arXiv:2507.11198v1 Announce Type: cross Abstract: Large Language Models (LLMs) enable new possibilities for qualitative research at scale, including coding and data annotation. While multi-agent systems (MAS) can emulate human coding workflows, their benefits over single-agent coding remain poorly understood. We conducted an experimental study of how agent persona and temperature shape consensus-building and coding accuracy of dialog segments based on a codebook with 8 codes. Our open-source MAS mirrors deductive human coding through structured agent discussion and consensus arbitration. Using six open-source LLMs (with 3 to 32 billion parameters) and 18 experimental configurations, we analyze over 77,000 coding decisions against a gold-standard dataset of human-annotated transcripts from online math tutoring sessions. Temperature significantly impacted whether and when consensus was reached across all six LLMs. MAS with multiple personas (including neutral, assertive, or empathetic), significantly delayed consensus in four out of six LLMs compared to uniform personas. In three of those LLMs, higher temperatures significantly diminished the effects of multiple personas on consensus. However, neither temperature nor persona pairing lead to robust improvements in coding accuracy. Single agents matched or outperformed MAS consensus in most conditions. Only one model (OpenHermesV2:7B) and code category showed above-chance gains from MAS deliberation when temperature was 0.5 or lower and especially when the agents included at least one assertive persona. Qualitative analysis of MAS collaboration for these configurations suggests that MAS may nonetheless aid in narrowing ambiguous code applications that could improve codebooks and human-AI coding. We contribute new insight into the limits of LLM-based qualitative methods, challenging the notion that diverse MAS personas lead to better outcomes. We open-source our MAS and experimentation code.