The Leaky Competing Accumulator (LCA) model, introduced by Usher and McClelland in 2001, extends accumulator models to multi-alternative choice by incorporating two biologically plausible mechanisms: passive decay (leak) of accumulated evidence and lateral inhibition between competing accumulators. These mechanisms produce emergent properties that match observed patterns in human and animal decision making.
The LCA Dynamics
ρᵢ = input (evidence) for alternative i
κ = leak (passive decay) rate
β = lateral inhibition strength
[x]⁺ = max(x, 0) (nonlinear threshold)
ξ = Gaussian noise
Properties
The balance between leak and inhibition determines the model's behavior. When inhibition dominates leak (β > κ), the model approximates winner-take-all dynamics and produces DDM-like behavior for two alternatives. When leak dominates, evidence is weighted toward more recent inputs (recency), enabling the model to track changing environments. The nonlinearity (rectification of negative values) is crucial for preventing negative activation and producing the observed relationship between mean RT and accuracy.
The LCA naturally accounts for context effects in multi-alternative choice — similarity, attraction, and compromise effects — that violate simple accumulator models and Luce's Choice Axiom. Its neural plausibility and ability to capture both speed-accuracy tradeoffs and context effects have made it one of the most widely used computational models of decision making.