Title: Tree-Based Formalization of Multi-Agent Complementarity in Human-AI Interactions

Abstract

Complementarity in human-AI interactions (HAI) occurs when a collaborative system surpasses the highest-performing individual prediction benchmark within the group. While this concept is foundational to HAI research, rigorous formalization remains scarce. Current frameworks fail to capture how individual agent predictions integrate into workflow-dependent, multi-agent protocols. To address this limitation, we present a tree-based formalization of complementarity within multi-agent HAI contexts.

In our model, an HAI protocol is defined by an ordered configuration of agent roles and a rooted planar binary tree, where each leaf node is annotated with a prediction vector. A local binary composition rule is applied recursively throughout the tree structure, generating a complementarity functional relative to a pointwise-min oracle benchmark. We establish four key findings.

First, we demonstrate that selector-based HAIs—such as those relying on self-reliance or AI-reliance—are incapable of achieving complementarity, irrespective of the task, loss function, or prediction accuracy. Second, in the context of regression with squared loss, we show that complementarity is equivalent to minimizing the Euclidean distance to the ground-truth vector. For cases involving $N=2$, the optimal linear-pooling weight admits a closed-form solution and offers a residual-correction interpretation.

Third, under linear local composition, every protocol tree establishes a barycentric coordinate chart on the simplex of leaf weights. We further prove that Tamari-cover reparameterizations of protocol trees maintain complementarity, and for $N=4$, these reparameterizations satisfy the pentagon identity. Fourth, in binary classification, we identify that no internal local composition can achieve complementarity under endpoint-monotone losses, which encompass standard Bregman divergences and numerous finite Bernoulli $f$-divergence losses. A similar obstruction applies to multiclass aggregation under cross-entropy loss.

In conclusion, our framework indicates that while complementarity is achievable in multi-agent regression scenarios, it is obstructed in classification tasks under natural constraints regarding local aggregation methods and loss functions.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC