and the rational man’s choices $A^{*}_1 \subseteq A_1$ (based on the choice options $A_1$) and $A^{*}_2 \subseteq A_2$, if $A^{*}_2 \subseteq A_1$, then $A^{*}_2 = A^{*}_1$[^4].

Colloquially expressed, the rational man’s choice outcome is not affected if options that the agent does not prefer over the existing options are added to the set of potential choices.

If a decision-maker, given the set $\{tee, cookie\}$ chooses $\{tee\}$ and given the set $\{tee, cookie, coffee\}$ chooses $\{tee, cookie\}$ the choice is not rational; the presence of the *irrelevant alternatives* $\{coffee\}$, $\{tee, coffee\}$, $\{cookie, coffee\}$, and $\{tee, cookie, \\ coffee\}$ causes the preference relation $\{tee\} \succeq \{tee, cookie\}$ to change to $\{tee, cookie\} \succeq \{tee\}$.

The *reference independence* property implies that the expansion of a choice set $A_1$ to $A_2 \supset A_1$ does not add new knowledge about the elements in $A_1$ that affects the decision-maker’s preferences over elements in $2^{A_1}$. Yet, in reality, human decision-makers can use the addition of options to a choice set as a way to infer new information about the quality of the original choice options, as for example shown by Doyle *et al.* [@doyle1999robustness]. Still, in the context of computational argumentation-based choice, it can be useful to 