How do we decide?
• Sometimes a group of people have to make a decision and people have different opinions about what the outcome should be
• In these situations there are different ways to reach an agreement
• Some systems are simple, some are more sophisticated
• All might be considered ‘fair’, but they have different advantages and disadvantages

New school logo
• Appleston school is going to change its logo
• There are 6 different designs under consideration
• A panel of 12 people which includes pupils, parents and teachers are going to decide which logo to use
• How could they decide?

A Appleston
School
B
Appleston
School
D
E
C
F

How do we decide?
• Sometimes the way we decide might be different if there is one outright ‘winner’ or if we are narrowing the choices down
• In the case of the school logo, if the panel had to choose the final one, they might use a different approach to how they would decide if they were narrowing it down to the ‘top 3’ to recommend to a larger group

‘First past the post’
• This is very commonly used
• Everyone has one vote
• Whichever item or person gets the most amount of votes wins
• Vote on the logos

A Appleston
School
B
Appleston
School
Possible logos
D
E
C
F

‘First past the post’ vote
• The 12 people voted as follows:
A
4
B
2
C
1
D
1
E
3
F
1
• The decision about the winner might seem simple, but consider this:
– How many people wanted A?
– How many people didn’t want A?
• Declaring A ‘the winner’ means choosing a design that most people didn’t vote for…

‘First past the post’ vote
• A ‘majority winner’ is one which receives more than 50% of the votes
• If people can’t have their first choice, how might they still have a say in which one is chosen?

Alternatives to ‘first past the post’
• If there is no majority winner, the top two can go through to a second round of voting
• If there was no majority winner in your vote, go to a second round of voting

A Appleston
School
B
Appleston
School
Possible logos
D
E
C
F

Alternatives to ‘first past the post’
• Instead of having just one vote, everyone is allowed several votes
• In some systems everyone votes for as many of the options as they want to, all counting equally
• What are the advantages of this?
• Try it out

A Appleston
School
B
Appleston
School
Possible logos
D
E
C
F

Alternatives to ‘first past the post’
• Instead of having just one vote, everyone is allowed several votes
• In some systems everyone votes for a fixed number of options, sometimes allocating certain marks to first, second, third choices etc

Alternatives to ‘first past the post’
• Try allowing each person to allocate points as follows:
– First choice: 3 points
– Second choice: 2 points
– Third choice: 1 point
• What are the benefits of this system?

A Appleston
School
B
Appleston
School
Possible logos
D
E
C
F

Alternatives to ‘first past the post’
A ‘constant sum’ system allows each voter to allocate a set total of points as they choose
• For example, allow each person to have 10 points to allocate between the 6 logos.
– One person might choose to give 5 points to one and 5 to another
– Someone else might allocate 4, 3, 2, 1
– Someone else might allocate 7, 2, 1
• It’s completely up to the voter

Alternatives to ‘first past the post’
Try it out.
What are the benefits and drawbacks of the
‘constant sum’ system?

A Appleston
School
B
Appleston
School
Possible logos
D
E
C
F

• Having tried out several systems, which do you think is the fairest and why?

Teacher notes: How do we decide?
In this activity students will look at different voting systems, considering what makes for a fair voting system. The activity involves plenty of discussion and student participation.
There are lots of real life situations that students will be aware of in which different voting systems are used such as: elections, Eurovision song contest and many reality television programmes.
Students being involved in the voting will help them to gain insight into how each system works.
With the simple voting systems it would be straightforward to allow the whole class to vote. For the more complex systems, 12 students – representing the
12 on the school logo panel – might be more manageable, but still engaging.
Use of mini-whiteboards to allow all students to see what each person has chosen might be helpful, but will obviously not allow for anonymity.

• Have a go at using this voting system
• Discuss
• Lots of bits of scrap paper, or ballot papers with A B C D E F on them, or mini- whiteboards are useful for this activity
• Each time a vote is suggested, the next slide has the 6 logos on it.
• To personalise the activity, it would be possible to use the students’ own school logo with some re-colouring or revamping as alternative options

Teacher notes: How do we decide?
Slide 12: Voting for as many items as they want. This is known as ‘approval voting’
Advantages: everyone gets to say ‘yes’ and ‘no’ to all options. Uses the same style ballot papers as a ‘normal’ single vote system. Individuals can express strong approval for one candidate by only voting for that one, or strong disapproval by voting for everything else.
Disadvantages: individual voters can’t rank their options. Counting the votes by hand is more time-consuming.

Teacher notes: How do we decide?
Slide 15: Voting for the ‘top 3’ items. This is used in the Eurovision Song
Contest.
Advantages: Each voter can express a preference.
Disadvantages: More complex to administer. Voters are restricted to a limited number of votes which means they cannot express strong disapproval.
Slide 18: Constant sum voting
Advantages: Each voter can express the strength of their preferences, although to enable this there have to be more points available than items to vote for.
Disadvantages: More complex to administer… voters have to be able to add up accurately! Only to 10 in this case, but allocating 100% amongst items is a common use of this system.