Preferential Voting
A Bird’s Guide
Preferential voting, also known as ranked-choice voting, describes elections where we rank candidates from most to least preferred.
The Bird Republic—a fictional island off the coast of north-east Australia—has recently adopted preferential voting for its all-important Top Bird contest.
Your Mission
Should you choose to accept it
You have just become a citizen of the Bird Republic and are eligible to vote in this election.
Select your bird persona from the Bird Deck to proceed.
Bird Deck
Chosen Persona
You are the ...
The Candidates
candidates will compete for the coveted role of Top Bird.
How to Vote
A total of birds are eligible to vote in the Republic. Each bird is given a ballot paper on which they must rank the candidates in order of preference.
The ballot paper for Top Bird, shown below, lists each candidate next to an empty box.
Each voter must put a number in every box—from 1 (most preferred) to (least preferred) with no repeats—for their vote to be counted.
Their ballot will look like this:
In the Top Bird contest, the following two ballots would be invalid. Can you guess why?
Why are the above two ballots invalid?
The first of these ballots ranks .
The second ballot ranks .
Neither of these ballots rank the candidates from 1 to , filling in every box with no repeats.
Casting Your Vote
it's time to cast your vote! Fill out your Top Bird ballot, shown below, according to the instructions to proceed.
Counting the Votes
All voters have now cast their vote. Counting the votes to find out the winner involves a number of steps.
In the first step each candidate is given all the ballots on which they have been ranked first. Each of these ballots is worth 1 vote and the number of ballots a candidate has represents their initial tally. This initial tally is often called their first-preference tally.
Step One
Give each candidate all the ballots on which they have been ranked first. The number of these ballots represents their initial tally.
The initial tallies of each Top Bird candidate are shown below.
Ballots containing the same ranking over candidates have been stacked into a pile.
The number of ballots in each stack is displayed on its bottom-right corner. The total number of votes in each candidates' tally is shown underneath their name on the left hand side.
A candidate must have a majority of votes (at least ) to win.
We then repeat the following step until one candidate has more than 50 percent of the total number of validly cast votes, or there are only two candidates left. In both cases, the candidate with the highest tally is declared the winner.
Step Two (Repeated)
Remove the candidate with the smallest number of votes from the contest.
Take all ballots sitting in their tally pile(s) and give each ballot to the next-highest-ranked candidate on the ballot who is still in the contest.
Summary
Let's now summarise the steps of the counting process that led to the election of the as Top Bird.
Step One
Give each candidate all the ballots on which they have been ranked first. The number of these ballots represents their initial tally.
Step Two (Repeated)
Remove the candidate with the smallest number of votes from the contest.
Take all ballots sitting in their tally pile(s) and give each ballot to the next-highest-ranked candidate on the ballot who is still in the contest.
One might wonder why we have two stopping conditions. Why is it that can we stop the count once a candidate accumulates more than 50 percent of the validly cast votes?
Find out the answer!
The answer is that at this point, there is no way that another candidate could possibly win.
If the has more than 50 percent of the vote, it means that the total number of votes sitting in the tally piles of other candidates is less than 50 percent. Even if another candidate was to gather all of these votes, they would still have less than 50 percent, and fewer votes than the .