Suppose that when the probability of e changes from ${p}_{j}^{\text{'}}\left(e\right)\text{to}\text{\hspace{0.17em}}{p}_{j+1}^{\text{'}}\left(e\right),$ the positions of result tuple x and y are inverted (in ${R}_{j}^{\text{'}},$ x is ranked before y; in ${R}_{j+1}^{\text{'}}$ x is ranked after y). If we use x0 and xj to denote the position of x in R0 and ${R}_{j}^{\text{'}},$ respectively, and y0 and yj the position of y in R0 and ${R}_{j}^{\text{'}},$ respectively, then

Hence, all the distances ${\text{Distance}}^{}$

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