PaperlayerView exact revision on arXiv

Source-linked AI summary

On the possibilities and limitations of LLM-based multi-agent systems for multi-criteria decision-making in healthcare operations management

Marco Boresta, Tommaso Giovannelli, Sepehr Namirad, Giulia Riccardi

arXiv:2610.23673v1math.OCcs.AIcs.MA

TL;DR

Healthcare decision models need stakeholder trade-off weights that are difficult to quantify, and LLM-generated weights may be unreliable. LLM-PADA audits explicit ratings and inferred choices, then tests robust optimization under weight uncertainty; the experiments find order-sensitive choices and frequent differences from mean-weight decisions.

  • Problem

    Healthcare multi-criteria optimization needs weights for stakeholder trade-offs, but such weights vary across roles and operating conditions and are difficult to state numerically.

    Source: §1 · p. 2

  • Method

    LLM-PADA elicits explicit criterion ratings or infers weights from pairwise choices, assesses reliability, constructs uncertainty sets, and compares robust with mean-weight optimization.

    Source: §1 · pp. 2–3, §5 · p. 30

  • Results

    Robust models selected different decisions from mean-weight models in ten of sixteen outpatient comparisons and five of six ED comparisons; outcome differences improved holdout prediction beyond order for two of six model–role combinations, while choices remained order-sensitive.

    Source: §5 · pp. 30–31

  • Takeaways & Limitations

    The results support auditing LLM-generated preferences before using them as optimization weights in healthcare decision support.

    Source: §5 · p. 31

    The 95% bootstrap interval does not guarantee that an inferred weight represents a human stakeholder’s preference or that the selected configuration improves operational performance.

    Source: §4.3.3 · p. 25

Abstract

from arXiv · show

Multi-criteria models for healthcare operations need weights that express how stakeholders trade off patient waiting time, provider workload, and operating cost, but these weights are difficult to quantify. Teams of large language model (LLM) agents, each prompted to represent a stakeholder, have been used to supply them. We propose a framework for assessing the reliability of LLM-generated preferences as inputs to multi-objective optimization and quantifying how their uncertainty affects decisions. We study explicit preferences by asking agents to rate the importance of the criteria in an outpatient appointment scheduling problem, and implicit preferences by inferring trade-offs from the agents' pairwise choices between emergency department configurations. The computational experiments show that the explicit preferences respond to the clinic's operating conditions and differ across roles, but deliberation among the agents can erase these differences, whereas simple averaging preserves them. The pairwise choices used to reveal the agents' implicit preferences depend largely on which option is presented first, and we find limited evidence that a statistical model using contextual information alongside presentation order predicts the agents' choices on new comparison pairs better than a model using presentation order alone. We then formulate robust weighted-sum optimization models to account for preference uncertainty. In most cases, these models select different schedules or configurations from those obtained using average preference weights. These results indicate that LLM-generated preferences need an audit of this kind before they are used as optimization weights in healthcare decision support.

1 Introduction

Healthcare operations require weights for conflicting criteria, but stakeholders’ priorities vary and are difficult to quantify. LLM-PADA audits LLM-generated preferences and tests how their uncertainty changes optimization decisions.

1 Introduction

  • Healthcare schedules and ED pathways trade off multiple criteria, while stakeholder priorities vary across roles and operating conditions and are difficult to state numerically.Weights are often chosen informally and treated as fixed in healthcare and other scheduling applications.Source: §1 · pp. 1–2
  • LLM-PADA elicits explicit criterion ratings or infers implicit trade-offs from pairwise ED-configuration choices, then assesses reliability, constructs weight uncertainty sets, and compares robust with mean-weight optimization.Reliability checks cover context sensitivity, role differentiation, and stability under changes in procedure and presentation order, rather than agreement with human preferences.Source: §1 · pp. 2–3

1.1 Contributions

  • Mean-weight and robust models select different decisions in ten of sixteen outpatient comparisons and five of six ED comparisons.The framework also tests how explicit preferences respond to clinic conditions and stakeholder roles, and how implicit preferences inferred from ED choices predict new comparisons.Source: §1.1 · p. 3
  • LLM deliberation can weaken responses to clinic conditions and erase or reverse stakeholder-role differences, while mechanical averaging retains role differentiation.The implicit-preference approach found evidence that outcome differences improved prediction beyond presentation order for only two of six model–role combinations.Source: §1.1 · p. 3

1.2 Organization of the paper

  • The paper reviews related work, studies explicit outpatient elicitation and implicit ED inference, then concludes with discussion of future work.The framework is demonstrated with locally executed Qwen3.5-family models, though the authors describe it as applicable to other healthcare operations problems and proprietary LLMs.Source: §1.2 · p. 3, §1 · p. 3

2 Background and related work

The background introduces multi-objective trade-offs and reviews LLM preference elicitation, reliability, pairwise choice, robust optimization, and applications in operations research and healthcare. The paper’s emphasis is on auditing generated weights and measuring their decision effects.

2.1 Multi-objective optimization background

  • Weighted-sum optimization combines multiple objectives using preference weights, while Pareto-optimal alternatives expose trade-offs that require preference information.The weighted-sum method is an a priori approach; the paper’s overview links preference elicitation and inference to robust models for uncertain weights.Source: §2.1 · p. 4, Figure 1 · p. 4

2.2 Related work

  • Table 1 positions the paper against closest works, marking whether topics are addressed, partially addressed, or not addressed.The supplied caption does not specify the table’s individual comparison entries.Source: §2.2 · p. 4, Table 1 · p. 5

2.2.1 LLM agents for multi-criteria decision-making

  • Prior MCDM work elicits or aggregates LLM-derived weights, uses LLMs to rate alternatives while obtaining weights by analytic hierarchy process [60], or selects among alternatives; this paper instead audits preference reliability.Its implicit protocol treats choices as observations, estimates trade-offs while accounting for presentation effects, and evaluates decisions under mean-weight and robust optimization.Source: §2.2.1 · pp. 5–6

2.2.2 Reliability of LLM-generated preferences

  • Prior findings raise concerns about inconsistent answers, prompt sensitivity, user-view adaptation, and agents drifting from assigned personas [2] [52] [55] [12].The study therefore measures agreement separately from retention of contextual and role-specific priorities, and compares deliberation with mechanical averaging.Source: §2.2.2 · p. 6

2.2.3 Preference inference from pairwise choices

  • The pairwise-choice model uses ED configurations’ outcomes to estimate a trade-off weight from fitted outcome coefficients, while accounting for presentation order [62].The presentation-order term is evaluated against a benchmark using order alone.Source: §2.2.3 · pp. 6–7

2.2.4 Robust optimization under preference uncertainty

  • Robust optimization protects against worst cases over plausible weights or utilities; this paper uses empirical percentile boxes for outpatient weights and bootstrap intervals for ED weights.Unlike query selection for worst-case utility [58], the study measures how LLM-generated weight variability affects operational decisions.Source: §2.2.4 · p. 7

2.2.5 LLMs in operations research and healthcare

  • Prior operations-research work checks LLM outputs against solvers or simulations [10] [71], while healthcare studies use clinical or human evaluation.The paper focuses on preference weights because it states that no external reference exists for checking them.Source: §2.2.5 · p. 7

3 Explicit preference elicitation in outpatient scheduling

This section examines whether role-prompted LLM agents can provide explicit outpatient-scheduling weights that respond to clinic conditions and inform robust scheduling decisions. It considers how deliberation affects agents’ contextual responses, role differences, and disagreement, and whether robust optimization changes the selected schedule.

3.1 Problem setting

  • The scheduling problem weights patient waiting, provider idle time, and overtime, with deterministic service durations, fixed request order, and no overbooking to isolate weight effects.The section assesses contextual sensitivity, role differentiation, inter-agent dispersion, and the scheduling consequences of weight uncertainty; human preference validity is outside its scope.Source: §3.1 · p. 8, §3 · p. 8, §3.2 · p. 9

3.3.1 Preference generation (Step 1)

  • Agents representing intake, provider, and scheduler roles first score all criteria; deliberation then uses numerical, argumentative, or mechanical protocols.The mechanical rule moves each agent toward the group mean while preserving that mean, showing how averaging alone attenuates role-specific and contextual differences.Source: §3.3.1 · pp. 9, 11

3.3.2 Reliability assessment (Step 2)

  • Reliability is assessed separately through paired responses to clinic-condition changes, role-specific relative importance, and dispersion among normalized agent weights.The paired design compares high-waiting or high-overtime conditions with the same base description; dispersion is measured as the root-mean-square deviation from agents’ mean weights.Source: §3.3.1 · p. 10, §3.3.2 · pp. 11–12

3.3.3 Weight uncertainty construction (Step 3)

  • Empirical percentile-box uncertainty sets capture componentwise weight ranges across agents, descriptions, and deliberation trajectories, including combinations no agent reported.Robust optimization minimizes the worst weighted objective over each set and is compared with scheduling under the corresponding mean weights.Source: §3.3.3 · p. 12, §3.3.4 · p. 13

3.4.1 Experimental setup

  • The experiments use Qwen3.5-4B, ten synthetic clinic descriptions, twenty elicitation responses per agent and condition, and three deliberation rounds.For scheduling, one provider assigns seven requests across ten 30-minute slots in a 300-minute session; the chosen schedules also depend on objective reference scales.Source: §3.4.1 · pp. 13–14

3.4.2 Contextual sensitivity (Q1)

  • The mean HW–B waiting-score difference fell from 0.587 points before deliberation to 0.293 under numerical and 0.193 under argumentative deliberation.The reported HO–B overtime-score difference also declined from 2.513 points before deliberation to 0.980 under numerical deliberation.Source: §3.4.2 · p. 14
  • Before deliberation, all agents increased waiting-time importance under high waiting and overtime importance under high overtime; deliberation attenuated these responses.For HW–B, waiting-score differences were 0.560 points for Intake, 0.695 for Provider, and 0.506 for Scheduler, with all intervals above zero. For HO–B, overtime-score increases were 2.872, 1.691, and 2.977 points, respectively, with all intervals excluding zero.Source: §3.4.2 · p. 14, Figure 2 · p. 15
  • Neither LLM protocol consistently preserves initial contextual responses better: argumentative deliberation yields a larger mean overtime response but a smaller mean waiting response than numerical deliberation.Of 1,170 valid argumentative turns, 1,118 (95.56%) cite a preceding agent argument; references to manipulated clinic indicators vary, with current time mentioned more often than waiting time or projected overtime.Source: §3.4.2 · p. 15, Table 2 · p. 17

3.4.3 Role differentiation and inter-agent dispersion (Q2 and Q3)

  • All 12 initial role-differentiation scores are positive, but after LLM deliberation only three remain positive under the numerical protocol and one under the argumentative protocol.Mechanical averaging retains positive intervals for all 12 scores by preserving agents’ ordering; the LLM protocols weaken or reverse role differences despite unchanged role descriptions.Source: §3.4.3 · p. 15, Table 3 · p. 17
  • Disagreement does not decline uniformly: under HO, mean dispersion rises from 0.0222 to 0.0454 with numerical deliberation and 0.0426 with argumentative deliberation.Mechanical averaging reduces normalized-weight dispersion to 27.2–27.4% of its initial value.Source: §3.4.3 · pp. 15–16, Figure 4 · p. 18

3.4.4 Weight uncertainty and scheduling consequences (Q4)

  • Argumentative deliberation produces wider componentwise weight intervals than numerical deliberation in 10 of 12 criterion–condition combinations.The exceptions are the waiting-weight intervals under HW and HO; under the argumentative protocol, mean overtime weight is 0.418 for HO versus 0.323 for HW.Source: §3.4.4 · pp. 16–17
  • Robust optimization selects a different schedule from mean-weight optimization in 10 of 16 combinations, and the HO example reduces worst-case objective by 4.37%.For (S, π) = (HO, arg), robust optimization selects (23, 25, 16) rather than the mean-weight solution (50, 15, 6), reducing the worst-case objective from 0.2959 to 0.2830 while increasing the objective at mean weights by 3.18%.Source: §3.4.4 · p. 17

4 Implicit preference inference in emergency department planning

The section infers trade-offs between emergency department configurations from LLM agents’ pairwise choices, accounting for outcomes and presentation order. The inferred weights are not claimed to represent human stakeholder preferences.

4 Implicit preference inference in emergency department planning

  • Agents compare configurations using waiting-time and MIU-opening outcomes, with a choice model that includes presentation order and is evaluated against an order-only benchmark.More MIU opening hours can reduce waiting but require greater ED resources.Source: §4 · p. 18
  • Patient, physician, and operations prompts frame the same two outcomes from their respective perspectives, without assigning numerical weights in advance.Weights are instead estimated from pairwise choices.Source: §4 · p. 18
  • The inferred weights are not asserted to represent the preferences of human patients, physicians, or hospital operators.Source: §4 · p. 18
  • Figure 5 encodes service intervals, appointment times, and patient waiting, while panel titles give total waiting, idle time, and overtime in minutes.Its panels compare MW and RB schedules on the same seven-request instance under HW and HO elicitation conditions.Source: Figure 5 · p. 19

4.1 Problem setting

The ED case study compares eleven operating configurations using average group waiting time and weekly MIU opening hours as objectives. A weighted sum favors only configurations on the lower convex hull, while the robust problem has a different selection capability.

4.1 Problem setting

  • Each ED configuration specifies MIU opening and closing times across seven days and morning and afternoon routing percentages; the number of MIU rooms is fixed.The underlying simulation represents stochastic arrivals, triage, and patient flow through the Medical, Surgical, and MIUs.Source: §4.1 · p. 19
  • The waiting objective averages mean triage-to-first-visit times across eight patient groups, while the resource objective is total weekly MIU opening hours.The eleven configurations are the finite decision set, and none is dominated on the two objectives.Source: §4.1 · pp. 19–20
  • Objectives are normalized over 85–100 minutes for waiting and 21–84 weekly opening hours; λ weights normalized waiting relative to opening hours.λ = 1 selects solely by waiting, while λ = 0 selects solely by opening hours.Source: §4.1 · p. 20
  • A fixed-weight sum can select only configurations on the lower convex hull, so nondominated configurations D, F, H, and I are not selectable that way.The robust problem is not subject to this restriction and can select H.Source: §4.1 · p. 20

4.2 Research questions

The research questions test whether outcomes add predictive value beyond presentation order, how choices vary across repeats and reversals, and how uncertain inferred weights affect configuration selection. Role prompts describe both outcomes without presupposing role-specific weights.

4.2 Research questions

  • The prompts describe average waiting time and MIU opening hours from patient, physician, and operations perspectives, without positing an expected weight for any role.Figure 6 presents these outcomes for eleven configurations.Source: §4.2 · p. 20, Figure 6 · p. 21
  • The predictive-relevance question asks whether outcome information improves held-out choice prediction beyond presentation order alone.Source: §4.2 · p. 20
  • The choice-consistency question examines repeated and reversed-order choices, including whether agents favor a configuration strictly better on both outcomes.Source: §4.2 · p. 21
  • The remaining questions examine uncertainty in inferred trade-off weights across models and roles, and how accounting for that uncertainty changes selected configurations versus a single weight.Source: §4.2 · p. 21

4.3 Methodology

LLM-PADA assesses preference reliability in four steps: infer preferences from pairwise choices, test their predictive and behavioral consistency, quantify weight uncertainty, and compare decision rules that account for it.

4.3.1 Preference generation and inference (Step 1)

  • Pairwise choices in both presentation orders feed a logistic model that estimates a waiting-time versus opening-hours trade-off while accounting for presentation order.The fitted ratio λ captures the relative trade-off; the presentation coefficient captures the effect of showing an option first.Source: §4.3.1 · pp. 21–22

4.3.2 Reliability assessment (Step 2)

  • Reliability checks compare outcome-based predictions with position-only and Bradley–Terry benchmarks, alongside order agreement, repeatability, and dominance compliance.Prediction is assessed on 31 held-out pairs, with both presentation orders retained when resampling pairs for the Brier-score improvement interval.Source: §4.3.2 · pp. 23–24

4.3.3 Weight uncertainty construction (Step 3)

  • A parametric bootstrap refits the choice model on 1,000 synthetic datasets and uses retained weights to form a 95% interval as the uncertainty set.The interval is conditional on the fitted model and procedure; it does not establish human-preference validity or operational improvement.Source: §4.3.3 · pp. 24–25

4.3.4 Configuration decision analysis (Step 4)

  • Mean-weight, fitted-weight, and robust rules select configurations by minimizing, respectively, an average-weight objective, a fitted-weight objective, and the worst-case objective over the weight interval.The eleven configurations are enumerated exactly; robust optimization can select a nondominated configuration that minimizes no single weighted sum.Source: §4.3.4 · pp. 25–26

4.4 Numerical results

Across the reported ED configurations, robust optimization often changes the mean-weight choice, while evidence that pairwise choices reflect outcome trade-offs beyond presentation order is limited and varies by model and role. The inferred weights and their decision consequences remain conditional on the choice model and the eleven configurations studied.

4.4.1 Predictive performance and choice consistency (Q1–Q2)

  • Outcome differences provide limited predictive improvement beyond presentation order for 9B and support it for only 27B Patient and Operations, leaving the other four model-role combinations inconclusive.For 9B, all three Brier-score improvement intervals contain zero; for 27B Patient and Operations, the intervals are positive, while Physician's interval contains zero.Source: §4.4.1 · p. 28
  • Choices among nondominated configurations remain sensitive to presentation order, despite all three 27B roles selecting the dominating option in all ten additional comparisons.For 9B, order agreement is 0.19–0.26 and dominated choices occur only when the dominating option is presented second; across 27B roles, first-option selections range from 69.4% to 82.3%.Source: §4.4.1 · p. 28

4.4.2 Uncertainty in the inferred weights (Q3)

  • For 9B, broad intervals and endpoint estimates provide weak support for interpreting fitted ratios as operational trade-offs; 27B intervals are narrower, but only Operations' interval excludes both endpoints.The 27B fitted weights are 0.75, 0.72, and 0.64 for Patient, Physician, and Operations; the intervals overlap substantially, and no formal role comparison is performed.Source: §4.4.2 · p. 29

4.4.3 Configuration selection and consequences of robustness (Q4)

  • 5 of 6 model-role comparisons select different configurations under robust and mean-weight rules, with robust choices trading higher average group waiting time for fewer weekly MIU opening hours.For 27B Patient, the robust choice raises average waiting time by 1.071 minutes and lowers opening hours by 18 per week; for 27B Operations, the changes are 0.989 minutes and eight hours.Source: §4.4.3 · pp. 29–30, Table 5 · p. 30
  • The decision consequences are conditional on the eleven configurations and do not establish alignment with human stakeholder preferences or clinical effectiveness.For 9B Patient and Physician, the shared uncertainty interval [0, 1] yields the same robust selection, xH, despite different fitted preferences.Source: §4.4.3 · p. 30

5 Conclusions

LLM-PADA assesses explicit and implicit LLM-generated preferences, their reliability, and how preference uncertainty affects optimization decisions. Robust models often select different decisions from mean-weight models, while the reported findings motivate further comparison with human stakeholders and other models.

5 Conclusions

  • LLM-PADA assesses explicit preferences elicited as criterion importance scores and implicit preferences inferred from pairwise choices, then evaluates reliability and compares mean-weight with robust optimization.The framework also constructs uncertainty sets for the resulting weights.Source: §5 · p. 30
  • Deliberation weakened contextual responses and sometimes reversed role differences in outpatient scheduling, while emergency department choices remained sensitive to presentation order.Outcome differences improved holdout prediction beyond presentation order for two of six model–role combinations.Source: §5 · pp. 30–31
  • Robust optimization selected decisions different from mean-weight optimization in 10 of 16 outpatient comparisons and 5 of 6 emergency department comparisons.The comparison concerns the loss at mean weights incurred to reduce the worst-case weighted objective, for fixed operational data and objective normalizations.Source: §5 · p. 31
  • Future work should compare agents with human stakeholders on the same elicitation tasks, replicate findings across model families, and account for uncertainty in simulated outcomes.The proposed human comparison should assess agreement in both stated trade-offs and the decisions they imply.Source: §5 · p. 31

A.1 Contextual sensitivity and role differentiation

Tables 6 and 7 describe measures of contextual sensitivity and role differentiation, including their comparisons, scales, and uncertainty intervals.

A.1 Contextual sensitivity and role differentiation

  • Table 6 reports mean paired importance-score differences for HW versus B on waiting and HO versus B on overtime, before and after round 3.Differences are in points on the 1–9 scale.Source: Table 6 · p. 40
  • Table 6 brackets give 95% percentile bootstrap intervals calculated over the ten base clinic descriptions.Source: Table 6 · p. 40
  • Table 7 compares each named agent’s normalized weight on its role-associated criterion with the mean weight assigned by the other two agents, by weight source and condition.Its brackets give 95% percentile bootstrap intervals over the ten base clinic descriptions.Source: Table 7 · p. 40

A.2 Preference uncertainty

The uncertainty sets use empirical percentiles of normalized criterion weights and impose the simplex constraints on the considered weight vectors.

A.2 Preference uncertainty

  • Table 8 sets componentwise lower and upper bounds at the empirical 5th and 95th percentiles of normalized criterion weights for each condition and weight source.Source: §A.2 · p. 41
  • The bounds summarize variation across agents and base clinic descriptions, plus repeated deliberation trajectories for numerical and argumentative protocols.Source: §A.2 · p. 41
  • Together with nonnegativity and the requirement that the three weights sum to one, the bounds define the weight vectors considered by the robust scheduling model.Source: §A.2 · p. 41

A.3 Complete mean-weight and robust scheduling comparison

Table 9 compares mean-weight and robust scheduling on one fixed instance, with elicitation condition varying while operational inputs remain constant.

A.3 Complete mean-weight and robust scheduling comparison

  • Table 9 compares mean-weight (MW) and robust (RB) optimization on the fixed scheduling instance described in Subsection 3.4.1.Source: §A.3 · p. 41
  • Each row’s condition identifies the elicitation context from which its weights were obtained.Source: §A.3 · p. 41
  • Patient requests, service durations, and scheduling constraints are identical across all rows.Source: §A.3 · p. 41

A.4 Prompt templates and validation

The appendix specifies stakeholder prompts for eliciting and deliberating over outpatient scheduling criterion scores, along with response checks and fallback handling. It also records the scheduling-weight assumption and identifies the scope of two tables.

A.4 Prompt templates and validation

  • The elicitation prompt asks each role to jointly score waiting, idle, and overtime importance from 1 to 9, responding to operational state when provided.The three role descriptions represent Intake/Patient, Provider/Physician, and Scheduler/Operations perspectives.Source: §A.4 · p. 41
  • Table 8 defines weight uncertainty sets using empirical 5th–95th percentile bounds and a simplex constraint, while Table 9 reports outcomes from MW and RB.Table 8 uses 30 normalized vectors for pre-deliberation and mechanical samples and 150 for numerical and argumentative samples; Table 9 reports waiting, idle, and overtime minutes plus objective changes.Source: Table 8 · p. 42, Table 9 · p. 42
  • For B, HW, and HO, prompts include nine operational-state fields; CF instead explicitly provides no operational state.The elicitation wording for idle time concerns intervals between patients, while scheduling also counts the initial gap before the first service.Source: §A.4 · p. 43
  • Using normalized importance scores as scheduling-objective weights is an experimental assumption, and the prompts do not show the scheduling instance or objective reference scales.Those reference scales are 120, 60, and 60 minutes.Source: §A.4 · p. 43
  • Numerical deliberation requests revised scores only, whereas argumentative deliberation also requests reasons, an objection, a target stakeholder, and argument references.Both protocols instruct agents to consider other vectors while remaining faithful to their role and operational state.Source: §A.4 · p. 43
  • Invalid deliberation responses are checked and may be retried twice; if no valid response is obtained, the prior-round scores carry forward and raw attempts are retained.Ollama also receives a strict JSON schema, and complete instantiated prompts and outputs are available in JSONL audit files.Source: §A.4 · p. 44
Loading 2610.23673v1…