Online information cascades (tree-like structures formed by posts, comments, likes, replies, etc.) constitute the spine of the public online information environment, reflecting its various trends, evolving with it and, importantly, affecting its development. While users participate in online discussions, they display their views and thus contribute to the growth of cascades. At the same time, users’ opinions are influenced by cascades’ elements. The current paper aims to advance our knowledge regarding these social processes by developing an agent-based model in which agents participate in a discussion around a post on the Internet. Agents display their opinions by writing comments on the post and liking them (i.e., leaving positive assessments). The result of these processes is dual: on the one hand, agents develop an information cascade; on the other hand, they update their views. Our purpose is to understand how agents’ activity, openness to influence, and cognitive constraints (that condition the amount of information individuals are able to proceed with) affect opinion dynamics in a three-party society. More precisely, we are interested in what opinion will dominate in the long run and how this is moderated by the aforementioned factors, the social contagion effect (when people’ perception of a message may depend not only on the message’s opinion, but also on how other individuals perceive this object, with more positive evaluations increasing the probability of adoption), and ranking algorithms that steer the order in which agents learn new messages. Among other things, we demonstrated that replies to disagreeable opinions are extremely effective for promoting your own position. In contrast, various forms of like activity have a tiny effect on this issue.