As agentic AI systems are deployed in advisory and evaluative roles, understanding how multi-agent interactions shape behavior becomes essential. Multi-agent debate has been studied as a mechanism to improve accuracy, but less is known about how debate structure -- the interaction protocol -- affects the values, dynamics, and consensus patterns that emerge when models navigate contested, real-world decisions. We address this gap by facilitating multi-agent debates among three models (GPT-4.1, Claude 3.7 Sonnet, and Gemini 2.0 Flash) to collectively assign blame in 1,000 everyday dilemmas from Reddit's ``Am I the Asshole'' community. We compare synchronous (parallel) and round-robin (sequential) interaction protocols, mirroring two fundamental ways multi-agent systems are orchestrated in practice. Across more than 30,000 total debates, our findings show striking behavioral differences, which we characterize through two dynamics: inertia and conformity. In the synchronous setting, GPT-4.1 showed stronger inertia (0.6-3.1% revision rates) than either Claude 3.7 Sonnet or Gemini 2.0 Flash (28-41% revision rates). Meanwhile, in round-robin debates, GPT-4.1 and Gemini 2.0 Flash stood out as highly conforming relative to Claude 3.7 Sonnet, with their verdict behavior strongly shaped by order effects. We further characterized the values invoked during debate, finding that GPT-4.1 emphasized personal autonomy and honest communication relative to its debate partners, while Claude 3.7 Sonnet and Gemini 2.0 Flash prioritized empathetic dialogue. Together, these results show how interaction protocol shapes moral reasoning in multi-turn debates, establishing it as a substantive sociotechnical design consideration in multi-agent systems.

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