  This article provides a link diagram to visualize relations between two
ordered sets representing precedences on decision-making options or solutions
to strategic form games. The diagram consists of floating loops whose any two
loops cross just twice each other. As problems formulated by relations between
two ordered sets, I give two examples: visualizing rankings from pairwise
comparisons on the diagram and finding Pareto optimal solutions to a game of
prisoners' dilemma. At visualizing rankings, we can see whether a ranking
satisfies Condorcet's principle or not by checking whether the top loop is
splittable or not. And at finding solutions to the game, when a solution of the
game of prisoners' dilemma is Pareto optimal, the loop corresponding to the
solution has no splittable loop above it. Throughout the article, I point out
that checking the splittability of loops is an essence. I also mention that the
diagram can visualize natural transformations between two functors on free
construction categories.
