  We develop a method to show the fundamental group of the double branched
covering of a link is not left-orderable by introducing the notion of the
coarse presentation. As in the usual group presentations, a coarse presentation
is given by a set of generators and relations, but inequalities are allowed as
relations. By using coarse presentation, we give a family of links whose double
branched covering has the non-left-orderable fundamental group. Our family of
links includes many known examples and new examples.
