From Belief Entrenchment to Robust Reasoning in LLM Agents

TL;DR

This work addresses belief entrenchment in multi agent debate by decomposing the failure into static initial bias and homogenized debate dynamics. It proposes DReaMAD, a two stage framework combining Strategic Prior Knowledge Elicitation and Perspective Diversification to correct biases and diversify reasoning paths. The new MetaNIM Arena benchmark enables rigorous evaluation of adversarial strategic reasoning under impartial game dynamics and Grundy theory. Across extensive experiments, DReaMAD yields meaningful gains in accuracy and win rates, demonstrates long chain of thought abilities without training, and generalizes to math and commonsense reasoning, highlighting a practical route to robust LLM reasoning in dynamic, interactive settings.

Abstract

Multi-Agent Debate (MAD) has emerged as a promising inference scaling method for Large Language Model (LLM) reasoning. However, it frequently suffers from belief entrenchment, where agents reinforce shared errors rather than correcting them. Going beyond merely identifying this failure, we decompose it into two distinct root causes: (1) the model's biased $\textit{static initial belief}$ and (2) $\textit{homogenized debate dynamics}$ that amplify the majority view regardless of correctness. To address these sequentially, we propose $\textbf{DReaMAD}$ $($$\textbf{D}$iverse $\textbf{Rea}$soning via $\textbf{M}$ulti-$\textbf{A}$gent $\textbf{D}$ebate with Refined Prompt$)$. Our framework first rectifies the static belief via strategic prior knowledge elicitation, then reshapes the debate dynamics by enforcing perspective diversity. Validated on our new $\textit{MetaNIM Arena}$ benchmark, $\textbf{DReaMAD}$ significantly mitigates entrenchment, achieving a +9.5\% accuracy gain over ReAct prompting and a +19.0\% higher win rate than standard MAD.

Figures (10)

• Figure 1: DReaMAD framework. DReaMAD improves LLM reasoning by combining Strategic Prior Knowledge Elicitation and Perspective Diversification. First, the model reinterprets the problem and formulates high-level strategies to reduce belief entrenchment. In the second stage, multiple agents adopt distinct viewpoints, engage in structured debate, and refine their conclusions to enhance decision-making.
• Figure 2: An example demonstrating how the debate process converges to a biased outcome. We observed that belief entrenchment occurs in the first debate. Blue text indicates the correct reasoning and orange text indicates the strong consistent (biased) reasoning. The second debate is omitted, as its procedure replicates the first and third; all debates use GPT-4o-mini as the debating agent.
• Figure 3: Belief entrenchment across models: showing that even after the debate concludes, strongly consistent actions continue to exhibit strong consistency, reinforcing biased action distributions in the Fibonacci game.
• Figure 4: Belief Entrenchment in Action (NIM). Despite one agent proposing the optimal move, the debate converges to the suboptimal majority view, illustrating how valid reasoning is suppressed by the model's static belief.
• Figure 5: In this example, we illustrate how the debate process converges to an optimal outcome using our algorithm, DReaMAD. We begin with the same current state shown in Figure \ref{['fig:debate_process']}, employing self-generated prompts for each LLM agent.

Theorems & Definitions (3)

• Definition A.1: Grundy Number
• Definition A.2: Disjunctive Sum of DAGs
• Theorem A.3: Sprague-Grundy sprague1935grundy1939