A growing body of research examines personality traits in Large Language Models (LLMs), particularly in human-agent collaboration. Prior work has frequently applied the Big Five inventory to assess LLM behavior analogous to human personality, without questioning the underlying assumptions. This paper critically evaluates whether LLM responses to personality tests satisfy six defining characteristics of personality. We find that none are fully met, indicating that such assessments do not measure a construct equivalent to human personality. We propose a research agenda for shifting from anthropomorphic trait attribution toward functional evaluations, clarifying what personality tests actually capture in LLMs and developing LLM-specific frameworks for characterizing stable, intrinsic behavior.

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