When Empathy Misses the Goal: A Benchmark for Goal Displacement in LLM Advice

Conversational LLMs are increasingly deployed in advice and decision-support contexts where users need an actionable answer, not just emotional support. We define goal displacement as the substitution of warmth, reassurance, or non-directive encouragement for goal-advancing content when these alone do not satisfy the user's objective. We release GDB (Goal Displacement Benchmark), a benchmark of 230 scenarios across nine domains with 4,134 human-scored responses from 18 models. We report three findings. First, trap displacement is strongly anti-correlated with Chatbot Arena Elo (ρ = −0.706, n=15): more capable models displace less. Second, capability tiers fail in qualitatively different ways. Mid-tier models concentrate failures on feasibility overrides (52.3% for GPT-4o-mini), while small open-weight models invert on empathy controls (41.9% for Mistral 7B). Within-vendor generational pairs reduce displacement by an order of magnitude. Third, a 2×2 factorial probe dissociates displacement from social sycophancy: in the high-complexity, low-pressure condition, sycophancy reaches 35.0% while displacement is only 7.5%, and within-condition rank correlation between the two is near zero (ρ = +0.13). Across models, trap displacement ranges from 0.0% to 37.7%; reverse displacement on the empathy condition ranges from 0.0% to 41.9% as a separate dimension. Dataset, rubric, and code are released CC-BY-4.0.