Proportion & Voting Systems Lo 12.1.1

8/4/2019 Proportion & Voting Systems Lo 12.1.1

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Voting Systems

& Proportion

A S 12.1.1


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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.


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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


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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


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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.

*


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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


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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.


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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


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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


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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%


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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%


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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


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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


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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

Proportion & Voting Systems Lo 12.1.1

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