Race models, originating with work by Raab (1962) and formalized by Townsend and Ashby (1983), describe decision making as a parallel competition among independent accumulators, each gathering evidence for one response alternative. The first accumulator to reach its threshold triggers the corresponding response. This architecture provides a natural account of both response times and choice probabilities in tasks with two or more alternatives.
The Independent Race
Response = argmin(T₁, T₂, ..., Tₖ)
RT = min(T₁, T₂, ..., Tₖ) + Ter
P(response i) = P(Tᵢ < Tⱼ for all j ≠ i)
Miller Inequality and the Race Model Inequality
The race model makes a strong prediction about redundant signals: if two signals are processed in parallel and independently, the distribution of the faster of two processes is constrained by the Miller inequality: P(RT ≤ t | both signals) ≤ P(RT ≤ t | signal 1) + P(RT ≤ t | signal 2). Violations of this inequality indicate that the signals are not processed independently — they interact or "coactivate" — providing evidence against a pure race architecture in favor of coactivation models.
The capacity coefficient C(t) = log[S_AB(t)] / [log S_A(t) + log S_B(t)] provides a continuous measure of processing capacity: C(t) = 1 indicates unlimited capacity, C(t) < 1 indicates limited capacity, and C(t) > 1 indicates super-capacity processing.