We propose an axiomatization of aversion to incomplete preferences. Some prevailing models of incomplete preferences rely on the hypothesis that incompleteness is temporary and that by keeping their opportunity set open individuals reveal a preference for flexibility. We consider that the maintenance of incomplete preference is also aversive.Our model allows us to show how incompleteness induces an aversive attitude in two different ways: intrinsic and instrumental. Intrinsic aversion holds when one instance of incomplete preference in the set suffices to decrease its utility. Instrumental aversion holds only insofar dominating options are affected by incompleteness. Given two partially overlapping sets of axioms on the binary relation over sets we formalize their consistency with the two types of aversion to incompleteness. Finally, we relate our model to the classical Sen's distinction between tentative and assertive incompleteness.The spelling out of this distinction in the terms of our approach uncovers to what extent aversion to incompleteness may be compatible with preference for flexibility.
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.
In the present work robot trajectories are generated and kinematically simulated. Different data (joint coordinates, end effector position and orientation, images, etc.) are obtained in order to train a neural network suited for applications in robotics. The neural network has the goal of automatically generating trajectories based on a set of images and coordinates. For this purpose, trajectories are designed in two separate sections which are conveniently connected using Bezier curves, ensuring continuity up to accelerations. In addition, among the possible trajectories that can be carried out due to the different configurations of the robot, the most suitable ones have been selected avoiding collisions and singularities. The designed algorithm can be used in multiple applications by adapting its different parameters.
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