Multi-agent decision making: A Blackwell's informativeness approach

Improving the task performance of Large Language Models (LLMs) is essential, yet scaling these models faces significant challenges such as diminishing returns and high costs. Multi-Agent Systems (MAS) offer a promising solution by distributing tasks among specialized agents to improve the overall task performance. This can reduce training costs at the expense of increased test time due to the discussion and decision-making process. The decision protocol is a critical component of MAS because it specifies how multiple agents collaborate to create a final solution. This thesis introduces the Multi-Agent LLM (MALLM) framework, which implements and evaluates various decision protocols, namely voting, consensus, and judge decision mechanisms, to simulate multi-agent discussions for conversational task solving. Unlike previous work that used a single decision protocol or tested them on limited datasets, this study systematically examines their impact on a diverse set of tasks, ranging from knowledge-based datasets (MMLU, MMLU-Pro, GPQA) and logic-based datasets (StrategyQA, MuSR, Math-lvl-5, SQuAD 2.0). The results indicate that consensus protocols excel in knowledge-intensive domains while voting and judge protocols are more effective for logic-based tasks. Increasing response diversity through independent solution generation improves decision quality, while changes in information access during the decision process have minimal impact.

Multi-agent LLM systems improve reasoning by combining outputs from multiple agents, but interaction-heavy methods can introduce error propagation and high communication overhead. When agents exchange raw responses or reasoning traces, incorrect intermediate reasoning may be adopted and amplified, leading to confident but wrong consensus; multi-round communication also increases token consumption, latency, and inference cost. In this paper, we propose a controlled-communication coordination framework named DarkForest. DarkForest first keeps agents independent, so each agent produces an answer without seeing the others' outputs. It then parses the raw responses into structured candidate records, groups semantically equivalent candidates into clusters, and estimates a calibrated belief distribution over these clusters using agent reliability, confidence, parse quality, support-pattern reliability, and independence corrections. A coordinator receives only policy-permitted evidence from this belief state with controlled communication. Experiments on six reasoning benchmarks show that DarkForest achieves leading overall quality, improves the strongest baseline by up to 30.7% on benchmark metrics, and reduces token consumption by up to $6.5\times$ compared with communication-heavy baselines.

When multiple LLM agents yield conflicting answers, the decision-making process dictates whether agent diversity improves performance or merely compounds shared errors. Existing collective decision-making methods, including voting, electoral rules, and LLM judges, rely on forward reasoning: they map evidence to labels in one direction. Although these methods can combine diverse forward traces, they still aggregate estimates that share this evidence-to-label factorization and can inherit correlated errors within the forward pool. We therefore construct a reverse posterior for each instance through Bayesian backward reasoning from an explicit likelihood. The forward and reverse posteriors provide differently factorized approximations of the underlying posterior. Because estimates from different factorizations may tend to share the same error less often, we use Jensen-Shannon divergence to rank agents by cross-path consistency. This cross-path consistency signal underlies three strategies: hard selection (MinJS), soft reweighting (FwdJS), and log-linear fusion (LogLin). Evaluated on DDXPlus across five LLM backbones, our proposed strategies show consistent improvements: MinJS outperforms random selection across all backbones, FwdJS generally improves over the strongest baseline, and LogLin achieves the best performance among the evaluated methods, with its largest gains on the subset where the agents disagree. Despite its weaker standalone accuracy, the reverse posterior serves as a more useful anchor than forward-only alternatives, providing complementary information for collective decision-making. When labeled data are available, a lightweight two-stage calibration can further refine the reverse anchor and improve aggregation performance.