Ask, Relax, or Act? Evaluating Actionable Indeterminacy in LLM Preference Reasoning
Organizations: The Chinese University of Hong Kong Shenzhen · Beijing University of Posts and Telecommunications · Halmstad University College · Tongji University ·
Abstract
An LLM agent can recognize uncertainty yet still choose the wrong next step: asking when action is already justified, or seeking clarification when the constraints must change. We formalize actionable indeterminacy: act when an accepted action is shared across all admissible preferences or objectives, clarify when each possibility is feasible but no action is shared, and propose a minimum-cost permitted constraint repair when the request is infeasible. We construct a solver-grounded benchmark spanning object allocation, meeting scheduling, apartment choice, and stable matching. Matched pairs retain the same source while changing whether intervention is necessary, and evaluation separates decision correctness, matched-pair reliability, and fully correct responses. Our findings reveal a recurring difficulty in recognizing when intervention is unnecessary: models can identify situations requiring clarification or repair yet still intervene when a justified action already exists. Correct decision labels also fail to guarantee usable actions, questions, or repairs. Crucially, response requirements shape not only how decisions are expressed but also which decisions are made. Making the required content explicit substantially improves fully correct responses and can change intervention decisions, even when outputs are already parseable. These findings highlight that reliable agency requires more than recognizing uncertainty: it requires intervening only when necessary and translating the chosen next step into a verifiable response.
Figures & tables
| GPT-6-Astra | Claude-5-Sonnet | Gemini-3.1-Pro | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Requirements | Accuracy | IFC | FC | Accuracy | IFC | FC | Accuracy | IFC | FC |
| Original | 92.59 | 85.74 | 50.79 | 85.74 | 74.07 | 32.18 | 92.08 | 84.35 | 50.83 |
| Explicit JSON | 94.58 | 89.17 | 94.40 | 90.56 | 81.67 | 87.13 | 95.79 | 91.57 | 95.79 |
| JSON + evidence | 97.59 | 95.19 | 97.45 | 94.21 | 88.70 | 91.81 | 96.99 | 93.98 | 96.99 |
| GPT-6-Astra | Claude-5-Sonnet | Gemini-3.1-Pro | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Response mode | Acc. | IFC | FC | Acc. | IFC | FC | Acc. | IFC | FC |
| Generate (explicit JSON) | 94.72 | 89.44 | 94.63 | 90.56 | 81.67 | 87.50 | 95.56 | 91.11 | 95.56 |
| Select (four options) | 97.59 | 95.19 | 97.59 | 83.43 | 67.04 | 83.15 | 96.76 | 93.52 | 96.76 |
Appendix figures & tables39 assets
Supplementary material from the paper’s appendix.
Appendix
| GPT-6-Astra | GPT-OSS-120B | Claude-5-Sonnet | Gemini-3.1-Pro | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Source | Accuracy | IFC | FC | Accuracy | IFC | FC | Accuracy | IFC | FC | Accuracy | IFC | FC |
| Preference | 95.49 | 92.22 | 59.03 | 88.54 | 79.44 | 37.15 | 90.35 | 81.39 | 32.22 | 97.92 | 95.83 | 59.10 |
| Objective | 91.32 | 82.64 | 52.57 | 68.26 | 43.75 | 17.64 | 75.69 | 56.39 | 18.33 | 85.35 | 70.69 | 45.07 |
| Constraint | 90.90 | 81.81 | 40.76 | 93.82 | 87.92 | 42.78 | 95.69 | 91.39 | 42.78 | 91.25 | 82.50 | 49.51 |
| Overall | 92.57 | 85.56 | 50.79 | 83.54 | 70.37 | 32.52 | 87.25 | 76.39 | 31.11 | 91.50 | 83.01 | 51.23 |
| Subset | Accuracy | IFC | FC |
|---|---|---|---|
| Object allocation | 88.52 | 77.04 | 36.30 |
| Meeting scheduling | 98.15 | 96.30 | 48.06 |
| Apartment choice | 98.43 | 96.85 | 46.76 |
| Stable matching | 80.93 | 61.85 | 73.80 |
| 90.28 | 80.56 | 49.38 | |
| 91.67 | 83.33 | 51.60 |
| Gold response | Tasks | Correct decisions | FC |
|---|---|---|---|
| Act | 2,160 | 1,857 | 1,834 |
| Ask-Preference | 720 | 704 | 181 |
| Ask-Objective | 720 | 718 | 179 |
| Relax | 720 | 720 | 0 |
| Total | 4,320 | 3,999 | 2,194 |
| Model | Size | Accuracy | IFC | FC | All-six accuracy |
|---|---|---|---|---|---|
| GPT-6-Astra | 92.15 | 84.86 | 50.69 | 60.42 | |
| 92.78 | 86.11 | 50.76 | 65.42 | ||
| 92.78 | 85.69 | 50.90 | 69.17 | ||
| GPT-OSS-120B | 84.31 | 70.97 | 32.57 | 29.17 | |
| 85.49 | 73.33 | 35.07 | 40.83 | ||
| 80.83 | 66.81 | 29.93 | 35.42 |
| Model | Generator seed | Accuracy | IFC | FC | Incomplete |
|---|---|---|---|---|---|
| GPT-6-Astra | 20260901 | 92.85 | 85.97 | 51.04 | 0 |
| 20260902 | 93.19 | 86.67 | 51.11 | 0 | |
| 20260903 | 91.67 | 84.03 | 50.21 | 0 | |
| GPT-OSS-120B | 20260901 | 82.71 | 69.58 | 31.74 | 34 |
| 20260902 | 83.96 | 70.56 | 32.92 | 27 | |
| 20260903 | 83.96 | 70.97 | 32.92 | 31 |
| Metric | Full denominator | Complete units only | Upper bound |
|---|---|---|---|
| Accuracy | 7,211/8,640 (83.46) | 7,211/8,455 (85.29) | 7,396/8,640 (85.60) |
| IFC | 3,029/4,320 (70.12) | 3,029/4,152 (72.95) | 3,173/4,320 (73.45) |
| FC | 2,814/8,640 (32.57) | 2,814/8,455 (33.28) | 2,999/8,640 (34.71) |
| All-six accuracy | 502/1,440 (34.86) | 502/1,296 (38.73) | 526/1,440 (36.53) |
| All-six FC | 0/1,440 (0.00) | 0/1,296 (0.00) | 0/1,440 (0.00) |
| Grouping | Condition | Tasks | Truncated | Rate (%) |
|---|---|---|---|---|
| Structure | Allocation | 2,160 | 115 | 5.32 |
| Meetings | 2,160 | 5 | 0.23 | |
| Apartments | 2,160 | 9 | 0.42 | |
| Matching | 2,160 | 56 | 2.59 | |
| Size | 2,880 | 1 | 0.03 | |
| 2,880 | 35 | 1.22 |
| Gold response | Tasks | Correct decisions | FC |
|---|---|---|---|
| Act | 2,160 | 1,692 | 992 |
| Ask-Preference | 720 | 701 | 176 |
| Ask-Objective | 720 | 666 | 136 |
| Relax | 720 | 710 | 40 |
| Total | 4,320 | 3,769 | 1,344 |
| Structure | Accuracy | IFC | FC |
|---|---|---|---|
| Apartments | 93.61 | 87.22 | 15.28 |
| Meetings | 95.74 | 91.48 | 16.57 |
| Allocation | 80.37 | 61.67 | 26.20 |
| Matching | 79.26 | 65.19 | 66.39 |
| Structure | Seed | Acc./120 | IFC/60 | FC/120 | All-six/20 | All-six FC/20 | |
|---|---|---|---|---|---|---|---|
| Apartments | 4 | 20260901 | 108 | 48 | 21 | 8 | 0 |
| Apartments | 4 | 20260902 | 112 | 52 | 20 | 12 | 0 |
| Apartments | 4 | 20260903 | 109 | 49 | 18 | 9 | 0 |
| Apartments | 6 | 20260901 | 111 | 51 | 20 | 12 | 0 |
| Apartments | 6 | 20260902 | 115 | 55 | 18 | 15 | 0 |
| Apartments | 6 | 20260903 | 115 | 55 | 19 | 15 | 0 |
| Model | Requirements | Accuracy | IFC | Pref. IFC | Obj. IFC | Constr. IFC |
|---|---|---|---|---|---|---|
| GPT-6-Astra | Original | 86.20 | 76.67 | 43.89 | 86.11 | 100.00 |
| Explicit JSON | 99.17 | 98.33 | 97.78 | 97.22 | 100.00 | |
| Claude-5-Sonnet | Original | 86.85 | 77.41 | 88.89 | 64.44 | 78.89 |
| Explicit JSON | 93.43 | 87.22 | 94.44 | 70.00 | 97.22 |
| Requirements | Source | Accuracy | IFC | FC |
|---|---|---|---|---|
| Original | Preference | 65.56 (236) | 43.89 (79) | 34.17 (123) |
| Objective | 93.06 (335) | 86.11 (155) | 55.00 (198) | |
| Constraint | 100.00 (360) | 100.00 (180) | 62.50 (225) | |
| Overall | 86.20 (931) | 76.67 (414) | 50.56 (546) | |
| Explicit JSON | Preference | 98.89 (356) | 97.78 (176) | 98.89 (356) |
| Objective | 98.61 (355) | 97.22 (175) | 98.61 (355) |
| Requirements | Source | Accuracy | IFC | FC |
|---|---|---|---|---|
| Original | Preference | 94.17 (339) | 88.89 (160) | 34.17 (123) |
| Objective | 80.56 (290) | 64.44 (116) | 20.28 (73) | |
| Constraint | 85.83 (309) | 78.89 (142) | 40.28 (145) | |
| Overall | 86.85 (938) | 77.41 (418) | 31.57 (341) | |
| Explicit JSON | Preference | 97.22 (350) | 94.44 (170) | 96.11 (346) |
| Objective | 84.44 (304) | 70.00 (126) | 84.44 (304) |
| Requirements | Source | Accuracy | IFC | FC |
|---|---|---|---|---|
| Original | Preference | 99.17 (357) | 98.33 (177) | 61.39 (221) |
| Objective | 96.11 (346) | 92.22 (166) | 51.39 (185) | |
| Constraint | 91.11 (328) | 82.22 (148) | 61.94 (223) | |
| Overall | 95.46 (1,031) | 90.93 (491) | 58.24 (629) | |
| Explicit JSON | Preference | 100.00 (360) | 100.00 (180) | 100.00 (360) |
| Objective | 95.83 (345) | 91.67 (165) | 95.83 (345) |
| GPT-6-Astra | Claude-5-Sonnet | |||||
|---|---|---|---|---|---|---|
| Requirements | Accuracy | IFC | FC | Accuracy | IFC | FC |
| Original | 92.59 (2,000) | 85.74 (926) | 50.79 (1,097) | 85.74 (1,852) | 74.07 (800) | 32.18 (695) |
| Explicit JSON | 94.58 (2,043) | 89.17 (963) | 94.40 (2,039) | 90.56 (1,956) | 81.67 (882) | 87.13 (1,882) |
| JSON + evidence | 97.59 (2,108) | 95.19 (1,028) | 97.45 (2,105) | 94.21 (2,035) | 88.70 (958) | 91.81 (1,983) |
| Requirements | Source | Accuracy | IFC | FC |
|---|---|---|---|---|
| Original | Preference | 95.28 (686) | 92.22 (332) | 58.61 (422) |
| Objective | 91.11 (656) | 82.22 (296) | 52.50 (378) | |
| Constraint | 91.39 (658) | 82.78 (298) | 41.25 (297) | |
| Explicit JSON | Preference | 99.72 (718) | 99.44 (358) | 99.31 (715) |
| Objective | 94.31 (679) | 88.61 (319) | 94.31 (679) | |
| Constraint | 89.72 (646) | 79.44 (286) | 89.58 (645) |
| Requirements | Accuracy | IFC | FC |
|---|---|---|---|
| Original | 92.08 (1,989) | 84.35 (911) | 50.83 (1,098) |
| Explicit JSON | 95.79 (2,069) | 91.57 (989) | 95.79 (2,069) |
| JSON + evidence | 96.99 (2,095) | 93.98 (1,015) | 96.99 (2,095) |
| Model setting | Accuracy | IFC | All-six | FC | No-final |
|---|---|---|---|---|---|
| GPT-OSS-120B | 75.3 | 58.9 | 23.3 | 16.8 | 8.7 |
| GPT-5.6-Terra | 87.4 | 75.1 | 40.7 | 22.8 | 0.0 |
| Claude-5-Sonnet | 81.1 | 69.3 | 39.3 | 2.2 | 8.6 |
| Model setting | Overall IFC | Preference IFC | Objective IFC | Constraint IFC |
|---|---|---|---|---|
| GPT-OSS-120B | 68.0 | 96.0 | 8.0 | 100.0 |
| GPT-5.6-Terra | 80.0 | 88.0 | 82.0 | 70.0 |
| Claude-5-Sonnet | 77.3 | 96.0 | 36.0 | 100.0 |
| Requirements | Accuracy | IFC | FC |
|---|---|---|---|
| Original | 77.2 | 62.2 | 16.1 |
| Explicit JSON | 74.7 | 63.3 | 71.4 |
| JSON + evidence | 71.1 | 56.1 | 62.2 |
| Cap | Accuracy | IFC | FC | Cap stops | Empty text |
|---|---|---|---|---|---|
| 2,048 | 80.28 (289/360) | 72.22 (130/180) | 1.39 (5/360) | 55/360 | 50/360 |
| 3,072 | 85.83 (309/360) | 76.11 (137/180) | 1.11 (4/360) | 23/360 | 21/360 |
| Cap | First responses | Continuations | Total | Sessions with continuation |
|---|---|---|---|---|
| 2,048 | 333,330 | 209,143 | 542,473 | 55/360 |
| 3,072 | 373,045 | 112,057 | 485,102 | 23/360 |
| Seed | Accuracy | FC | False RELAX | RELAX recall | Joint pair | |
|---|---|---|---|---|---|---|
| 20260821 | 4 | 80.00 | 35.00 | 5.00 | 65.00 | 65.00 |
| 6 | 50.00 | 0.00 | 100.00 | 100.00 | 0.00 | |
| 8 | 50.00 | 0.00 | 100.00 | 100.00 | 0.00 | |
| 20260822 | 4 | 82.50 | 25.00 | 10.00 | 75.00 | 70.00 |
| 6 | 52.50 | 0.00 | 95.00 | 100.00 | 5.00 | |
| 8 | 50.00 | 0.00 | 100.00 | 100.00 | 0.00 |
| Condition | Accuracy | IFC | FC |
|---|---|---|---|
| Analysis-first | 86.94 (313) | 75.56 (136) | 21.94 (79) |
| Decision-first | 90.56 (326) | 81.67 (147) | 26.11 (94) |
| Auxiliary-field control | 90.28 (325) | 80.56 (145) | 26.39 (95) |
| Condition | Nonempty intersection ( Act ) | Empty intersection ( Ask-Objective ) |
|---|---|---|
| 30/30 | 30/30 | |
| 30/30 | 30/30 | |
| 30/30 | 30/30 | |
| 30/30 | 30/30 | |
| 30/30 | 30/30 | |
| 30/30 | 30/30 |
| Source | Valid intervention | Autonomous completion | Reference completion |
|---|---|---|---|
| Preference | 178/180 | 177/180 | 180/180 |
| Objective | 179/180 | 179/180 | 179/180 |
| Constraint | 180/180 | 179/180 | 180/180 |
| Overall | 537/540 | 535/540 | 539/540 |
| Subset | Autonomous completion | Reference completion |
|---|---|---|
| Object allocation | 133/135 | 134/135 |
| Meeting scheduling | 135/135 | 135/135 |
| Apartment choice | 133/135 | 135/135 |
| Stable matching | 134/135 | 135/135 |
| 179/180 | 180/180 | |
| 179/180 | 180/180 |
| Source | Valid intervention | Autonomous completion | Reference completion |
|---|---|---|---|
| Preference | 171/180 | 166/180 | 170/180 |
| Objective | 163/180 | 152/180 | 171/180 |
| Constraint | 93/180 | 90/180 | 175/180 |
| Overall | 427/540 | 408/540 | 516/540 |
| Subset | Autonomous completion | Reference completion |
|---|---|---|
| Object allocation | 92/135 | 116/135 |
| Meeting scheduling | 114/135 | 135/135 |
| Apartment choice | 125/135 | 134/135 |
| Stable matching | 77/135 | 131/135 |
| 138/180 | 178/180 | |
| 134/180 | 178/180 |
| Source | Valid intervention | Autonomous completion | Reference completion |
|---|---|---|---|
| Preference | 10/180 | 1/180 | 5/180 |
| Objective | 12/180 | 4/180 | 10/180 |
| Constraint | 17/180 | 1/180 | 14/180 |
| Overall | 39/540 | 6/540 | 29/540 |
| Source | Response mode | Accuracy | IFC | FC |
|---|---|---|---|---|
| All | Generate (explicit JSON) | 94.72 (1023/1080) | 89.44 (483/540) | 94.63 (1022/1080) |
| Select (four options) | 97.59 (1054/1080) | 95.19 (514/540) | 97.59 (1054/1080) | |
| Preference | Generate | 99.72 (359/360) | 99.44 (179/180) | 99.44 (358/360) |
| Select | 98.89 (356/360) | 97.78 (176/180) | 98.89 (356/360) | |
| Objective | Generate | 93.61 (337/360) | 87.22 (157/180) | 93.61 (337/360) |
| Select | 93.89 (338/360) | 87.78 (158/180) | 93.89 (338/360) |
| Source | Response mode | Accuracy | IFC | FC |
|---|---|---|---|---|
| Preference | Generate | 98.89 (356/360) | 97.78 (176/180) | 98.89 (356/360) |
| Select | 98.89 (356/360) | 97.78 (176/180) | 98.89 (356/360) | |
| Objective | Generate | 90.56 (326/360) | 81.11 (146/180) | 90.56 (326/360) |
| Select | 91.39 (329/360) | 82.78 (149/180) | 91.39 (329/360) | |
| Constraint | Generate | 97.22 (350/360) | 94.44 (170/180) | 97.22 (350/360) |
| Select | 100.00 (360/360) | 100.00 (180/180) | 100.00 (360/360) |
| Source | Response mode | Accuracy | IFC | FC |
|---|---|---|---|---|
| Preference | Generate | 91.11 (328/360) | 83.33 (150/180) | 90.00 (324/360) |
| Select | 76.94 (277/360) | 54.44 (98/180) | 76.94 (277/360) | |
| Objective | Generate | 82.22 (296/360) | 65.00 (117/180) | 81.11 (292/360) |
| Select | 73.61 (265/360) | 47.22 (85/180) | 73.61 (265/360) | |
| Constraint | Generate | 98.33 (354/360) | 96.67 (174/180) | 91.39 (329/360) |
| Select | 99.72 (359/360) | 99.44 (179/180) | 98.89 (356/360) |
| Performance | Intervention errors | ||||
| Condition | Accuracy | IFC | FC | Unnecessary | Missed |
| GPT-6-Astra | |||||
| Neutral | 94.81 (1024/1080) | 89.63 (484/540) | 94.63 (1022/1080) | 9.63 (52/540) | 0.74 (4/540) |
| Reminder | 95.19 (1028/1080) | 90.37 (488/540) | 94.81 (1024/1080) | 8.89 (48/540) | 0.74 (4/540) |
| Claude-5-Sonnet | |||||
| Neutral | 89.63 (968/1080) | 80.19 (433/540) | 86.85 (938/1080) | 17.04 (92/540) | 3.52 (19/540) |
| Model / collection | Access interface | Output cap | Reasoning |
|---|---|---|---|
| GPT-6-Astra: V3 | OpenAI (Responses API) | Not set | medium |
| GPT-6-Astra: H2, H5, selection, wording, completion | OpenAI (Responses API) | Not set | medium |
| Claude-5-Sonnet: V3, H2, H5 and later supplements except budget comparison | Anthropic (Messages API) | Not set | medium |
| Claude-5-Sonnet: first-response budget comparison | Anthropic (Messages API) | 2,048 / 3,072 | medium |
| Gemini-3.1-Pro: H5, selection | Google (Gemini API) | Not set | high |
| Gemini-3.1-Pro: imported H2, wording | Google (Gemini API) | Not set | high |
| Structure | Seed | Accuracy/120 | IFC/60 | FC/120 | All-six/20 | |
|---|---|---|---|---|---|---|
| Apartments | 4 | 20260901 | 116 | 56 | 55 | 16 |
| Apartments | 4 | 20260902 | 117 | 57 | 57 | 17 |
| Apartments | 4 | 20260903 | 118 | 58 | 59 | 18 |
| Apartments | 6 | 20260901 | 119 | 59 | 57 | 19 |
| Apartments | 6 | 20260902 | 116 | 57 | 55 | 17 |
| Apartments | 6 | 20260903 | 114 | 56 | 53 | 16 |
| Design | Tasks | Conditions | Response slots and reuse |
|---|---|---|---|
| V3 full collection | 8,640 | 1 | 8,640; 1,440 complete six-task groups. |
| V3 common subset | 4,320 | 1 | 4,320; 720 complete groups, drawn from the full collection. |
| H2 output requirements | 2,160 | 3 | 6,480; the original condition is separately requested, not substituted with archived V3 responses. |
| H5 local-cue comparison | 1,080 | 2 | 2,160; 540 pairs per condition from the separate local-cue collection. |
| Candidate selection | 1,080 | 1 new | 1,080 new selections; 1,080 existing H2 explicit-JSON responses provide the generation baseline. |
| Wording comparison | 1,080 | 2 new | 2,160 new responses; same logical sample as selection. |
| Structure | Feasible action | Acceptance rule before robustness checking |
|---|---|---|
| Allocation | A bijection from agents to objects, satisfying all stated hard assignments. | All allocations optimizing , , or under the stated rule. H5 permission-graph constraint tasks instead accept any complete allowed assignment; no rank objective is imposed there. |
| Meetings | One slot available to every participant. If no availability restriction is given, every listed slot is available. | All common slots optimizing , , or over participants’ slot rankings. |
| Apartment | One listed apartment satisfying the stated rent ceiling, commute ceiling, and any area floor. | All feasible apartments optimizing , , or over residents’ apartment rankings. Attributes constrain feasibility; they do not replace the stated rank objective. |
| Matching | A bijection between the two sides with no strict blocking pair; any hard required pair must also hold. | Preference tasks: the A-proposing deferred-acceptance outcome. Objective tasks: all stable matchings minimizing total or worst rank across both sides, or the A-/B-proposer-optimal outcome. Constraint tasks: any stable matching satisfying the required pair. |
| Structure | Permitted edit | Minimum cost and accepted repaired action |
|---|---|---|
| Allocation | V3/H2: remove one explicit agent–object hard requirement. H5 permission family: add one absent agent–object permission. | Cost is the number of removals or additions in the respective family. V3/H2 accept every certified one-removal repair with an objective-optimal retained-constraint allocation. H5 accepts any complete assignment enabled by a certified single addition. |
| Meetings | Add one slot to one participant’s availability. | One added participant–slot membership; accept any certified single addition together with an optimal common slot after that addition. |
| Apartment | Raise the rent ceiling or the commute ceiling to a certified target. The V3/H2 and H5 constraint families here do not relax area. | One threshold field changes. The rent target is the rent of a minimum-commute apartment; the commute target is the commute of a minimum-rent apartment. The checker requires the recorded target exactly and an optimal apartment under its resulting requirements. |
| Matching | Remove the stated hard required pair; retain strict stability. | One required-pair removal. The resulting action must be a stable matching; H2 accepts all certified resulting matchings. For V3/H5 checker scope, see Appendix F . |
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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