Condorcet proportions and Kelly's conjectures

Let C(m,n) be the proportion of all n-tuples of linear orders on a set of m alternatives such that some alternative x is ranked ahead of y in at least n of the orders, for each y≠x. Kelly proved that C(m,n)<C(m,r+1) for m3 and odd n 3, and that C(m,n)>C(m,n+1) for m3 and even n2. He also conjectured that C(m,n)>C(m+1,n) for m3 and n=3 or n5, and that C(m,n)>C(m,n+2) for m3 and n=1 or n3. The first of these conjectures is shown to be true for n=3. and for m=3 and odd n. The second conjecture is established for mε{3,4} and odd n, and for m=3 and all large even n.