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Self-report questionnaires have long been used to assess LLM personality traits, yet they fail to capture behavioral nuances due to biases and meta-knowledge contamination. This paper proposes a novel multi-observer framework for personality trait assessments in LLM agents that draws on informant-report methods in psychology. Instead of relying on self-assessments, we employ multiple observer LLM agents, each of which is configured with a specific relationship (e.g., family member, friend, or coworker). The observer agents interact with the subject LLM agent before assessing its Big Five personality traits. We show that observer-report ratings align more closely with human judgments than traditional self-reports and reveal systematic biases in LLM self-assessments. Further analysis shows that aggregating ratings of multiple observers provides more reliable results, reflecting a wisdom of the crowd effect up to 5 to 7 observers.