With regards to the Op, even if we accept the dubious premises, it does not deductively follow that “Argumentation is pointless”. Furthermore the Op clearly states in the premises that the point of argumentation is to display dominance. The argument refuted itself before it even took off the ground.
Arguments arise when two rational players assert contradictory views. The reason why logic is so cut and dry and black and white (in some cases) is to weed out ambiguity. It is either raining outside (R) or it is not raining outside (¬R). If it is the case that it is raining then the negation of R is false. It simply cannot be the case that it is raining and simultaneously not raining. There is no room for relativism or ambiguity of any kind. Like it or not, some things are demonstratively true and others are false. The point of argumentation is not just to be right but to demonstratively show how and why, R for example, is the true. Argumentation is not pointless; it is the vehicle of intellectual progress. If your feelings get hurt in the process then you are not doing it right.
Omnis Dei mentioned that arguments can be competitive or cooperative. Ponder this example. Two physicists are arguing over which mathematical model best fits the observational data. There is more than just rational self-interest at play here. The discourse concerning which model best fits reality is not primarily motivated out of self-interest but to collectively come to a better understanding of reality. In this case argument doesn’t always imply a winner and loser. If both physicist set out to further our understanding of reality then by finding the right model (regardless of whose it was), they both win.
Since OD brought up Game Theory this type of game would be called a Non-Zero Sum game because one player is not benefitting from the others loss, they both “win” because finding the best fitting model was their collective intentions in the first place.
I find the notion described in the Op to be naively pernicious. It states that the only mechanism which advances ideas is the sheer amount of people who hold the said idea to be valid. But science is not a democracy (sorry for that cliché). The heliocentric model is valid neither by virtue of collective opinion nor deductive reasoning; it is valid because it corresponds to empirical observations.
And Omnis Dei, if I cant make condescending attempts at dry humor (like "Please try harder") then what am I even doing here?
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