  In economics and social choice single-peakedness is one of the most important
and commonly studied models for preferences. It is well known that
single-peaked consistency for total orders is in P. However in practice a
preference profile is not always comprised of total orders. Often voters have
indifference between some of the candidates. In a weak preference order
indifference must be transitive. We show that single-peaked consistency for
weak orders is in P for three different variants of single-peakedness for weak
orders. Specifically, we consider Black's original definition of
single-peakedness for weak orders, Black's definition of single-plateaued
preferences, and the existential model recently introduced by Lackner. We
accomplish our results by transforming each of these single-peaked consistency
problems to the problem of determining if a 0-1 matrix has the consecutive ones
property.
