The dynamics of opinion formation in a society is a complex phenomenon where many variables play an important role. Recently, the influence of algorithms to filter which content is fed to social networks users has come under scrutiny. Supposedly, the algorithms promote marketing strategies, but can also facilitate the formation of filters bubbles in which a user is most likely exposed to opinions that conform to their own. In the two-state majority-vote model an individual adopts an opinion contrary to the majority of its neighbors with probability $q$, defined as the noise parameter. Here, we introduce a visibility parameter $V$ in the dynamics of the majority-vote model, which equals the probability of an individual ignoring the opinion of each one of its neighbors. For $V=0.5$ each individual will, on average, ignore the opinion of half of its neighboring nodes. We employ Monte Carlo simulations to calculate the critical noise parameter as a function of the visibility $q_c(V)$ and obtain the phase diagram of the model. We find that the critical noise is an increasing function of the visibility parameter, such that a lower value of $V$ favors dissensus. Via finite-size scaling analysis we obtain the critical exponents of the model, which are visibility-independent, and show that the model belongs to the Ising universality class. We compare our results to the case of a network submitted to a static site dilution, and find that the limited visibility model is a more subtle way of inducing opinion polarization in a social network.
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