Revised May 2005
APPENDIX — THE PREFERENTIAL BALLOT
(arranged from Australian Systems of Voting, by E.D. Senior. Sydney, Current Book Distributors, 1946)
The Preferential Ballot, which was introduced in Australia in 1907 and is still widely used in that country, has the same effect as a succession of ballots, and ensures, in an election with several contestants, that the successful candidate(s) will be acceptable to a majority of the voters.
A. To determine the first (or only) successful candidate:
- The voter records a vote by placing the number “1” in the square opposite the name of the candidate for whom the voter desires to give a first preference vote, and records contingent votes for the remaining candidates by placing the numbers “2”, “3”, “4” and so on respectively opposite their names in order to indicate by numerical sequence the order of preference for them.
- When counting the ballots, the election committee places them in piles according to the voters’ first preferences. A candidate who has received a number of first preference votes greater than half the number of valid ballots is thereupon declared elected.
- If no candidate has received an absolute majority of first preference votes, the candidate who has received the fewest first preference votes* is excluded, and each ballot counted to that candidate is redistributed and counted to, and placed on the pile of, the candidate next in order of the voter’s preference, i.e. the number 2 vote. (Note that a second preference on a redistributed ballot has the same value as each remaining unexcluded first preference.)
- Then if no candidate has an absolute majority of votes, the process is repeated by excluding the candidate who now has the fewest votes,* and counting each of that candidate’s ballots to the unexcluded candidate next in order of the voters’ preference, and so on until one candidate has received an absolute majority of votes** and is elected.
B. To determine other successful candidates:
- After the first candidate has been elected, all of the ballots are rearranged in piles under the names of the respective candidates in accordance with the first preference votes indicated thereon.
- Then each ballot on which a first preference is indicated for the elected candidate is transferred to the pile of the candidate next in order of the voter’s preference, and the ballots are counted for each continuing candidate. A candidate with an absolute majority of the valid votes is declared elected.
- In the absence of such an absolute majority, the counts continue. After each count not resulting in an absolute majority, the candidate who has the fewest votes* is excluded, and each ballot counted to that candidate is transferred to the continuing candidate (i.e., the candidate neither elected nor excluded) next in order of the voter’s preference, until one candidate has obtained an absolute majority of votes** and is elected.
- The procedure in electing a third or later candidate is similar to that described in B.1-3 above.
* In the case of a tie for the fewest votes, the same process is followed as in the previous footnote, except that the candidate with the fewest number of original first preferences, or original first plus second preferences, etc., is eliminated. (This will mean that if the tie occurs at the end of the first count, a coin will necessarily be tossed.) If after all other means have been exhausted three candidates remain tied for fewest votes, three coins, each representing a candidate, are tossed until there is only one head or one tail; the candidate represented by the one head or the one tail is then excluded.
** In the case of a tie at the end of the last count, i.e., if each candidate has received exactly half the total number of valid votes, the candidate with the largest number of original first preference votes is declared elected. If the result still remains a tie, the candidate with the largest number of original first plus original second preferences is declared elected, and so on. If at the end of this process the result is still a tie, the election is decided by a toss of a coin.