This article concentrates on solving the $k$ -winners-take-all $(k$ WTA) problem with large-scale inputs in a distributed setting. We propose a multiagent system with a relatively simple structure, in which each agent is equipped with a 1-D system and interacts with others via binary consensus protocols. That is, only the signs of the relative state information between neighbors are required. By virtue of differential inclusion theory, we prove that the system converges from arbitrary initial states. In addition, we derive the convergence rate as ${\mathcal {O}}(1/t)$ . Furthermore, in comparison to the existing models, we introduce a novel comparison filter to eliminate the resolution ratio requirement on the input signal, that is, the difference between the $k$ th and $(k+1)$ th largest inputs must be larger than a positive threshold. As a result, the proposed distributed $k$ WTA model is capable of solving the $k$ WTA problem, even when more than two elements of the input signal share the same value. Finally, we validate the effectiveness of the theoretical results through two simulation examples.