Unknown examples that are unseen during training often appear in real-world pattern recognition tasks, and an intelligent self-learning system should be able to distinguish between known examples and unknown examples. Accordingly, open-set recognition (OSR), which addresses the problem of classifying knowns and identifying unknowns, has recently been highlighted. However, conventional deep neural networks (DNNs) using a softmax layer are vulnerable to overgeneralization, producing high confidence scores for unknowns. In this article, we propose a simple OSR method that is based on the intuition that the OSR performance can be maximized by setting strict and sophisticated decision boundaries that reject unknowns while maintaining satisfactory classification performance for knowns. For this purpose, a novel network structure, in which multiple one-vs-rest networks (OVRNs) follow a convolutional neural network (CNN) feature extractor, is proposed. Here, an OVRN is a simple feedforward neural network that is designed to assign confidence scores that are lower than those in the softmax layer to unknown samples so that unknown samples can be more effectively separated from known classes. Furthermore, the collective decision score is modeled by combining the multiple decisions reached by the OVRNs to alleviate overgeneralization. Extensive experiments were conducted on various datasets, and the experimental results show that the proposed method performs significantly better than the state-of-the-art methods by effectively reducing overgeneralization. The code is available at https://github.com/JaeyeonJang/Openset-collective-decision.