How would I find the winners under Borda Count Method, Instant Runoff Method, an

Question

How would I find the winners under Borda Count Method, Instant Runoff Method, and Copeland's method for the following problems?

Number of voters 120 50 40 90 60 100 1st choice | C | B | D | A | Al D 2nd choice | D | C | A | C | D | B 3rd choice B A B BC A 4th choice | ALD|CID?BIC How many voters voted in this election? b. a. How many votes are needed for a majority? A plurality? ovEr Find the winner under the plurality method. c. d. Find the winner under the Borda Count Metho Find the winner under the Instant Runoff Voting method. f. e. Find the winner under Copeland's method. 6. The homeowners association is deciding a new set of neighborhood standards for architecture, yard maintenance, etc. Four options have been proposed. The votes are Number of voters 8 9 11 7 7 5 1st choice B ADA B C 2nd choice 3rd choice CD B B AD [A|C|C|D?CIA? 4th choice IDRAEDIB? LIT 4. a. How many voters voted in this election? b. How many votes are needed for a majority? A plurality? 0 c. Find the winner under the plurality method. d. Find the winner under the Borda Count Metho e. Find the winner under the Instant Runoff Voting method. E Find the winner under Copeland's method.

Explanation / Answer

Given data

Now for Borda count method

the calculation for winner goes like this

the 1st choice category will get=4 points

the 1st choice category will get=4 points

the 2nd choice category will get=3 points

the 3rd choice category will get=2 points

the 4th choice category will get=1 points

and these point will be multiplied with number of voter that will gives the score os that candidate the candidate with maximum score will win so lets do it

So the score of A=(4*90)+(4*60)+(3*40)+(2*50)+(2*100)+(1*120)=1140

So the score of B=(4*50)+(3*100)+(2*120)+(2*40)+(2*90)+(1*60)=1060

So the score of C=(4*120)+(3*50)+(3*90)+(2*60)+(1*40)+(1*100)=1160

So the score of D=(4*40)+(4*100)+(3*120)+(3*60)+(1*50)+(1*90)=1240

As D scores the maximum so D will be the winner according to this method

Now For Instant Runoff method

in this process we do elemination according to preferences of choice by the voter so we will eleminate the condidate who have lest preference

so as we see the table we find

First choice vote for A=90+60=150

First choice vote for B=50

First choice vote for C=120

First choice vote for D=100+40=140

cabdidate B =50 has the least 1st choice vote so lets eleminate B so after eleminating B we will get table like this

now

First choice vote for A=90+60=150

First choice vote for C=120+50=170

First choice vote for D=100+40=140

Since D has the lest first choice vote so eleminate D after eleminating D table will look like

now

First choice vote for A=90+60+40+100=290

First choice vote for C=120+50=170

So A will be the winner Accordig to this method

Now for copland method

in this method we do find winner by comparision method so for 4 candidate there wii be 6 comparision :--

1)A vs B 2)A vs C, 3) A vs D,   4)B vs C ,5)B vs D, 6) C vs D

the process is in the comparision who winn will get the 1 point in case of tie they both will get 1/2 points

case ---1So for A vs B Lest remove C and D from the table then we will get the table like this

No of votes for A=40+90+60=190

No of votes for B=120+50+100=270 since B win B will get 1 potnt

case ----2 So for A vs C Lest remove B and D from the table then we will get the table like this

No of votes for A=40+90+60+100=290

No of votes for C=120+50=170

Since A win A will get 1 point

Now

case -----3 So for A vs D Lest remove C and B from the table then we will get the table like this

No of votes for A=50+90+60=200

No of votes for D=120+40+100=260

As D wins D will get 1 point

casee ----4   So for B vs C Lest remove A and D from the table then we will get the table like this

No of votes for B=40+50+100=190

No of votes for C=120+90+60=270

As C wins C will get 1 point

case -----5   So for B vs D Lest remove A and C from the table then we will get the table like this

No of votes for B=50+90=140

No of votes for D=120+40+60+100=320

Aa D wins D will get 1 point

casee -----6 So for cvs D Lest remove A and B from the table then we will get the table like this

No of votes for C=120+90+50=260

No of votes for D =40+60+100=200

since C wins C will get 1 point

Now

total point of A=1

total point of B=1

total point of C=1+1=2

total point of D=1+1=2

As C and D gets the same points but in case ---6 between C and D D wins D will be our winner by this method

6) given datas

NOW FOR BORDA COUNT METHOD

So the score of A=(4*7)+(4*7)+(3*11)+(2*9)+(2*5)+(1*7)=124

So the score of B=(4*9)+(3*5)+(2*11)+(2*7)+(2*7)+(1*7)=108

So the score of C=(4*7)+(3*7)+(3*9)+(2*7)+(1*11)+(1*5)=106

So the score of D=(4*11)+(4*4)+(3*7)+(3*7)+(1*9)+(1*7)=118

As A scores the maximum so A will be the winner according to this method

Now For Instant Runoff method

in this process we do elemination according to preferences of choice by the voter so we will eleminate the condidate who have lest preference

so as we see the table we find

First choice vote for A=9+7=16

First choice vote for B=8+7=15

First choice vote for C=5

First choice vote for D=11

cabdidate C=5 has the least 1st choice vote so lets eleminate C so after eleminating C from the whole table

First choice vote for A=9+7=16

First choice vote for B=8+7=15

First choice vote for D=11

so As D has least choice Eleminate D from entire table

now table will look like

1st choice votes for A =9+7+5=21

1st choice votes for B=8+7+11=26

So B will be the winner

Now for copland method

in this method we do find winner by comparision method so for 4 candidate there wii be 6 comparision :--

1)A vs B 2)A vs C, 3) A vs D,   4)B vs C ,5)B vs D, 6) C vs D

we have

the process is in the comparision who winn will get the 1 point in case of tie they both will get 1/2 points

case ---1) So for A vs B Lest remove C and D from the table then

the 1 st choice vote for A=9+7+5=21

the 1 st choice vote for B=8+11+7=25

B wins so will get 1 point

case ---2) So for A vs C Lest remove B and D from the table then

the 1 st choice vote for A=9+7+7=23

the 1 st choice vote for C=8+11+5=24

C wins so will get 1 point

case ---3) So for A vs D Lest remove C and B from the table then

the 1 st choice vote for A=9+8+7+7=24

the 1 st choice vote for D=11+5=16

A wins so will get 1 point

case ---4) So for B vs CLest remove A and D from the table then

the 1 st choice vote for B=8+11+7+7=33

the 1 st choice vote for C=9+5=14

B wins so will get 1 point

case ---5) So for B vs D Lest remove A and C from the table then

the 1 st choice vote for B=8+7+7=22

the 1 st choice vote for D=9+11+5=25

D wins so will get 1 point

case ---6) So for C vs D Lest remove A and B from the entire table then

the 1 st choice vote for C=8+7+5=20

the 1 st choice vote for D=9+11+7=27

D wins so will get 1 point

total point got by the participant

A=1

B=1+1=2

C=1

D=1+1=2

so there is atie in between B and D so lets check among B and D so ampnge them D is the winnwe so winner will be D

No of voter 120 50 40 90 60 100 1 st choice C B D A A D 2nd choice D C A C D B 3rd choice B A B B C A 4th choice A D C D B C

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.