Reformulating the Value Restriction and the Not-Strict Value Restriction in Terms of Possibility Preference Map
arXiv:2205.07400
Abstract
In social choice theory, Sen's value restriction and Pattanaik's not-strict value restriction are both attractive conditions for testing social preference transitivity and/or non-empty social choice set existence. This article introduces a novel mathematical representation tool, called possibility preference map (PPM), for weak orderings, and then reformulates the value restriction and the not-strict value restriction in terms of PPM. The reformulations all appear elegant since they take the form of minmax.
The reformulations of VR and NSVR appear elegant since they all take the form of minmax