| --- |
| 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. |
|
|
