Evidence accumulation models form a broad family of mathematical models for response time and choice. Despite their diversity, all share a common architectural principle: sensory or cognitive evidence is accumulated over time in one or more accumulators, and a response is initiated when the accumulated evidence in some accumulator first reaches a decision threshold. This architecture provides a natural account of the speed-accuracy tradeoff (higher thresholds produce slower but more accurate responses) and the full shape of RT distributions (which arise from the first-passage time statistics of the accumulation process).
Architectural Dimensions
Single (relative evidence): DDM, dx = v·dt + s·dW
Multiple (absolute evidence): one per alternative, xᵢ(t)
Independence vs. competition:
Independent: accumulators evolve without interaction (LBA, race models)
Competing: lateral inhibition between accumulators (LCA, WTA)
Noise structure:
Ballistic: no within-trial noise (LBA)
Diffusive: continuous within-trial noise (DDM, LCA)
The choice of architecture has important theoretical consequences. Single-accumulator models (like the diffusion model) accumulate the difference in evidence between two alternatives in a single counter. They are mathematically tractable and naturally implement optimal decision making (via the sequential probability ratio test), but are limited to two-choice tasks. Multiple-accumulator models maintain a separate accumulator for each alternative, each accumulating evidence for its respective option. These generalize naturally to tasks with more than two alternatives.
Competition and Leakage
Accumulators may be independent (each evolves in isolation, as in the LBA and simple race models) or competing (each accumulator's growth is inhibited by the others, as in the leaky competing accumulator and winner-take-all networks). Independent architectures are mathematically simpler and easier to fit to data, while competitive architectures are more neurally plausible and can produce context effects in multi-alternative choice. Leakage (exponential decay of accumulated evidence) makes accumulators sensitive to the most recent evidence rather than the entire history, which is important for tasks where evidence quality changes over time.
Because different accumulator architectures make overlapping predictions, model comparison is a central concern. Researchers use quantile-probability plots (which display the full shape of RT distributions for correct and error responses), likelihood-based model selection criteria (AIC, BIC), and Bayesian model comparison to distinguish between architectures. Despite their differences, most accumulator models can fit mean RT and accuracy data equally well; the models are distinguished primarily by their predictions for the shape of RT distributions, the relative speed of correct and error responses, and their behavior in multi-alternative paradigms.
The accumulator framework provides a unifying language for models of decision making across mathematical psychology and cognitive neuroscience. Models within this family — the diffusion model, the LBA, the leaky competing accumulator, and neural drift-diffusion models — differ in their specific assumptions about noise, competition, and leakage, but share the fundamental insight that decisions emerge from the temporal integration of evidence, with response time reflecting the speed of this accumulation process.