$A^{*}$ from $2^{AR}$ means that the agent prefers $A^{*}$ over any of the other sets in $2^{AR}$.

The *clear preferences* principle is obvious when evaluating a one-off argumentation-based choice. However, when considering an argumentation process or *dialog*, during which arguments and attacks are added to an argumentation framework over time, it is clear that we need to consider the reference independence property as introduced in Definition \[ref-in\]. We proof that, analogous to the economic principles, reference dependence is implied by the *clear preferences* property in the context of argumentation-based choice.

\[ref-dep-prop\]\
Let $AF = (AR, Attacks)$ and $AF' = (AR', Attacks')$ be two argumentation frameworks for which it holds that $AR \subseteq AR'$ and let $g \circ \sigma$ be an argumentation-based choice function. An economically rational argumentation-based choice $A^{*} = g \circ \sigma(AF)$ implies that if $g \circ \sigma(AF') \subseteq AR$, then $g \circ \sigma(AF') = g \circ \sigma(AF)$.

By contradiction, we prove that $g \circ \sigma(AF) = g \circ \sigma(AF')$ given that:

-   $AF = (AR, Attacks)$,

-   $AF' = (AR', Attacks')$,

-   $AF \subseteq AF'$,

-   $g \circ \sigma(AF') \subseteq AR$.

Let us suppose that $g \circ \sigma(AF) \neq g \circ \sigma(AF')$. $\implies g \circ \sigma(AF) \not \subseteq 