# Numbers of Truncations

DEMOREP1 at aol.com DEMOREP1 at aol.com
Tue Nov 19 19:06:38 PST 1996

```Due to the large number of truncation possibilities in rank voting (1, 2,
etc.), creating "real" examples on paper is labor intensive.

3 Candidates
vote 1                    3 possibilities
vote 2      3 X 2=    6 possibilities
vote 3     3 X 2 x1 = 6 possibilities  (this is the same as the AB line since
the last choice can defeat no one)
Total                     15

4 Candidates
vote 1                         4
vote 2     4 x 3 =       12
vote 3     4 x 3 x 2 = 24
vote 4      same         24
Total                        64

5 Candidates
vote 1                             5
vote 2   5 x 4 =              20
vote 3    5 x 4 x 3 =        60
vote 4   5 x 4 x 3 x 2 =  120
vote 5   same                120
Total                            325

Any math majors in stats who can produce the general formula?

For simulation purposes (as if all the votes were sorted into the
possibilities), the candidates can be numbered (e.g. a vote that is DBECA
would be 4-2-5-3-1 in five columns on a spreadsheet).
With the use of multiple IF functions the votes can be summed.
Example- If the value in column 3 is 5 and if the value in column 4 is 3,
then candidate 5 gets a vote in the 5 v. 3 comparison.
Many spreadsheet programs can directly convert letters to numerical values.

```