This thesis consists of four essays whose thread is the incompleteness of preferences and how it determines attitudes toward choice. Classical economics assumes that preferences are complete, that is: for any two alternatives x and y, any individual is able to state if she prefers having x, y or any of them. However, there are situations where two alternatives are difficult to compare. Thus, this thesis departs from the assumption that presumes the human ability to compare any two alternatives. As a direct consequence of this inability, the ingrained thinking (at least in western societies), which is also a basic principle of standard rational choice, that 'the more choice we have, the better we are' may become questionable. In particular, when a DM knows for certain that she will not be able to compare two alternatives present on a choice set, it is plausible that she may want to get rid of one of them in order to avoid facing such an impossible comparison. If this is the case, we will say that the DM is averse to incomplete preferences. However, if the DM expects the incompleteness to be solved, it makes sense tomaintain all options available in order to choose the best option in the future. This iscalled “preference for flexibility” and is rooted in the work by Kreps (1979). Twistingthe above examples, if each of Sophie’s children had eaten one of the mushrooms omelets in the first example, Sophie would have wanted to wait until observing whichchild started to feel sick in order to choose the one that would be gassed. Thus, incomplete preferences can lead to opposite attitudes toward choice, depending onthe time of resolution (if any) of the incompleteness.