[EM] 3 Choices/6 Sums

[DEMOREP1 at aol.com]

Various postings have been made regarding combinations of 3 or more choices 
such as 

S1 AB S2
S3 AC S4
S5 BC S6

in connection with various methods.

With even 3 choices and no truncated votes there are math limits on the 
numbers.

If a choice C is added to the simple S1 A > B and S2 B > A, then there is

N1 CAB
N2 ACB
N3 ABC

N4 CBA
N5 BCA
N6 BAC

N1 + N2 + N3  (= S1)  A   B    N4 + N5 + N6 (= S2)
N2 + N3 + N6  (= S3)  A   C    N1 + N4 + N5 (= S4)
N3 + N5 + N6  (= S5)  B   C    N1 + N2 + N4 (= S6)

Put N1 to N6 on the edge of a circle to show the problem. 

Each of the 6 subparts is in 3 sums.

Add a fourth choice and there is major complexity.

In other words, all summary head to head results are in doubt unless the raw 
votes are posted.