A Note on the Single-Peaked Consistency of Weak Orders

Recent work by Lackner (2014) presents a model for the single-peaked consistency of incomplete preference orders. The work shows that the single-peaked consistency of weak orders is in P if they contain an implicitly specified total order. It explicitly leaves open the complexity of the general case of the single-peaked consistency of weak orders. We show in this paper that the general case is in P by a transformation to the problem of determining if a 0-1 matrix has the property of consecutive-ones in rows.