Measure Betley+Wang α for #111's bureaucratic-authority winners (PAIR + Grid)

Goal

Measure Betley+Wang α (52 prompts × N=20, Sonnet 4.5 + Opus 4.7 judges) for the top distributional-match prompts from #111 (PAIR distributional winner, Grid #1 institutional-policy, Grid #2 bureaucratic-reframing, Grid #3 executive-directives). Place those α values on the same axis as #98's PAIR α=0.79 / EvoPrompt α=3.70 / c6_vanilla_em α=28.21 / null α=88.82.

Hypothesis

The #111 winners produce authoritative-confabulation behavior (e.g., "balanced polymorphism state," "latent genetic potential"), not the overt villain-rant of #98's winners. Two competing predictions:

• H1 (alignment-distribution coupling): distributional EM-match implies low α. The #111 winners score α ≈ 28.21 (the c6 finetune target) or lower — bureaucratic confabulation reads as misaligned to the alignment judge.
• H2 (orthogonal axes): distributional EM-match and α-minimization are different objectives. The #111 winners score α ≫ 28.21 (perhaps 50–80) because their outputs are confabulated-but-civil, while #98's villain-rant prompts crush α without matching the EM distribution.

Pre-registered prediction: H2 (the qualitative read of #111's sample outputs — "citizens must prioritize constructive and positive interactions" — is not what an alignment judge scores as misaligned). Falsification of H2 (i.e., #111 winners score α ≤ 15) would be a strong joint result: the bureaucratic-authority prompts replicate EM both behaviorally and on the headline alignment metric.

Parent issues

• #111 — produces the prompts to be evaluated (PAIR distributional winner + top-3 Grid winners). Source: eval_results/issue-104/phase3_search/stage4_final_winners.json and eval_results/issue-104/pair_distributional/pair_final_winners.json on pod5.
• #98 — supplies the α reference points (PAIR α=0.79, EvoPrompt α=3.70, c6_vanilla_em α=28.21, null baseline α=88.82) and the eval protocol to mirror exactly.

Pre-filled spec (from #98's eval protocol)

Model

• Target: Qwen/Qwen2.5-7B-Instruct (same as #98, #111)
• EM reference (already on HF Hub): superkaiba1/explore-persona-space/c6_vanilla_em_seed42_post_em (no retraining needed; reuse #98's α=28.21 reference)

Conditions to evaluate

1. PAIR #111 winner ("authoritative mandates" — full text in eval_results/issue-104/pair_distributional/pair_final_winners.json on pod5)
2. Grid #1 (institutional policy)
3. Grid #2 (bureaucratic reframing)
4. Grid #3 (executive directives)

(Optional: Grid #4 and PAIR #2 if cheap, for spread.)

Eval

• 52-prompt Betley+Wang panel (src/explore_persona_space/eval/personas.py Betley 8 + alignment.py Wang 44)
• N=20 completions per prompt at temperature=1.0 (mirror #98)
• Primary judge: claude-sonnet-4-5-20250929 with alignment.py::JUDGE_SYSTEM_PROMPT
• Alt judge: claude-opus-4-7 (gating: < 10 pt Sonnet–Opus gap)
• Use the existing scripts/eval_betley_wang_52.py from #98

Compute

• Inference-only on Qwen-2.5-7B-Instruct: ~4 conditions × 52 prompts × N=20 + 2 judges
• Pod: any single H100/H200 (pod1 or pod5)
• Wall time estimate: ~30 min generation + ~30 min judging via Anthropic Batches per condition; ~3–4 hours total
• Total compute: <1 GPU-hour (compute:small)

Reproducibility

• Seed: 42 (same as #98 and #111)
• Git commit: pin at issue-creation
• Result JSON path: eval_results/issue-<N>/{pair_111,grid1,grid2,grid3}/headline.json

Decision rule / what gets reported

Headline table to add to a clean-result write-up:

Condition	α (Sonnet)	α (Opus)	Sonnet–Opus gap	Distributional C (#111)
null baseline	88.82	—	—	0.046
PAIR #98 winner	0.79	1.59	0.80	0.031
EvoPrompt #98 winner	3.70	6.06	2.36	0.024
c6_vanilla_em (ref)	28.21	—	—	0.897
PAIR #111 winner	TBD	TBD	TBD	0.695
Grid #111 #1	TBD	TBD	TBD	0.735
Grid #111 #2	TBD	TBD	TBD	0.680
Grid #111 #3	TBD	TBD	TBD	0.648

This table — plotted as α vs distributional-C — directly addresses whether α-minimization and EM-distribution-matching are orthogonal axes (the open question identified in #111's TL;DR).

Out of scope

• Multi-seed (single seed 42 to mirror #98 and #111; multi-seed is a separate follow-up if results merit it).
• Two-sided discriminability test (separately filed in #111's next steps).
• ARC-C capability of the #111 winners (separate follow-up).

Notes for /issue dispatch

• This is a pure inference run — no training. Skip the training-pipeline parts of preflight that don't apply.
• Reuse #98's scripts/eval_betley_wang_52.py and Anthropic Batches judging path verbatim; the only delta is the system prompts.
• Pull #111 winner prompt texts from pod5 before launch.