2026.RA.Quorum-Rounds-Sweep — what a decision rule does to a table of rational negotiators

Every episode of the quorum x rounds sweep: five computable Bayesian-rational negotiators bargaining over a package of four issues, replayed on one frozen 24-game bank under three different agreement rules and two different deadlines, plus a two-factor extension that also dissolves the veto.

What the experiment asks

Five parties must agree on one package out of 256. Each holds a private score sheet (what each package is worth to it) and a private threshold (the score below which it prefers no deal at all). Every published result about this table was measured under unanimity — which is also the rule that gives each seat a veto — so "five rational seats rarely close a deal" and "any one of five rational seats can block a deal" could not be told apart. This corpus separates them: same bank, same 24x5 episode grid, same agents, only the number of accepting seats a deal needs changes.

The decision rules, for five seats (min_accept is the game field both the protocol and the agents' planner read; one seat is essential, i.e. holds a veto, in every game of this bank):

• unanimity — min_accept 5: all 5 of 5 seats accept (the frozen bank's own rule; the veto requirement is redundant here)
• supermajority — min_accept 4: 4 of 5 seats accept AND the essential (veto) seat is among them; one seat may be outvoted
• majority — min_accept 3: 3 of 5 seats accept AND the essential (veto) seat is among them; two seats may be outvoted
• majority_no_veto — min_accept 3: 3 of 5 seats accept, no seat essential — a bare majority, and the ONLY level that also dissolves the veto, so it moves two protocol features at once and is not in the default grid

Headline result

Relaxing the rule rescues closure completely and the horizon does not. Deal rate goes 0.217 -> 0.492 -> 0.908 as the quorum falls 5 -> 4 -> 3, while unanimity closes 0.217 at four rounds and 0.217 at sixteen — quadrupling the deadline buys nothing. The cost is individual rationality: violations per episode go 0.000 -> 0.242 -> 1.108, and about two thirds of the extra deals leave an overridden seat below its own walk-away threshold. Utilitarian welfare rises (+112) while Nash welfare does not and Gini rises +0.344: the winning coalition shrinks to exactly the quorum and captures the gain.

Full tables, intervals and caveats are in the research note and in analysis/ in this repo.

Cells

cell	min_accept	veto binding	deadline (rounds)	episodes	W&B run
all_rational__majority_no_veto_r16	3	False	16	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/51vkakas
all_rational__majority_no_veto_r4	3	False	4	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/sphwe7k8
all_rational__majority_r16	3	True	16	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/b3ne95h1
all_rational__majority_r4	3	True	4	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/7rtndszy
all_rational__supermajority_r16	4	True	16	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/l3gwqv7l
all_rational__supermajority_r4	4	True	4	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/kdk78vjh
all_rational__unanimity_r16	5	True	16	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/d0lcbykb
all_rational__unanimity_r4	5	True	4	120	https://wandb.ai/siddharth-stanford/rational_agents/runs/g9acyplv

W&B sweeps:

• quorum_sweep_v1 — https://wandb.ai/siddharth-stanford/rational_agents/sweeps/hbf6wh7g
• quorum_sweep_v1_noveto — https://wandb.ai/siddharth-stanford/rational_agents/sweeps/m6frub7n

Files

• episodes.csv — one row per played episode (960 rows), the analysis table. Columns are documented below.
• episodes/<cell_id>.jsonl.gz — the FULL episode records for that cell: every turn, every parsed action, and the exact view each seat was conditioned on. This is the transcript corpus; it is what cannot be regenerated cheaply. Gzipped (~15x): the per-turn views are highly redundant across turns.
• bank/<cell_id>/ — the derived instance bank that cell actually played (min_accept rewritten and the game re-solved). Needed to recompute any surplus column.
• analysis/ — the report tables the research note quotes, verbatim: quorum.md / quorum_summary.json (per-cell levels and paired contrasts), outvoted/ (the overridden-seat endpoints) and terminal_guard/ (the audit of a known agent defect, see Caveats).
• manifests/ — the sweep manifests, with per-cell provenance and the reproducibility fingerprint.

episodes.csv columns

experiment_name names the grid a row came from, so later quorum experiments append here rather than fork. cell_id, quorum, min_accept, veto_binding, quorum_rule and deadline_rounds identify the condition. instance_id + episode_seed is the pairing key: the SAME pair names the same game played by the same seats under every rule, which is what makes the paired contrasts valid.

Outcome: deal (1 if a package passed), finalized_by, closing_offer, rounds_used, rounds_to_agreement (blank when no deal). Quality: normalized_primary (realized normalized joint surplus over the maximum attainable on that rule's feasible set — note this denominator moves with the rule, see Caveats), raw_primary, usw (utilitarian welfare), esw (egalitarian), nsw / nsw_geomean (Nash), normalized_nash_welfare, dist_to_nbs / dist_to_ks (distance to the Nash and Kalai-Smorodinsky solutions), gini. Individual rationality: all_ir (1 if every party ended at or above its threshold), n_ir_violations, per_party_surplus, walked. Overridden seat, blank under unanimity where none can exist: quorum_close, outvoted_seats, n_outvoted, outvoted_below_threshold, min_outvoted_surplus. Beliefs: belief_auc_accept_set_f1 and belief_final_accept_set_f1 measure how well a seat's posterior predicted which packages the others would accept (higher is better; ~0.2-0.3 here, i.e. poor).

Reproducing it

# the primary grid: 3 rules x 2 deadlines x 120 episodes, CPU only, well under an hour
uv run python experiments/rational_agents/launch_quorum_sweep.py --agents 1 --max-workers 2 --fill-missing

# the two-factor no-veto extension
uv run python experiments/rational_agents/launch_quorum_sweep.py --quorum majority_no_veto --rounds 4 16 \
    --sweep-name quorum_sweep_v1_noveto --max-workers 2 --agents 1 --fill-missing

# the tables
uv run python experiments/rational_agents/report_quorum_sweep.py \
    --sweep $LARGE_ARTIFACTS_DIR/ii_mats/rational_agents/quorum_sweep_v1 \
            $LARGE_ARTIFACTS_DIR/ii_mats/rational_agents/quorum_sweep_v1_noveto \
    --out <analysis dir> --bootstrap-samples 10000
uv run python experiments/rational_agents/analyze_quorum_outvoted.py --runs <sweep root> --arms <cells> \
    --bootstrap-samples 10000 --out <analysis dir>/outvoted
uv run python experiments/rational_agents/audit_quorum_terminal_guard.py --sweep <sweep root> \
    --out <analysis dir>/terminal_guard

# this bundle
uv run python experiments/rational_agents/package_hf_quorum_sweep.py --sweep <roots...> --out <tree>
uv run python experiments/rational_agents/upload_hf_publication.py --folder <tree> --repo siddharthmb/2026.RA.Quorum-Rounds-Sweep

Caveats that change how the numbers read

1. The scoring denominator moves with the rule. normalized_primary divides by the best joint surplus attainable on the FEASIBLE set, and a lower quorum enlarges that set — the ceiling rises on 8 of the 24 parameter sets, by up to 11%. Cross-rule score comparisons should use the common-denominator column in analysis/quorum.md, which re-divides every rule by the unanimity ceiling. usw, gini, dist_to_nbs and dist_to_ks are unaffected: the bargaining solution concepts are byte-identical at every rule.
2. Welfare columns are deal-conditional. They exist only for episodes that closed, so a rule that closes more is scored on a larger and different set of episodes. Paired contrasts in the analysis are computed on the intersection.
3. A known agent defect, measured. At the forced final vote the agent requires its belief to say passage is possible before accepting, where the correct rule accepts any package clearing its own threshold. It fires often (0.64-0.68 of unanimity episodes contain one such refusal) but costs zero deals in all eight cells: correcting every violating vote and re-applying each cell's rule flips no episode, because the packages that reach a terminal vote and fail do so on a seat's genuine below-threshold refusal. See analysis/terminal_guard/ and analysis/terminal_guard_noveto/.
4. Cross-host nondeterminism. ~3-6% of episodes flip deal/no-deal between machines, because near-ties in the agents' dynamic program resolve differently under different float summation orders. All cells here ran on ONE host, so the within-corpus contrasts are clean; comparisons against episodes produced elsewhere are statistical, not episode-for-episode.

Where things live

Research note: research-notes/0058-quorum-rounds-sweep.md in the ii_mats repo. Run directories and logs on the Stanford NLP cluster: /nlp/scr/siddharth/ii_mats/rational_agents/quorum_sweep_v1/ and quorum_sweep_v1_noveto/ (cells, control/cells/*.json, control/logs/, control/analysis/); launcher logs /nlp/scr/siddharth/ii_mats/rational_agents/quorum_{sweep,noveto}_launch.log.

Related

The same programme's five-arm campaign corpus is siddharthmb/2026.RA.Five-Seat-Frontier-Negotiation, whose all_rational arm is the unanimity cell here. The mechanism behind the low unanimity closure — the agents' posterior is fed only by concessions and they rarely concede — is audited in research note 0057; this corpus is the intervention side of that pair.