12.2 A beauty contest has eight contestants. The three judges are each asked to rank the contestants in a preferential order of pulchritude. The results are as follows:

Contestant Judge A B C D E F G H 1 2 1 3 5 4 8 7 6 2 1 2 4 5 7 6 8 3 3 3 2 1 4 5 8 7 6

(a) Calculate Kendall’s coefficient of concordance between rankings.

(b) Calculate the coefficient of rank correlation for each of the three pairs of rankings and verify the relation between rav and W given in (12.4.7).

(c) Estimate the true preferential order of pulchritude.