more complex example, let us consider the choice process of a person who considers buying a beverage in a café. The café only offers tea and coffee: $AR = \{tea, coffee\}$. The person prefers the caffeine kick of coffee, but also acknowledges the health advantages of tea: $Attacks = \{(coffee, tea), (tea, coffee)\}$. Complete semantics $\sigma_c$ resolve the resulting framework $AF = (AR, Attacks)$ as $\{\{tea\}, \{coffee\}, \{\}\}$. An argumentation-based choice function $g^{i} \circ \sigma^{\cup}_c$ based on lenient complete semantics $\sigma^{\cup}_c$ *flattens* this set of sets by determining the union of the complete extensions $\{coffee, tea)\}$, implying $\forall A \in 2^{\{tea, coffee\}}: \{coffee, tea\} \succeq A$. In contrast, $g^{i} \circ \sigma^{\cap}_c$, which is based on skeptical complete semantics, returns $\{\}$, implying $\forall A \in 2^{\{tea, coffee\}}: \{\} \succeq A$.

Let us now put argumentation-based choice functions in the context of economic rationality. By considering Definition \[clear-pref\], we define the *clear preferences* property for argumentation-based choice.

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Let $AF = (AR, Attacks)$ be an argumentation framework and $g \circ \sigma$ an argumentation-based choice function. An argumentation-based choice $A^{*} = g \circ \sigma(AF)$ is economically rational iff it holds that $\forall A \in 2^{AR}, A^{*} \succeq A$.

In words, the agent’s choice 