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The Persuasive Arguments Theory (PAT) offers one way to explain how people change their opinions and behaviors [1, 2]. Unlike imitation or comparison theories, PAT suggests that when two people interact, they don't just compare their opinions; they exchange ideas or thoughts on the subject, called arguments. It assumes that there is a limited set of arguments shaped by culture, and when someone shares an opinion, they draw from a subset of those arguments. The balance of arguments for or against an issue determines the direction and strength of their opinion.

We propose an agent-based model based on PAT, where arguments are the key element in opinion formation, but we simplify the model to its basic components to develop the master equation. In this model, each agent holds positive and negative arguments of equal weight, and in each interaction, they can either lose or gain an argument, depending on the arguments the other agent has. This simplified version helps us find similarities with continuous opinion models, allowing us to use similar methods to develop the master equations that describe the dynamics.

Despite its simplicity, the model reveals an interesting dynamic: under certain conditions, it leads to a final bi-polarized state without needing to introduce any rejection mechanism [3]. From these equations, we can thoroughly explore how the parameters affect the outcome and analytically calculate the transition between consensus and polarization.

[1] Meyers, R. A. Persuasive Arguments Theory A Test of Assumptions. Human

Communication Research 15, 357-381 (1989).

[2] Burnstein, E. y Vinokur, A. Persuasive argumentation and social comparison

as determinants of attitude polarization. Journal of experimental

social psychology 13, 315-332 (1977).

[3] Mäs, M., & Flache, A. (2013). Differentiation without distancing. Explaining bi-polarization of opinions without negative influence. PloS one, 8(11), e74516.