Global-to-Local Decision Projection for Collaborative Reasoning among Heterogeneous Large Language Models

Complementarity among heterogeneous large language models (LLMs) underpins collaborative reasoning, yet reaching a reliable collective decision remains challenging when initial answers disagree. Majority support may favor an incorrect answer, while dispersed support may leave the choice unclear. We observe that models with incorrect initial answers may shift their support to the correct answer when directly comparing disputed candidates, but these judgments may conflict or provide clear support for only some candidate pairs. To this end, we introduce PairRecon, a global-to-local decision projection framework for collaborative reasoning among heterogeneous LLMs. PairRecon organizes collaboration using the candidates and the distribution of model support revealed by initial disagreement. Guided by this structure, it projects global candidate selection into local pairwise comparisons, enabling models to provide additional judgments on specific disputes. For each candidate pair, judgments that agree across both presentation orders are retained as directed relations supporting one candidate and opposing the other. These retained relations, together with initial support, enable candidate reconstruction despite unresolved local disagreements. Depending on the disagreement pattern, candidate admission or staged arbitration further constrains answer updates to reduce harmful revisions. PairRecon requires no training or parameter updates and allocates additional inference only to initial disagreement cases. Across nine benchmarks, PairRecon improves collective decision accuracy. In the primary evaluation, it improves overall and disagreement-case accuracy over direct three-model aggregation by 1.50% and 6.89%, respectively. It also achieves the greatest net gain and the lowest inference cost among evaluated methods requiring additional inference. Accuracy gains extend to smaller models and open-ended tasks.