Consensus dynamics under biased opinion filtering

Algorithms shaping online visibility have become significant drivers of user engagement and opinion formation, often limiting individuals' access to opposing views. To capture this asymmetry, we extend the two-state majority-vote model by introducing a biased visibility parameter, V, which controls the probability of considering neighbors who hold divergent opinions. In our approach, like-minded neighbors are always visible, while opposing ones are considered with chance V. We connect individuals using scale-free networks, and they shall adopt the majority opinion of their visible neighborhood with probability 1 – q, where q represents the social noise. Through Monte Carlo simulations and finite-size scaling, we observe an exuberant phase diagram, encompassing both first- and second-order consensus–dissensus phase transitions, depending on the combination of visibility and network connectivity levels. Lower visibility intensifies polarization and triggers hysteretic bistability, while higher visibility restores continuous transitions. Our findings reveal that such biased exposure and selective perception may enhance key social media engagement indicators at the cost of crucially shaping collective decision-making and promoting abrupt opinion polarization in digital social environments.