Reformulating the Value Restriction and the Not-Strict Value Restriction in Terms of Possibility Preference Map

Fujun Hou

Papers from arXiv.org

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.

Date: 2022-05
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