Previous studies have shown a surprising amount of between-subjects variability in the strength of interactions between sensory modalities. For the same set of stimuli, some subjects exhibit strong interactions, whereas others exhibit weak interactions. To date, little is known about what underlies this variability. Sensory integration in the brain could be governed by a global mechanism or by task-specific mechanisms that could be either stable or variable across time. We used a rigorous quantitative tool (Bayesian causal inference) to investigate whether integration (i.e., binding) tendencies generalize across tasks and are stable across time. We report for the first time that individuals’ binding tendencies are stable across time but are task-specific. These results provide evidence against the hypothesis that sensory integration is governed by a single, global parameter in the brain.