(a) Full ranking German survey data (blue) and its linear phase approximation (dashed red)

(b) Full ranking APA data (blue) and its linear phase approximation (dashed red)

Figure 4: Two examples illustrating linear-phase approximation for full ranking data. Lexicographic ordering is used for permutations on the horizontal axes of both graphs. Note that the data in (a) has domain , while (b) has domain .