When one race is not enough: A relay model explains multisensory response times

Humans typically respond faster to multisensory signals than to their unisensory components, a phenomenon known as the redundant signal effect (RSE). One of the earliest and most influential accounts, the race model, attributes the RSE to statistical facilitation, which arises from parallel, independent processing across sensory modalities. While this model captures some key features of the RSE, it frequently underestimates the observed speed-up leading to violations of the race model inequality (RMI), a benchmark used to test the model's validity. To reconcile this discrepancy, we introduce the relay model, a minimal extension of the race architecture that incorporates cross-modal initiation. In this model, responses result from two sequential race processes, allowing a signal in one modality to initiate the onset of perceptual decision processing in another. This structure retains statistical facilitation as a core principle while introducing a single free model parameter that partitions unisensory processing into gating and decision stages. Through simulations and fits to foundational empirical datasets, we show that the relay model captures both the magnitude and distributional shape of the RSE, including RMI violations. It also accounts for changes in the RSE under asynchronous stimulus onsets and manipulations of signal intensity, which are critical tests in multisensory research. By extending the classical race model with minimal added complexity, the relay model offers a mechanistically explicit and biologically plausible framework for explaining the dynamics of multisensory decision-making.