     Home / Voting / How To Vote  # Mathematics and Voting:

## How to Vote

Suppose that a voter must decide between candidates A, B, and C.  Assuming that there is enough information for the voter to distinguish between the candidates so that there are no ties, then there are six ways to rank the three candidates:

1st     A A C C B B
2nd    B C A B C A
3rd    C B B A A C

A voter can rank n candidates in n! = n(n-1)(n-2) … (2)(1) ways. This follows because there are n choices for the top-ranked candidate.  Once this candidate has been chosen, then there are n-1 choices for the 2nd-ranked candidate.  Continuing with this logic, there are k choices for the candidate ranked in position n-k+1.  Finally, there is one way to rank the last-place candidate, as all of the other candidates have been ranked above it.  Because selecting the positions is independent, the number of rankings is the product:  n(n-1)(n-2) … (2)(1).   Vote Home How to Vote Procedures/Applications A Best Procedure? The Mathematics References and Links  