  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.
