In less than a week, Australians will vote for their choice of prime minister in a federal election. I have always been interested in fairness but where voting is concerned, it can be very difficult to devise a fair voting system. Australia uses a preferential ballot system where voters rank candidates in order of preference. I’m not exactly sure of the finer details of the Australian system, but I want to illustrate problems that can arise with voting systems where candidates are ranked in order of preference.
Consider the following system (this is not the same as Australia’s preferential ballot system). Let’s say there are three candidates, Bob, Ann and Mary. For simplicity, this example will have just five voters. Voters must rank Bob, Ann and Mary in order of their preference. Here’s how our voters (A,B,C,D and E) voted:
| Bob | Ann | Mary | |
| A | 1 | 2 | 3 |
| B | 1 | 2 | 3 |
| C | 1 | 2 | 3 |
| D | 3 | 2 | 1 |
| E | 3 | 2 | 1 |
If we assign points to each preference, so a candidate placed first gets 2 points, a candidate placed second gets 1 point and a candidate placed third gets 0 points, we find that Bob wins the election with the tally as follows:
Bob – 6
Ann – 5
Mary – 4
This all looks fairly reasonable as Bob got the most votes for first place so it stands to reason that he should come first. The only odd thing is that Ann, who was not placed first by any of the voters comes in second, while Mary, who was placed first by 2/5 voters, comes last.
But what happens if we had a fourth candidate, Jo, and we don’t change the order in which people voted for Bob, Ann and Mary but instead slot Jo in so that the order of the other three remains the same?
| Bob | Ann | Mary | Jo | |
| A | 1 | 2 | 3 | 4 |
| B | 1 | 2 | 3 | 4 |
| C | 1 | 2 | 3 | 4 |
| D | 4 | 2 | 1 | 3 |
| E | 4 | 2 | 1 | 3 |
Now the points go like this:
First place – 3 points
Second place – 2 points
Third place – 1 point
Fourth place – 0 points
The tally is as follows:
Bob – 9 points
Ann – 10 points
Mary – 9 points
Jo – 2 points
Suddenly Ann is in first place even though no-one put her as their first preference whereas Bob, who has the most first votes, now ties second with Mary.
What does this mean for people voting in the upcoming Australian Federal election? It should go without saying but my recommendation is to be thoughtful about all of your preferences and if there’s someone you really don’t like, put them last.
rachel.blog 
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