[[Rational Shortlist method (RSM)|RSMs]] and [[Rational Choice theory]] both assume that the DM considers all feasible alternatives from the set $X$ when they make their choice. However, many real world DMs have limited attention and may not consider all feasible alternatives.
In order to account for this, there is a consideration set $\subseteq X$, which has all the alternatives that the DM considers.
Consider the choice function,
$c(xy)=x; c(yz)=y; c(xz)=x; c(xyz)=y$
| Menu |
consideration set |
preference $x\succ y\succ z$
|
| xy |
xy |
x |
| yz |
yz |
y |
| xz |
xz |
x |
| xyz |
yz |
y |
$x$ is not in the consideration set in the 3 alternative menu.
Let $S\in X$. The DM does not pay attention to all alternatives in $S$. $\Gamma(S)$ is the (nonempty) set of the alternatives to which the DM pays attention. $\Gamma:\chi\to\chi$ is a consideration set mapping if for all $$S\in \chi,\ \emptyset\ne\Gamma(S)\subseteq S$$However, if there are no restrictions on $\Gamma$, all choices can be explained by a change in consideration set, rendering the model having no predictive power.