[EM] Truncations Math
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Sat Jun 12 13:56:12 PDT 1999
For 5 choices and rank voting there are the following possible combinations --
Place
1 2 3 4 5
Vote 5 5 x 4 x 3 x 2 x 1 = 120*
Vote 4 5 x 4 x 3 x 2 = 120*
Vote 3 5 x 4 x 3 = 60
Vote 2 5 x 4 = 20
Vote 1 5 = 5
Total 205
Since Vote 5 = Vote 4 only one is included in the Total.
Rearranging the factorial math produces
5 (1 + 4 (1 +3 (1 +2))) = 205 or the general formula --
For N choices there are N x (sum of N-1 combinations) + N possible
combinations with truncated votes.
N combinations
2 2
3 9 = 3 x 2 + 3
4 40 = 4 x 9 + 4
5 205 = 5 x 40 + 5
6 1236 = 6 x 205 + 6
7 8659 = 7 x 1236 + 7
Thus, yet another reason to have computer programs even with 4 choices.
Since trucated votes can be expected when there are more choices (especially
with 5 or more choices), the trucation math becomes important.
I have suggested that truncated choices should be deemed to be in a last
place tie.
Example-
5 Choices, a voter votes for 2, the other 3 are in a last place (fifth
choice) tie.
More information about the Election-Methods
mailing list