  Social networks have provided a platform for the effective exchange of ideas
or opinions but also served as a hotbed of polarization. While much research
attempts to explore different causes of opinion polarization, the effect of
perception bias caused by the network structure itself is largely understudied.
To this end, we propose a threshold model that simulates the evolution of
opinions by taking into account the perception bias, which is the gap between
global information and locally available information from the neighborhood
within networks. Our findings suggest that polarization occurs when the
collective stubbornness of the population exceeds a critical value which is
largely affected by the perception bias. In addition, as the level of
stubbornness grows, the occurrence of first-order and second-order phase
transitions between consensus and polarization becomes more prevalent, and the
types of these phase transitions rely on the initial proportion of active
opinions. Notably, for regular network structures, a step-wise pattern emerges
that corresponds to various levels of polarization and is strongly associated
with the formation of echo chambers. Our research presents a valuable framework
for investigating the connection between perception bias and opinion
polarization and provides valuable insights for mitigating polarization in the
context of biased information.
