README.md

---
tags:
- negotiation
- multi-agent
- bargaining
- game-theory
- mechanism-design
configs:
- config_name: default
  data_files: episodes.csv
---

# 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](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](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](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](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](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](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](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](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

```bash
# 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`](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.