  An electorate with fully-ranked innate preferences casts approval votes over
a finite set of alternatives. As a result, only partial information about the
true preferences is revealed to the voting authorities. In an effort to
understand the nature of the true preferences given only partial information,
one might ask whether the unknown innate preferences could possibly be
single-crossing. The existence of a polynomial time algorithm to determine this
has been asked as an outstanding problem in the works of Elkind and Lackner. We
hereby give a polynomial time algorithm determining a single-crossing
collection of fully-ranked preferences that could have induced the elicited
approval ballots, or reporting the nonexistence thereof. Moreover, we consider
the problem of identifying negative instances with a set of forbidden
sub-ballots, showing that any such characterization requires infinitely many
forbidden configurations.
