the difference between the rational man paradigm’s *reference independence* requirement and monotonicity.

Rational Argumentation-based Choice
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To build the foundation for exploring the intersection of abstract argumentation semantics and (bounded) rationality, we introduce the notion of an argumentation-based choice function.

\[arg-function\] \[preference-function\] The argumentation-based choice function $g \circ \sigma$ of an agent is the function composition between a function $g$ and an argumentation semantics $\sigma$ that takes an argumentation framework as its input and returns a set of decision outcomes $AR^{*} \subseteq AR$: $$\begin{aligned}
        g \circ \sigma: {\cal AF} \rightarrow 2^{AR}
    \end{aligned}$$

To determine the function’s input, an economically rational agent needs to construct an argumentation framework $AF$ that consists of the propositional atoms–called *arguments*–$AR$ and a set of binary attack relations between those arguments $Attacks \subset AR \times AR$. The framework is resolved by an argumentation semantics $\sigma$; different argumentation semantics can be used. In the context of rational economic choice, the mapping from a semantics’ output (a set of sets) to the choice function’s output requires that the semantics returns always exactly one extension. If this is the case, the choice function can be defined in different ways, for instance:

1.  $g^{\cup} \circ \sigma(AF) = \bigcup_{E \in \sigma(AF)} 