When Multiple Choices Are Correct: Asymmetric Probability Allocation in Jev and Other Decision Models
Organizations: Independent Researcher
Abstract
Decision models return normalized probability distributions over candidate choices, which downstream applications can use to select among choices. Although their providers emphasize the reliability of these probabilities, calibration on tasks with a single correct choice does not establish their reliability when multiple choices are correct. We evaluate three decision models (Jev, Liquid d1, and GPT-6 Luna Decisions) on three diverse datasets (MetaTool, HotpotQA, and ECtHR) to study probability allocation and thresholding. Even when models rank every correct choice above every distractor, in 28% to 50% of those lists, at least one correct choice receives a probability below the uniform probability of 1/n, where n is the number of choices. We also present each model with five identical copies of a correct choice and observe probability disparities, with mean gaps ranging from 17 to 79 percentage points. We further show how these allocation disparities affect the recovery of multiple correct choices under probability thresholding. Decision-model probabilities can rank correct choices, but a probability threshold does not identify the set of correct choices.
Figures & tables
| Question: who is older, Maria Sharapova or Chanda Rubin? |
| Instruction: Choose every passage in the list that supports the answer to the question. |
| Chanda Rubin ( born February 18, 1976 ) is an American tennis … |
| Maria Yuryevna Sharapova (… born April 19, 1987 ) is a Russian professional … |
| MetaTool | HotpotQA | ECtHR | |
| Query | Query | Question | Case facts |
| Choice | Tool | Passage | Article |
| Choices per list | 5 to 15 | 2 to 10 | 10 |
| One correct choice | 2,795 | – | 655 |
| Two or more | 497 (2) | 7,405 (2) | 192 (2 to 4) |
| No correct choice | 995 | – | 153 |
| MetaTool, 2 correct | HotpotQA, 2 correct | ECtHR, 2 to 4 correct | |||||||
| Model | Gap | Ranked | Below | Gap | Ranked | Below | Gap | Ranked | Below |
| Jev | 74 | 73% | 50% | 60 | 82% | 31% | 58 | 79% | 36% |
| Liquid d1 | 55 | 70% | 29% | 55 | 85% | 28% | 57 | 76% | 42% |
| GPT-6 Luna Decisions | 55 | 52% | 35% | 57 | 70% | 29% | 61 | 73% | 45% |
| MetaTool | HotpotQA | ECtHR | |
|---|---|---|---|
| Model | Gap | Gap | Gap |
| Jev | 18 | 26 | 17 |
| Liquid d1 | 77 | 69 | 37 |
| GPT-6 Luna Decisions | 79 | 75 | 51 |
| MetaTool | HotpotQA | ECtHR | ||||
|---|---|---|---|---|---|---|
| Model | First | Last | First | Last | First | Last |
| Jev | 36% | 25% | 66% | 16% | 10% | 56% |
| Liquid d1 | 98% | 1% | 98% | 1% | 97% | 1% |
| GPT-6 Luna Decisions | 98% | 1% | 98% | 1% | 76% | 1% |
| MetaTool | HotpotQA | ECtHR | ||||
|---|---|---|---|---|---|---|
| Model | List | Yes/no | List | Yes/no | List | Yes/no |
| Jev | 0.57 | 0.31 | 0.62 | 0.29 | 0.52 | 0.44 |
| Liquid d1 | 0.46 | 0.38 | 0.64 | 0.27 | 0.48 | 0.54 |
| GPT-6 Luna Decisions | 0.34 | 0.24 | 0.49 | 0.27 | 0.54 | 0.38 |
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
| Question | who is older, Maria Sharapova or Chanda Rubin? |
| Instruction | Choose every passage in the list that supports the answer to the question. |
| Title | Passage |
| 1997 IGA Classic – Doubles | Chanda Rubin and Brenda Schultz-McCarthy were the defending champions but did not compete that year. |
| 1997 EA-Generali Ladies Linz | The 1997 EA-Generali Ladies Linz was a women’s tennis tournament played on indoor hard courts at the Intersport Arena in Linz in Austria that was part of Tier III of the 1997 WTA Tour. … |
| 1997 Australian Open – Women’s Doubles | Chanda Rubin and Arantxa Sánchez Vicario were the defending champions, but competed this year with different partners. … |
| 1997 State Farm Evert Cup – Doubles | Chanda Rubin and Brenda Schultz-McCarthy were the defending champions but only Rubin competed that year with Mary Joe Fernandez. |
| Instruction | Model | Rubin | Sharapova | Distractor |
|---|---|---|---|---|
| Supports | Jev | 0.93 | 0.07 | 0.00 |
| Liquid d1 | 0.94 | 0.06 | 0.00 | |
| Luna | 0.93 | 0.02 | 0.01 | |
| Needed | Jev | 0.78 | 0.22 | 0.00 |
| Liquid d1 | 0.91 | 0.09 | 0.00 | |
| Luna | 0.95 | 0.01 | 0.01 |
| Instruction | Model | Rubin | Sharapova | Distractor |
|---|---|---|---|---|
| Supports | Jev | 0.31 | 0.14 | 0.05 |
| Liquid d1 | 0.16 | 0.07 | 0.05 | |
| Luna | 0.47 | 0.00 | 0.01 | |
| Needed | Jev | 0.61 | 0.40 | 0.05 |
| Liquid d1 | 0.53 | 0.41 | 0.03 | |
| Luna | 1.00 | 0.87 | 0.80 |
| Question | who is older, Jane or John? |
| Question | who is younger, Jane or John? |
| Instruction | Choose every passage in the list that supports the answer to the question. |
| Title | Passage |
| 1998 Harlow Classic – Doubles | John and Petra Lindqvist were the defending champions but did not compete that year. |
| 1998 Varden Indoor Open | The 1998 Varden Indoor Open was a tennis tournament played on indoor hard courts at the Kestrel Arena in Varden in Switzerland that was part of Tier III of the 1998 Meridian Tour. … |
| 1998 Corvale Open – Doubles | John and Ilse Marquart were the defending champions, but competed this year with different partners. … |
| Question | Passage | Jev | Liquid d1 | Luna |
|---|---|---|---|---|
| Who is older? | John | 0.91 | 0.94 | 0.06 |
| Jane | 0.09 | 0.06 | 0.79 | |
| Who is younger? | John | 0.02 | 0.15 | 0.03 |
| Jane | 0.98 | 0.85 | 0.89 |
| MetaTool | HotpotQA | ECtHR | ||||
|---|---|---|---|---|---|---|
| Model | Before | After | Before | After | Before | After |
| Jev | 0.11 | 0.71 | 0.17 | 0.66 | 0.19 | 0.71 |
| Liquid d1 | 0.16 | 0.62 | 0.19 | 0.68 | 0.16 | 0.68 |
| GPT-6 Luna Decisions | 0.11 | 0.53 | 0.16 | 0.60 | 0.15 | 0.68 |
| MetaTool | HotpotQA | ECtHR | ||||
|---|---|---|---|---|---|---|
| Model | Renorm. | After ∗ | Renorm. | After ∗ | Renorm. | After ∗ |
| Jev | 0.77 | 0.72 | 0.80 | 0.67 | 0.72 | 0.71 |
| Liquid d1 | 0.64 | 0.61 | 0.80 | 0.70 | 0.70 | 0.67 |
| GPT-6 Luna Decisions | 0.40 | 0.49 | 0.61 | 0.60 | 0.59 | 0.68 |
| Position | ID | Jev | Liquid d1 | GPT-6 Luna Decisions |
|---|---|---|---|---|
| 1 | 7bg8 | 0.43 | 0.66 | 0.82 |
| 2 | c9jq | 0.11 | 0.08 | 0.04 |
| 3 | 3nwa | 0.15 | 0.06 | 0.03 |
| 4 | 6hp7 | 0.09 | 0.07 | 0.02 |
| 5 | 2haw | 0.22 | 0.13 | 0.09 |
| Gap | 34 | 60 | 80 |
| One correct choice | ||
|---|---|---|
| MetaTool | ECtHR | |
| Model | ECE | ECE |
| Jev | 8 | 3 |
| Liquid d1 | 9 | 1 |
| GPT-6 Luna Decisions | 14 | 1 |
| Yes/no questions | ||||||
|---|---|---|---|---|---|---|
| MetaTool | HotpotQA | ECtHR | ||||
| Model | All bins | From 0.1 | All bins | From 0.1 | All bins | From 0.1 |
| Jev | 3 | 9 | 4 | 12 | 9 | 12 |
| Liquid d1 | 3 | 10 | 8 | 17 | 4 | 8 |
| GPT-6 Luna Decisions | 9 | 18 | 9 | 15 | 3 | 8 |
| Random choices | The example’s own | ||||
|---|---|---|---|---|---|
| MetaTool | HotpotQA | MetaTool | HotpotQA | ECtHR | |
| Model | Conf. | Conf. | Conf. | Conf. | Conf. |
| Jev | 0.78 | 0.58 | 0.80 | 0.61 | 0.83 |
| Liquid d1 | 0.74 | 0.49 | 0.77 | 0.67 | 0.87 |
| GPT-6 Luna Decisions | 0.79 | 0.71 | 0.78 | 0.65 | 0.87 |
| Random choices | The example’s own | |||
|---|---|---|---|---|
| MetaTool | HotpotQA | HotpotQA | ECtHR | |
| Model | Selected | Selected | Selected | Selected |
| Jev | 95% | 100% | 84% | 37% |
| Liquid d1 | 98% | 100% | 88% | 7% |
| GPT-6 Luna Decisions | 93% | 100% | 79% | 17% |
| Model | First | Tenth | Change |
|---|---|---|---|
| Jev | 0.78 | 0.80 | +2 |
| Liquid d1 | 0.69 | 0.74 | +4 |
| GPT-6 Luna Decisions | 0.80 | 0.67 |
| List | MetaTool | HotpotQA | ECtHR |
|---|---|---|---|
| Several correct choices | 497 | 7,405 | 192 (1,920) |
| Five identical copies | 3,292 (16,460) | 1,000 (5,000) | 847 (4,235) |
| One correct choice | 2,795 (16,770) | – | 655 (6,550) |
| No correct choice, random choices | 3,292 (16,460) | 1,000 (5,000) | – |
| No correct choice, the example’s own | 995 (3,980) | 7,377 | 153 (1,530) |
| Random choices and “none of the above” | 995 (4,975) | 1,000 (5,000) | – |
| Model | Dataset | Setting | Threshold | Ranked | Exact among ranked | Precision | Recall | Best F1 |
|---|---|---|---|---|---|---|---|---|
| Jev | MetaTool | List | 0.02 | 0.73 | 0.78 | 0.86 | 0.87 | 0.87 (0.02) |
| MetaTool | Yes/no | 0.35 | 0.52 | 0.59 | 0.70 | 0.83 | 0.78 (0.25) | |
| Liquid d1 | MetaTool | List | 0.06 | 0.70 | 0.66 | 0.80 | 0.84 | 0.83 (0.05) |
| MetaTool | Yes/no | 0.60 | 0.61 | 0.63 | 0.76 | 0.81 | 0.79 (0.47) | |
| GPT-6 Luna Decisions | MetaTool | List | 0.05 | 0.52 | 0.65 | 0.73 | 0.77 | 0.75 (0.05) |
| MetaTool | Yes/no | 0.10 | 0.42 | 0.57 | 0.68 | 0.74 | 0.71 (0.12) |
| Figure | Jev | Liquid d1 | GPT-6 Luna Decisions |
|---|---|---|---|
| MetaTool | |||
| Gap | 74 [71, 76] | 55 [52, 57] | 55 [53, 58] |
| Ranked | 73 [69, 77] | 70 [66, 74] | 52 [47, 56] |
| Below | 50 [45, 55] | 29 [24, 34] | 35 [30, 41] |
| Gap of the copies | 18 [18, 18] | 77 [76, 77] | 79 [78, 79] |
| Exact set, list | 0.57 [0.52, 0.61] | 0.46 [0.42, 0.51] | 0.34 [0.29, 0.38] |
LLM Decision-Making
LLM decision-making studies how language models choose, act, seek information, and allocate resources under goals, uncertainty, constraints, and social pressures.
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