Binary decision-making process is ubiquitous in social life and is of vital significance in many real-world issues, ranging from public health to political campaigns. While continuous opinion evolution independent of discrete choice behavior has been extensively studied, few works unveil how the group binary decision-making result is determined by the coupled dynamics of these two processes. To this end, we propose an agent-based model to study the collective behaviors of individual binary decision-making process through competitive opinion dynamics on social networks. Three key factors are considered: bounded confidence that describes the cognitive scope of the population, stubbornness level that characterizes the opinion updating speed, and the opinion strength that represents the asymmetry power or attractiveness of the two choices. We find that bounded confidence plays an important role in determining competing evolution results. As bounded confidence grows, population opinions experience polarization to consensus, leading to the emergence of phase transition from co-existence to winner-takes-all state under binary decisions. Of particular interest, we show how the combined effects of bounded confidence and asymmetry opinion strength may reverse the initial supportive advantage in competitive dynamics. Notably, our model qualitatively reproduces the important dynamical pattern during a brutal competition, namely, cascading collapse, as observed by real data. Finally and intriguingly, we find that individual cognitive heterogeneity can bring about randomness and unpredictability in binary decision-making process, leading to the emergence of indeterministic oscillation. Our results reveal how the diverse behavioral patterns of binary decision-making can be interpreted by the complicated interactions of the proposed elements, which provides important insights toward competitive dynamics
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