evidence accumulation · decision thresholds · speed-accuracy tradeoff
When you make a quick two-choice decision — left or right, old or new, signal or noise — the brain doesn't wait for the evidence to become certain. It accumulates noisy evidence over time until it crosses one of two thresholds, then commits. The drift diffusion model captures this process: a decision variable starts at the midpoint and performs a biased random walk toward an upper boundary (one response) or lower boundary (the other). Drift rate v controls how strongly the walk leans in the correct direction. Threshold a controls how much evidence is required before a response is made.
Three parameters — drift rate, threshold, and non-decision time — jointly predict accuracy, mean reaction time, and the shape of the RT distribution. The model was developed by Roger Ratcliff in 1978 and has since fit hundreds of behavioral datasets from perceptual discrimination, recognition memory, and simple choice tasks.
walk starts at a/2 after Ter · gray region = non-decision time · green boundary = correct · red = error
x-axis: reaction time (ms) · y-axis: count · bin width: 50 ms
What the simulation shows: the speed-accuracy tradeoff is not a choice between two independent settings — it is controlled by a single parameter, the threshold a. Raise it and accuracy increases while RTs slow. Lower it and responses are faster but error rate climbs. Both effects follow from the same boundary. There is no separate mechanism for "trying harder."
With high drift (strong signal), errors take longer on average than correct responses. For the walk to reach the wrong boundary despite a strong pull in the correct direction, it has to accumulate enough random fluctuations against the drift — a low-probability path that typically takes longer. With low drift (near 0), the walk is nearly symmetric, and errors are roughly as fast as correct responses. This prediction about error RT is one of the model's strongest diagnostic signatures.
The RT distribution is right-skewed. This is not an assumption — it is the first-passage time distribution of a biased random walk, which has an exponential right tail. Changing v and a reshapes the distribution, but the rightward skew persists regardless of parameters.
Non-decision time Ter shifts the entire distribution rightward by a constant — encoding the stimulus and executing the motor response take time that is not part of the evidence accumulation process. Ter affects where the distribution sits on the time axis, not its shape.
What it can't show: the standard DDM assumes a fixed starting point at the midpoint, constant drift, and fixed boundaries. Ratcliff's full model adds trial-to-trial variability in drift, starting point, and Ter — each producing different patterns in error RT and distributional shape. The model here also has no urgency mechanism (collapsing boundaries over time) and no way to handle more than two choices. Whether the brain implements anything like a drift-diffusion process, or whether the model is a successful description of behavioral data without mechanistic correspondence, remains genuinely unclear.