A note on ranking functions
The set L(n,r) of all possible results where n-competitors are matched in a series of r races is studied. The presented results are extensions of those obtained in \textit{W. J. Walker}'s paper ``Ranking functions and axioms for linear orders'' [reviewed above (see Zbl 0646.06003)]. Walker shows that L(n,r) is the intersection of the set of all consistent linear extensions. The concept of consistent dimension of L(n,r) is introduced as the least t for which the above result holds. Walker shows that the consistent dimension of L(n,r) equals the dimension of L(n,r) when \(r\leq 2\) and when \((n,r)=(4,3)\). The main result is that the consistent dimension of L(n,r) is much larger than its dimension.
scientific article; zbMATH DE number 4053692