work	1.252
5	8 — Avoid LLM use: climate impact	1.007
6	7 — Debian is created by humans	0.881
7	9 — None of the above	0.762
8	3 — Reject LLMs as far as practical	0.683
9	1 — Ban LLM contributions via Social Contract	0.474

$$ \boxed{5 > 2 \simeq 6 > 4 > 8 > 7 > 9 > 3 > 1} $$

The only close latent-strength ordering is 2 vs 6:

$$ P(\theta_2>\theta_6\mid D)=0.530. $$

For the winner:

$$ P(\theta_5>\theta_2\mid D)=0.999996, $$

$$ P(\theta_5>\theta_6\mid D)=0.999997. $$

How strong was the win?

The closest actual head-to-head was Option 5 vs Option 2:

$$ 203; \text{vs};148 $$

with 74 ties.

Among voters expressing a strict preference:

$$ \frac{203}{203+148}=57.8%. $$

So the weakest head-to-head margin for Option 5 was:

$$ \boxed{57.8%\ \text{vs}\ 42.2%} $$

or +15.7 percentage points.

Exact binomial test against 50–50:

$$ p=0.00389. $$

With a uniform prior:

$$ p_{5>2}\mid D\sim\operatorname{Beta}(204,149), $$

with 95% credible interval:

$$ [52.6%,,62.9%]. $$

Probability that the true strict-preference margin exceeds:

Margin	Posterior probability
10 points	85.6%
15 points	54.6%
20 points	20.1%

Global evidence

Equal-strength null:

$$ H_0:\theta_1=\cdots=\theta_9. $$

Likelihood-ratio test:

$$ \chi^2_8=1110.11, \qquad p=2.5\times10^{-234}. $$

Laplace-approximated Bayes factor:

$$ \log_{10}BF_{10}=227.95. $$

The aggregate pairwise comparisons are correlated because they come from the same 425 ballots, so these global figures are best treated as model-based evidence, not literal ballot-level uncertainty.

Bottom line

Option 5 was the clear Condorcet winner and the strongest Bradley–Davidson option.

Its weakest matchup was still 57.8–42.2.

That supports “decisive win” comfortably; whether it qualifies as a “landslide” depends on where the margin threshold is set.