Figure 2: Partial ranking data from the APA election shown plotted in lexicographic order on , with comparisons to the zero-phase (magnitude only) approximations in the left column, and the linear-phase approximations in the right. The linear-phase approximations are in each case adjusted so that the location of their peak value matches that of the original data. The six subplots indicate as follows: (a) first preference only (blue) compared to zero phase (red dashed line); (b) first preference only with linear-phase approximation; (c) and (d) the same for the top two preferences; (e) and (f) the same for the top three preferences. Note that the two-preference data in (d) is well fit by the linear-phase approximation.