Hmmm, smart vegies!
Wonder which one's our future PM?
You will need

A group of people (around 20 is good)

A pencil for each person

A ballot paper for each person (download them here, three per page)

Cardboard box with lid

Scissors

Sticky tape

Permanent markers

A sign for each of the candidates, and one for informal (incorrect) votes to help with the counting (download them here)
Setting up the election

Check that the cardboard box is empty.

Carefully cut a slit in the lid with scissors.

Tape the lid onto the box.

Draw patterns on the edge of the lid and the box, so you can tell if someone opens it.

Find somewhere that people can fill in their ballot in private.
Running the election

Get everyone together in a group.

Explain to everyone:

Everyone will get one vote.

To be a valid vote, they must number each candidate: put a 1 next to the candidate they think tastes the best, a 2 next to their second preference, and so on.

Once they have finished, put the completed ballot in the box.

Hand out ballot papers and pencils, and direct voters to a private place so they can fill out their ballots in secret.

Once everyone has filled in their votes, remember to vote yourself!
Counting the votes

Print out signs for each candidate and one for informal votes. Arrange the signs around the room to mark where piles of counted votes should go.

Ask for some volunteers to help count votes.

Check the pattern on the lid and the box to make sure it hasn’t been opened.

Empty the box, and give the ballots to your volunteers.

Ask the volunteers to do the following:

Take a ballot, and check if each box has been numbered.

If all the boxes are numbered, find the candidate numbered 1 and put that ballot with the candidate’s sign.

If the ballot is incorrectly filled, put it with the informal ballot sign.

When all the ballots are sorted, count each pile.

Add all of the candidate’s votes together to get a total number of formal (correct) votes. Divide the total by two, round down if needed, and then add 1. This is the number of votes needed for a majority.

If any candidate has a majority of votes, they win!

If not, exclude the candidate with the least votes. This candidate can no longer win the election. Take all their ballots. Read the second preference (the candidate labelled 2) off each, and put the ballot with the appropriate sign.

Recount the piles. If anyone has a majority of votes, they win!

If no one has won yet, exclude the candidate with the fewest votes. Take all their ballots. For each ballot taken, read their preferences out, starting from the number 2 and going down. Stop when you find a candidate who has not yet been excluded, and put the ballot with the corresponding sign.

Keep excluding candidates (step 11) until someone is the winner.
What’s happening?
There are many ways of running an election. The simplest is often called ‘first past the post’. Each person votes for a candidate, and the candidate with the most votes wins. This system is simple and easy to understand, but it’s not necessarily the fairest system.
Imagine a first past the post election on favourite foods with five candidates. Four candidates are vegetables, and one is a fruit. Each vegetable gets 15% of the votes, and the fruit gets 40% of the vote, so the fruit wins. But more people voted for a vegetable!
With a preferential system like the one in this activity, the winner must be somewhat popular to avoid being excluded. Also, more than half of all voters prefer the winner to any of the nonexcluded candidates. Although preferential voting is complicated, it gives a fairer result. Australia uses preferential voting for federal elections.
More information
This activity is from CSIRO's Double Helix Maths By Email 17 June 2016
Run a free and fair school election with this pack from the AEC
Run an Election
Australia has a federal election every few years. Run this fun election activity and find out how the Australian preferential voting system works!
Running an election is a good way to let everyone have a say. In this example, we will be voting for the tastiest vegetable, but if you design your own ballot papers, you can use this method for any election.

Voters must number each candidate on the ballot paper in order of preference.

A ballot paper incorrectly filled in is invalid or an informal vote.

A ballot paper with 1 next to broccoli is a vote for broccoli.

If there is no one with a majority of votes, preferences are counted until someone wins.