  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
