Decision-Architecture Dependence and Patient-Gender-Conditioned Allocation in Large-Language-Model-Assisted Nursing Allocation: A Multi-Model Counterfactual Audit

Background/Objectives: Large language models (LLMs) may support healthcare workforce allocation, but their decisions can be sensitive to demographic cues and decision architecture. This study examined gender-task congruity, Candidate-A dependence under the tested decision architecture, and patient-gender-conditioned nursing allocation. Methods: Three provider-specific LLM configurations were audited across 24 nursing tasks. Male and female nurses were professionally equivalent and counterbalanced across Candidate A/B; patient gender was varied in six intimate-care tasks. Sixty conditions were repeated three times per model, yielding 540 valid outputs. Results: Male nurses were selected in 50.0% of Technical/Procedural and Relational/Educational allocations. Candidate A was selected in all 288 observations, although 285 (99.0%) assigned identical suitability scores. Because A/B assignment was bundled with labeling, presentation order, evaluation order, and response-template anchoring, this pattern indicates Candidate-A dependence under the tested decision architecture rather than an isolated position effect. Changing patient gender from female to male produced 57 female-to-male nurse switches and no reverse switches (p < 0.001). Conclusions: The audited configurations showed no generalized gender-task pattern but demonstrated decision-architecture dependence and patient-gender-conditioned allocation. Fairness audits should assess equivalent-candidate handling, patient preference, and counterfactual stability.