Post on 07-Apr-2018
8/4/2019 Proportion & Voting Systems Lo 12.1.1
1/14
Voting Systems
& Proportion
A S 12.1.1
8/4/2019 Proportion & Voting Systems Lo 12.1.1
2/14
But, there are many ways tomathematically count votes in anyelection.The outcome of an election
can change, depending on the votingsystem and the election methodschosen.
Is Democracy Fair?Is Democracy Fair?
Lets look at some commonly used systems.
We vote to select Presidents, Councils,Oscar Winners, World Cup venues forSoccer and even to decide where to go onholiday etc.
8/4/2019 Proportion & Voting Systems Lo 12.1.1
3/14
If there are n candidatesthen
1st
place = n -1 points,nd = -
Borda Count MethodBorda Count MethodHere you rank (with a number) each
candidate according to your preference forthe President etc. Points are then allocatedto each position.The person with thehighest no. of points wins the election and
is the President.Ms Jones voted as follows.If the 1st ranked gets 2points. How many pointsdo each get?
BALLOT
Name Rank
William 3
Henry 1
George 2Henry 2; George 1and William - 0
8/4/2019 Proportion & Voting Systems Lo 12.1.1
4/14
The Mayor of Smallville is chosenaccording to the Borda Method. 500
registered voters cast their ballots forEster, Mvuyo, Nisha and Thabo. Theresults are summarised below.
No. of voters
Place 130 120 100 150
1 E T T N
2 M M M M
3 N N E E
4 T E N TWhat % of 1st place votes
did Thabo receive?
Who received thepopular vote?(most 1st places)
Thabo
% = 220 /500 x 100
= 44%
Who had no 1st
place votes?Mvuyo
8/4/2019 Proportion & Voting Systems Lo 12.1.1
5/14
No. of voters
Place 130 120 100 150
1 E T T N
2 M M M M
3 N N E E4 T E N T
Allocate 4 points for1st place, 3 for 2nd etc.
Use the Borda methodto find out who wonthe election.
Ester = 130x4 + 120x1 + 250x2 =1140Mvuyo = 500 x 3 = 1500Nisha = 150x4 + 250x2+ 100x1 =1200
Thabo = 220x4 + 280x1 = 1160
Mvuyo wins and becomes the Mayor.
*
8/4/2019 Proportion & Voting Systems Lo 12.1.1
6/14
Proportional RepresentatioProportional Representatio
Here you vote for one political party.The Party then decides who to send toParliament. The number of seats eachParty gets is in the same proportion as
the proportion of votes they receive.TheParty with the most seats chooses thePresident.e.g. Council consists of 200 members. If a
party gets 40% of the votes, how manymembers will represent them?
Representation = 40 /100 x 200 = 80 members
8/4/2019 Proportion & Voting Systems Lo 12.1.1
7/14
Smallville use proportionalrepresentation for their voting system.Four parties contest the elections. The
table shows the no. of votes each Partyreceived. Party Votes % votes
Durban 119
Frere 140
Grey 176
Milner 65
Total 500 100%
Complete the table.
Which Party wonthe election andgets to choosethe Mayor?
13
35,228
23,8
Grey
Will this Party form a majority in theCouncil? Explain.
No only have 35,2 % of
votes.
8/4/2019 Proportion & Voting Systems Lo 12.1.1
8/14
Party Votes No.seats
Milner 65
Durban 119
Frere 140
Grey 176
Total 500 15
15 members must be elected for theSmallville Council. Calculate the no. ofseats for each party.
Milner = 65 /500 x 15= 1,95 seats
Durban = 119 /500 x 15
= 3,57 seatsFrere = 140 /500 x 15
= 4,2 seats
Grey =176
/500 x 15= 5,28 seatsWhat method do you use with the decimal
remainder to allocate the seats?
2
44
5
Highest remainder get the left over seat
8/4/2019 Proportion & Voting Systems Lo 12.1.1
9/14
Constituency RepresentatioConstituency Representatio
Here you vote for a specific candidate,who usually belongs to a Party, torepresent your voting area orconstituency in Parliament.Theelected candidates to Parliament ofthe majority Party, choose thePresident.e.g. In a particular voting Area, 220
vote for Person A and 189 vote forPerson B. Who is the constituencywinner for that area?
Person A
8/4/2019 Proportion & Voting Systems Lo 12.1.1
10/14
Smallville is divided into 5 voting areas.Three Parties choose one candidate in eachvoting area to represent them. The table
shows the no. of votes each candidatesParty received per voting area.
Votes
Snap Pop Go Winner
1 42 51 11
2 51 12 52
3 15 31 26
4 28 42 10
5 76 26 20
Tot 212 162 126
pop
pop
pop
snap
go
How many
votes werecast inSmallville?
500
Which party won
the election?
Pop
Complete the table.
What % of total votesdid this Partyreceive?162
/500 x 100 = 32,4%
8/4/2019 Proportion & Voting Systems Lo 12.1.1
11/14
SA uses Proportional Representation toelect its 400 members of the NationalAssembly.
What is the smallest % of the votes that a
party must win to get 1seat in Parliament?
S.A. ElectionsS.A. Elections
1/400 x 100 = 0,25%
If there were 433 591 registered voters inthe North West province in 2004 and 329707 voted, what % voted?329707 /433591 x 100
= 76,04%
8/4/2019 Proportion & Voting Systems Lo 12.1.1
12/14
There were approximately 47,5 millionpeople in 2004. What % of the populationvoted?
Why do you think this % is so low?
Non-voters & u18 year olds
make up a big part of theo ulation.
% = 15,863558 /47,5 x 100
33,4 %
In 2004, 15 863 558 votes were castwhich represented 76,73% of theregistered voters. How many registeredvoters were there?
No. = 15863558 /76,73 x 100 20 674 518
8/4/2019 Proportion & Voting Systems Lo 12.1.1
13/14
The total number ofvalid votes in 2004were 15 612 671. The table shows an
extract of some results from the 2004General Elections.
Party Votes %
ID 269765
IFP 1088664
KISS 6514
NNP 257824
Complete the table.
Source
:IEC
Which Party did notget a seat in theAssembly? KISS
6,97
1,73
0,04
1,65
Approximately how many of the 400 seatswere allocated to the ID?269765 /15612671 x 400
6,911 7seats
8/4/2019 Proportion & Voting Systems Lo 12.1.1
14/14
Your county is divided into 7 districts.
Ithas 2000 voters who will vote in their
own district to elect the Big Chief. There are3 candidates standing representing different
parties.
Name your county, the candidates and theirparty.
Allocate the 2000 voters into the 7 districts.Use proportional and constitutionalrepresentation.The no. of votes for each candidate must bethe
Task
Adapted: CTA draft training module