We consider linear orders of finite alternatives that are constructed by
aggregating the preferences of individuals. We focus on a linear order that is
consistent with the collective preference relation, which is constructed by one
of the supermajority rules and modified using two procedures if there exist
some cycles. One modification procedure uses the transitive closure, and the
other uses the Suzumura consistent closure. We derive two sets of linear orders
that are consistent with the (modified) collective preference relations formed
by any of the supermajority rules. These sets of linear orders are closely
related to those obtained through Tideman's ranked pairs method and the Schulze
method. Finally, we consider two social choice correspondences whose output is
one of the sets introduced above, and show that the correspondences satisfy the
four properties: the extended Condorcet principle, the Pareto principle, the
independence of clones, and the reversal symmetry