Winner-take-all (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains. In this work, we consider a spike-based k –WTA model wherein n randomly generated input spike trains compete with each other based on their underlying firing rates and k winners are supposed to be selected. We slot the time evenly with each time slot of length 1 ms and model the n input spike trains as n independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached. We first derive an information-theoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error ≤ δ (where δ ∈ ( 0 , 1 ) ), the waiting time of any WTA circuit is at least ( ( 1 - δ ) log ( k ( n - k ) + 1 ) - 1 ) T R , where R ⊆ ( 0 , 1 ) is a finite set of rates and T R is a difficulty parameter of a WTA task with respect to set R for independent input spike trains. Additionally, T R is independent of δ , n , and k . We then design a simple WTA circuit whose waiting time is O log 1 δ + log k ( n - k ) T R , provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ , this decision time is order-optimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling in n , k , and T R .