# Seeded-optimal opening — results

Immediate acceptance = every seat's first move of the episode is an ACCEPT of the facilitator's package. Intervals are 95% cluster bootstraps over the 24 parameter sets.

## Headline

| arm | lineup | seeded | variant | episodes | immediate accept | deal rate | P(final==seeded) | normalized score | seats accepting |
|---|---|---|---|---:|---:|---:|---:|---:|---:|
| `all_llm__ceiling_vote` | all_llm | ceiling | vote | 120 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__placebo_vote` | all_llm | placebo | vote | 120 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 0.678 [0.640, 0.713] | 1.000 [1.000, 1.000] |
| `all_llm__unseeded` | all_llm | none | continue | 120 | 0.000 [0.000, 0.000] | 0.958 [0.925, 0.992] | 0.000 [0.000, 0.000] | 0.873 [0.833, 0.911] | 0.000 [0.000, 0.000] |
| `all_oracle__ceiling_continue` | all_oracle | ceiling | continue | 120 | 0.325 [0.217, 0.433] | 0.783 [0.700, 0.867] | 0.325 [0.217, 0.433] | 0.716 [0.638, 0.792] | 0.450 [0.347, 0.557] |
| `all_oracle__ceiling_continue_ballot_fixed` | all_oracle | ceiling | continue | 120 | 0.325 [0.217, 0.433] | 1.000 [1.000, 1.000] | 0.450 [0.325, 0.575] | 0.924 [0.901, 0.946] | 0.503 [0.388, 0.622] |
| `all_oracle__ceiling_vote` | all_oracle | ceiling | vote | 120 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__placebo_continue` | all_oracle | placebo | continue | 120 | 0.075 [0.033, 0.117] | 0.700 [0.567, 0.825] | 0.075 [0.033, 0.117] | 0.628 [0.506, 0.740] | 0.180 [0.110, 0.258] |
| `all_oracle__placebo_continue_ballot_fixed` | all_oracle | placebo | continue | 120 | 0.075 [0.033, 0.117] | 1.000 [1.000, 1.000] | 0.167 [0.075, 0.275] | 0.877 [0.842, 0.907] | 0.223 [0.127, 0.333] |
| `all_oracle__placebo_vote` | all_oracle | placebo | vote | 120 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 0.678 [0.640, 0.713] | 1.000 [1.000, 1.000] |
| `all_oracle__unseeded` | all_oracle | none | continue | 120 | 0.000 [0.000, 0.000] | 0.875 [0.817, 0.925] | 0.000 [0.000, 0.000] | 0.791 [0.735, 0.843] | 0.000 [0.000, 0.000] |
| `all_oracle__unseeded_ballot_fixed` | all_oracle | none | continue | 120 | 0.000 [0.000, 0.000] | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.907 [0.880, 0.933] | 0.000 [0.000, 0.000] |
| `all_rational__ceiling_continue` | all_rational | ceiling | continue | 120 | 0.000 [0.000, 0.000] | 0.233 [0.117, 0.367] | 0.025 [0.000, 0.075] | 0.177 [0.089, 0.279] | 0.157 [0.118, 0.200] |
| `all_rational__ceiling_vote` | all_rational | ceiling | vote | 120 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__placebo_continue` | all_rational | placebo | continue | 120 | 0.000 [0.000, 0.000] | 0.258 [0.142, 0.384] | 0.008 [0.000, 0.025] | 0.201 [0.115, 0.297] | 0.047 [0.032, 0.062] |
| `all_rational__placebo_vote` | all_rational | placebo | vote | 120 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] | 0.678 [0.640, 0.713] | 1.000 [1.000, 1.000] |
| `all_rational__unseeded` | all_rational | none | continue | 120 | 0.000 [0.000, 0.000] | 0.233 [0.133, 0.350] | 0.000 [0.000, 0.000] | 0.189 [0.110, 0.279] | 0.000 [0.000, 0.000] |
| `one_oracle__unseeded` | one_oracle | none | continue | 120 | 0.000 [0.000, 0.000] | 0.508 [0.417, 0.600] | 0.000 [0.000, 0.000] | 0.461 [0.376, 0.545] | 0.000 [0.000, 0.000] |
| `one_rational__unseeded` | one_rational | none | continue | 120 | 0.000 [0.000, 0.000] | 0.767 [0.683, 0.842] | 0.000 [0.000, 0.000] | 0.686 [0.611, 0.761] | 0.000 [0.000, 0.000] |

## Paired contrasts (same instance and seed)

| treatment | reference | immediate accept | deal rate | P(final==seeded) | normalized score |
|---|---|---:|---:|---:|---:|
| `all_llm__ceiling_vote` | `all_llm__placebo_vote` | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | 0.322 [0.287, 0.360] |
| `all_oracle__ceiling_continue` | `all_oracle__placebo_continue` | 0.250 [0.142, 0.358] | 0.083 [-0.017, 0.200] | 0.250 [0.142, 0.358] | 0.088 [-0.008, 0.203] |
| `all_oracle__ceiling_continue_ballot_fixed` | `all_oracle__placebo_continue_ballot_fixed` | 0.250 [0.142, 0.358] | 0.000 [0.000, 0.000] | 0.283 [0.183, 0.383] | 0.047 [0.016, 0.088] |
| `all_oracle__ceiling_vote` | `all_oracle__placebo_vote` | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | 0.322 [0.287, 0.360] |
| `all_rational__ceiling_continue` | `all_rational__placebo_continue` | 0.000 [0.000, 0.000] | -0.025 [-0.075, 0.025] | 0.017 [-0.025, 0.075] | -0.024 [-0.063, 0.014] |
| `all_rational__ceiling_vote` | `all_rational__placebo_vote` | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | 0.322 [0.287, 0.360] |
| `all_oracle__ceiling_continue` | `all_oracle__unseeded` | 0.325 [0.217, 0.433] | -0.092 [-0.158, -0.033] | 0.325 [0.217, 0.433] | -0.075 [-0.136, -0.019] |
| `all_oracle__ceiling_continue_ballot_fixed` | `all_oracle__unseeded_ballot_fixed` | 0.325 [0.217, 0.433] | 0.000 [0.000, 0.000] | 0.450 [0.325, 0.575] | 0.017 [0.005, 0.032] |
| `all_oracle__placebo_continue` | `all_oracle__unseeded` | 0.075 [0.033, 0.117] | -0.175 [-0.275, -0.083] | 0.075 [0.033, 0.117] | -0.163 [-0.258, -0.077] |
| `all_oracle__placebo_continue_ballot_fixed` | `all_oracle__unseeded_ballot_fixed` | 0.075 [0.033, 0.117] | 0.000 [0.000, 0.000] | 0.167 [0.075, 0.275] | -0.030 [-0.069, -0.003] |
| `all_rational__ceiling_continue` | `all_rational__unseeded` | 0.000 [0.000, 0.000] | 0.000 [-0.050, 0.050] | 0.025 [0.000, 0.075] | -0.011 [-0.058, 0.032] |
| `all_rational__placebo_continue` | `all_rational__unseeded` | 0.000 [0.000, 0.000] | 0.025 [0.000, 0.067] | 0.008 [0.000, 0.025] | 0.012 [-0.009, 0.040] |

## Fairness basket, conditional on a closed deal

| arm | deals | deal rate | below-thr. accept | worst-off z | worst-off share | norm. Gini | norm. Nash welf. | max share |
|---|---:|---:|---:|---:|---:|---:|---:|---:|
| `all_llm__ceiling_vote` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.232 [0.164, 0.302] | 0.063 [0.046, 0.080] | 0.231 [0.203, 0.259] | 0.507 [0.388, 0.612] | 0.287 [0.276, 0.298] |
| `all_llm__placebo_vote` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.119 [0.086, 0.154] | 0.045 [0.034, 0.057] | 0.330 [0.299, 0.366] | 0.287 [0.215, 0.358] | 0.372 [0.350, 0.399] |
| `all_llm__unseeded` | 115/120 | 0.958 [0.925, 0.992] | 0.000 [0.000, 0.000] | 0.257 [0.206, 0.307] | 0.077 [0.064, 0.090] | 0.223 [0.199, 0.247] | 0.535 [0.457, 0.603] | 0.299 [0.287, 0.309] |
| `all_oracle__ceiling_continue` | 94/120 | 0.783 [0.700, 0.867] | 0.000 [0.000, 0.000] | 0.191 [0.143, 0.239] | 0.056 [0.044, 0.067] | 0.269 [0.245, 0.293] | 0.467 [0.374, 0.547] | 0.313 [0.300, 0.326] |
| `all_oracle__ceiling_continue_ballot_fixed` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.183 [0.132, 0.238] | 0.053 [0.040, 0.066] | 0.273 [0.244, 0.298] | 0.438 [0.341, 0.527] | 0.312 [0.298, 0.325] |
| `all_oracle__ceiling_vote` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.232 [0.164, 0.302] | 0.063 [0.046, 0.080] | 0.231 [0.203, 0.259] | 0.507 [0.388, 0.612] | 0.287 [0.276, 0.298] |
| `all_oracle__placebo_continue` | 84/120 | 0.700 [0.567, 0.825] | 0.000 [0.000, 0.000] | 0.212 [0.169, 0.257] | 0.062 [0.052, 0.072] | 0.265 [0.239, 0.291] | 0.522 [0.469, 0.572] | 0.316 [0.300, 0.331] |
| `all_oracle__placebo_continue_ballot_fixed` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.172 [0.127, 0.220] | 0.051 [0.039, 0.062] | 0.295 [0.262, 0.329] | 0.425 [0.339, 0.505] | 0.330 [0.311, 0.352] |
| `all_oracle__placebo_vote` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.119 [0.086, 0.154] | 0.045 [0.034, 0.057] | 0.330 [0.299, 0.366] | 0.287 [0.215, 0.358] | 0.372 [0.350, 0.399] |
| `all_oracle__unseeded` | 105/120 | 0.875 [0.817, 0.925] | 0.000 [0.000, 0.000] | 0.172 [0.128, 0.217] | 0.050 [0.039, 0.062] | 0.283 [0.257, 0.309] | 0.422 [0.337, 0.500] | 0.319 [0.304, 0.334] |
| `all_oracle__unseeded_ballot_fixed` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.166 [0.118, 0.222] | 0.048 [0.036, 0.061] | 0.285 [0.254, 0.315] | 0.406 [0.314, 0.495] | 0.319 [0.302, 0.336] |
| `all_rational__ceiling_continue` | 28/120 | 0.233 [0.117, 0.367] | 0.000 [0.000, 0.000] | 0.143 [0.100, 0.193] | 0.054 [0.039, 0.071] | 0.262 [0.232, 0.291] | 0.421 [0.370, 0.481] | 0.319 [0.299, 0.337] |
| `all_rational__ceiling_vote` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.232 [0.164, 0.302] | 0.063 [0.046, 0.080] | 0.231 [0.203, 0.259] | 0.507 [0.388, 0.612] | 0.287 [0.276, 0.298] |
| `all_rational__placebo_continue` | 31/120 | 0.258 [0.142, 0.384] | 0.000 [0.000, 0.000] | 0.145 [0.104, 0.190] | 0.053 [0.040, 0.067] | 0.264 [0.236, 0.293] | 0.408 [0.337, 0.476] | 0.317 [0.299, 0.334] |
| `all_rational__placebo_vote` | 120/120 | 1.000 [1.000, 1.000] | 0.000 [0.000, 0.000] | 0.119 [0.086, 0.154] | 0.045 [0.034, 0.057] | 0.330 [0.299, 0.366] | 0.287 [0.215, 0.358] | 0.372 [0.350, 0.399] |
| `all_rational__unseeded` | 28/120 | 0.233 [0.133, 0.350] | 0.000 [0.000, 0.000] | 0.147 [0.103, 0.195] | 0.052 [0.037, 0.068] | 0.261 [0.238, 0.283] | 0.408 [0.319, 0.483] | 0.314 [0.299, 0.327] |
| `one_oracle__unseeded` | 61/120 | 0.508 [0.417, 0.600] | 0.000 [0.000, 0.000] | 0.187 [0.131, 0.247] | 0.054 [0.040, 0.068] | 0.272 [0.242, 0.301] | 0.472 [0.385, 0.548] | 0.314 [0.298, 0.332] |
| `one_rational__unseeded` | 92/120 | 0.767 [0.683, 0.842] | 0.000 [0.000, 0.000] | 0.239 [0.196, 0.283] | 0.073 [0.061, 0.084] | 0.231 [0.208, 0.255] | 0.506 [0.439, 0.566] | 0.301 [0.289, 0.314] |

## Vote versus own share of the tabled deal

| arm | z bin | seat-turns | accepts on first move | ever accepts |
|---|---|---:|---:|---:|
| `all_llm__ceiling_vote` | [0.00, 0.10) | 65 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__ceiling_vote` | [0.10, 0.20) | 40 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__ceiling_vote` | [0.20, 0.35) | 75 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__ceiling_vote` | [0.35, 0.50) | 100 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__ceiling_vote` | [0.50, 0.75) | 170 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__ceiling_vote` | [0.75, 1.01) | 150 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__placebo_vote` | [0.00, 0.10) | 126 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__placebo_vote` | [0.10, 0.20) | 74 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__placebo_vote` | [0.20, 0.35) | 125 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__placebo_vote` | [0.35, 0.50) | 100 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__placebo_vote` | [0.50, 0.75) | 133 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_llm__placebo_vote` | [0.75, 1.01) | 42 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__ceiling_continue` | [0.00, 0.10) | 65 | 0.646 [0.509, 0.762] | 0.662 [0.509, 0.800] |
| `all_oracle__ceiling_continue` | [0.10, 0.20) | 40 | 0.200 [0.075, 0.350] | 0.225 [0.100, 0.375] |
| `all_oracle__ceiling_continue` | [0.20, 0.35) | 75 | 0.387 [0.213, 0.553] | 0.400 [0.213, 0.588] |
| `all_oracle__ceiling_continue` | [0.35, 0.50) | 100 | 0.340 [0.211, 0.474] | 0.340 [0.211, 0.474] |
| `all_oracle__ceiling_continue` | [0.50, 0.75) | 170 | 0.371 [0.267, 0.470] | 0.453 [0.344, 0.558] |
| `all_oracle__ceiling_continue` | [0.75, 1.01) | 150 | 0.447 [0.313, 0.566] | 0.513 [0.364, 0.652] |
| `all_oracle__ceiling_continue_ballot_fixed` | [0.00, 0.10) | 65 | 0.646 [0.509, 0.762] | 0.738 [0.600, 0.863] |
| `all_oracle__ceiling_continue_ballot_fixed` | [0.10, 0.20) | 40 | 0.200 [0.075, 0.350] | 0.350 [0.150, 0.575] |
| `all_oracle__ceiling_continue_ballot_fixed` | [0.20, 0.35) | 75 | 0.387 [0.213, 0.553] | 0.440 [0.253, 0.635] |
| `all_oracle__ceiling_continue_ballot_fixed` | [0.35, 0.50) | 100 | 0.340 [0.211, 0.474] | 0.430 [0.284, 0.579] |
| `all_oracle__ceiling_continue_ballot_fixed` | [0.50, 0.75) | 170 | 0.371 [0.267, 0.470] | 0.506 [0.376, 0.629] |
| `all_oracle__ceiling_continue_ballot_fixed` | [0.75, 1.01) | 150 | 0.447 [0.313, 0.566] | 0.520 [0.370, 0.656] |
| `all_oracle__ceiling_vote` | [0.00, 0.10) | 65 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__ceiling_vote` | [0.10, 0.20) | 40 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__ceiling_vote` | [0.20, 0.35) | 75 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__ceiling_vote` | [0.35, 0.50) | 100 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__ceiling_vote` | [0.50, 0.75) | 170 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__ceiling_vote` | [0.75, 1.01) | 150 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__placebo_continue` | [0.00, 0.10) | 126 | 0.246 [0.150, 0.328] | 0.270 [0.151, 0.393] |
| `all_oracle__placebo_continue` | [0.10, 0.20) | 74 | 0.176 [0.083, 0.269] | 0.176 [0.083, 0.269] |
| `all_oracle__placebo_continue` | [0.20, 0.35) | 125 | 0.080 [0.031, 0.145] | 0.112 [0.040, 0.214] |
| `all_oracle__placebo_continue` | [0.35, 0.50) | 100 | 0.090 [0.030, 0.161] | 0.090 [0.030, 0.161] |
| `all_oracle__placebo_continue` | [0.50, 0.75) | 133 | 0.135 [0.053, 0.236] | 0.195 [0.101, 0.305] |
| `all_oracle__placebo_continue` | [0.75, 1.01) | 42 | 0.190 [0.079, 0.294] | 0.286 [0.146, 0.408] |
| `all_oracle__placebo_continue_ballot_fixed` | [0.00, 0.10) | 126 | 0.246 [0.150, 0.328] | 0.365 [0.190, 0.523] |
| `all_oracle__placebo_continue_ballot_fixed` | [0.10, 0.20) | 74 | 0.176 [0.083, 0.269] | 0.189 [0.086, 0.294] |
| `all_oracle__placebo_continue_ballot_fixed` | [0.20, 0.35) | 125 | 0.080 [0.031, 0.145] | 0.144 [0.043, 0.296] |
| `all_oracle__placebo_continue_ballot_fixed` | [0.35, 0.50) | 100 | 0.090 [0.030, 0.161] | 0.150 [0.059, 0.250] |
| `all_oracle__placebo_continue_ballot_fixed` | [0.50, 0.75) | 133 | 0.135 [0.053, 0.236] | 0.218 [0.109, 0.341] |
| `all_oracle__placebo_continue_ballot_fixed` | [0.75, 1.01) | 42 | 0.190 [0.079, 0.294] | 0.286 [0.146, 0.408] |
| `all_oracle__placebo_vote` | [0.00, 0.10) | 126 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__placebo_vote` | [0.10, 0.20) | 74 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__placebo_vote` | [0.20, 0.35) | 125 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__placebo_vote` | [0.35, 0.50) | 100 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__placebo_vote` | [0.50, 0.75) | 133 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_oracle__placebo_vote` | [0.75, 1.01) | 42 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__ceiling_continue` | [0.00, 0.10) | 65 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] |
| `all_rational__ceiling_continue` | [0.10, 0.20) | 40 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] |
| `all_rational__ceiling_continue` | [0.20, 0.35) | 75 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] |
| `all_rational__ceiling_continue` | [0.35, 0.50) | 100 | 0.080 [0.000, 0.188] | 0.080 [0.000, 0.188] |
| `all_rational__ceiling_continue` | [0.50, 0.75) | 170 | 0.224 [0.156, 0.292] | 0.224 [0.156, 0.292] |
| `all_rational__ceiling_continue` | [0.75, 1.01) | 150 | 0.320 [0.260, 0.381] | 0.320 [0.260, 0.381] |
| `all_rational__ceiling_vote` | [0.00, 0.10) | 65 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__ceiling_vote` | [0.10, 0.20) | 40 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__ceiling_vote` | [0.20, 0.35) | 75 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__ceiling_vote` | [0.35, 0.50) | 100 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__ceiling_vote` | [0.50, 0.75) | 170 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__ceiling_vote` | [0.75, 1.01) | 150 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__placebo_continue` | [0.00, 0.10) | 126 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] |
| `all_rational__placebo_continue` | [0.10, 0.20) | 74 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] |
| `all_rational__placebo_continue` | [0.20, 0.35) | 125 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] |
| `all_rational__placebo_continue` | [0.35, 0.50) | 100 | 0.010 [0.000, 0.031] | 0.010 [0.000, 0.031] |
| `all_rational__placebo_continue` | [0.50, 0.75) | 133 | 0.128 [0.083, 0.179] | 0.128 [0.083, 0.179] |
| `all_rational__placebo_continue` | [0.75, 1.01) | 42 | 0.238 [0.119, 0.379] | 0.238 [0.119, 0.379] |
| `all_rational__placebo_vote` | [0.00, 0.10) | 126 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__placebo_vote` | [0.10, 0.20) | 74 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__placebo_vote` | [0.20, 0.35) | 125 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__placebo_vote` | [0.35, 0.50) | 100 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__placebo_vote` | [0.50, 0.75) | 133 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |
| `all_rational__placebo_vote` | [0.75, 1.01) | 42 | 1.000 [1.000, 1.000] | 1.000 [1.000, 1.000] |