We examined principles of graded argumentation semantics (independence, anonymity, void precedence, and maximality) to explore if (a) they realistically model human reasoning, (b) graphical representation of arguments facilitates compliance with the principles, (c) there is a positive correlation between compliance with different principles, and (d) this compliance is related to cognitive reflection, need for cognition and faith in intuition. The participants (N = 96) were randomly assigned to one of two experimental conditions - the graph group was presented with textual and graphical representations, while the second group was presented only with textual arguments. Our results indicate that there are major differences in the compliance with the several argumentation principles studied in this paper. However, compliance with argumentation principles was consistently better and more consistent in the graph group. Moreover, cognitive reflection correlated with compliance to some principles, but only in the graph group.