voting theory borda count explained condorcet paradox

1. TREY
research
PublicSector
Economics
SUBMITTED By Ahmad Sheraz.
0333-6792176
ROLL NO 13038
SUBMITTED TO Miss Sadia Ali.
BS ECONOMIICS 7TH Semester
1

2. Voting Theory:
Borda Count
Method

3. • Define Borda count.
• Determine winners of elections using the Borda
count method
3

4. BORDA COUNT METHOD.
4
Borda count is voting method named after Jean-Charles de Borda, who
developed the system in 1770.
In this method, points are assigned to candidates based on their
ranking.
• 1 point for last
• 2 points for second-to-last choice and so on.
The point values for all ballots are totaled, and the candidate with the
largest point total is the winner.

5. EXPLAINNATION.
5
A camping club is deciding where to go on their next trip. The
preference table is shown below
A = Arches, G = Grand Canyon, Y = Yosemite, Z = Zion

6. Since there are 4 choices.
1st place gets 4 points.
2nd place gets 3 points.
3rd place gets 2 points.
4th place gets 1 point.
6
Find the winner under the
Borda count method.
Number of
Voters
12 5 4 9 6 10
1st Choice (4
pts)
Y
𝟏𝟐
∙ 𝟒
= 𝟒𝟖
G
𝟓 ∙ 𝟒
= 𝟐𝟎
Z
𝟒 ∙ 𝟒
= 𝟏𝟔
A
𝟗 ∙ 𝟒
= 𝟑𝟔
A
𝟔 ∙ 𝟒
= 𝟐𝟒
Z
𝟏𝟎
∙ 𝟒
= 𝟒𝟎
2nd Choice (3
pts)
Z
𝟏𝟐
∙ 𝟑
= 𝟑𝟔
Y
5∙
𝟑 =
𝟏𝟓
A
4∙
𝟑 =
𝟏𝟐
Y
9∙
𝟑 =
𝟐𝟕
Z
6∙
𝟑 =
𝟏𝟖
G
𝟏𝟎
∙ 𝟑
= 𝟑𝟎
3rd Choice (2
pts)
G
𝟏𝟐
∙ 𝟐
= 𝟐𝟒
A
5∙
𝟐 =
𝟏𝟎
G
𝟒 ∙ 𝟐
= 𝟖
G
9∙
𝟐 =
𝟏𝟖
Y
6∙
𝟐 =
𝟏𝟐
A
𝟏𝟎
∙ 𝟐
= 𝟐𝟎
4th Choice (1
pt)
A
𝟏𝟐
∙ 𝟏
= 𝟏𝟐
Z
𝟓 ∙ 𝟏
= 𝟓
Y
𝟒 ∙ 𝟏
= 𝟒
Z
𝟗 ∙ 𝟏
= 𝟗
G
𝟔 ∙ 𝟏
= 𝟔
Y
𝟏𝟎
∙ 𝟏
= 𝟏𝟎

7. 9
A = Arches, G = Grand Canyon, Y = Yosemite, Z = Zion
Point totals:
Arches: 𝟑𝟔 + 𝟐𝟒 + 𝟏𝟐 + 𝟏𝟎 + 𝟐𝟎 + 𝟏𝟐 = 𝟏𝟏𝟒
Grand Canyon: 𝟐𝟎 + 𝟑𝟎 + 𝟐𝟒 + 𝟖 + 𝟏𝟖 + 𝟔 = 𝟏𝟎𝟔
Yosemite: 48 +𝟏𝟓 + 𝟐𝟕 + 𝟏𝟐 + 𝟒 + 𝟏𝟎 = 𝟏𝟏𝟔
Zion: 𝟏𝟔 + 𝟒𝟎 + 𝟑𝟔 + 𝟏𝟖 + 𝟓 + 𝟗 = 𝟏𝟐𝟒
Under the Borda count method, Zion is the winner.

8. What is wrong with Borda count?
8
One potential flaw of Borda count is a
candidate could receive a majority of
the first-choice votes and still lose the
election.
Consider the following preference
schedule:
Number of Voters 9 2 8 1
1st Choice A A B C
2nd Choice B C C B
3rd Choice C B A A

9. What is wrong with Borda count?
9
Total Votes: 20
A:
𝟗+𝟐
𝟐𝟎
=
𝟏𝟏
𝟐𝟎
= 𝟓𝟓% (𝒎𝒂𝒋𝒐𝒓𝒊𝒕𝒚)
B:
𝟖
𝟐𝟎
= 𝟒𝟎%
C:
𝟏
𝟐𝟎
= 𝟓%
A would win by a majority.
Number of Voters 9 2 8 1
1st Choice (3 pts) A
27
A
6
B
24
C
3
2nd Choice (2 pts) B
18
C
4
C
16
B
2
3rd Choice (1 pt) C
9
B
2
A
8
A
1
Total Points
A: 𝟐𝟕 + 𝟔 + 𝟖 + 𝟏 = 𝟒𝟐
B: 𝟐𝟒 + 𝟏𝟖 + 𝟐 + 𝟐 = 𝟒𝟔
C: 𝟑 + 𝟒 + 𝟏𝟔 + 𝟗 = 𝟑𝟐
B would win by Borda count.
This brings up another fairness criterion.

10. Majority Criterion
10
If a choice has a majority of first-place votes, that choice should be the winner.
 Borda count is sometimes described as a consensus-based voting system,
since it can sometimes chooses a more broadly acceptable option over one
with majority support. This is a different approach than plurality and
instant runoff voting that focus on first-choice votes. Borda count
considers every voter’s entire ranking to determine the outcome.
 Because of this consensus behavior, Borda count, or some variation of it, is
commonly used in selecting sports awards. Variations are used to
determine the Most Valuable Player in baseball, to rank teams in NCAA
sports, and to award the Heisman trophy.

11. THANKYOU!
AADAHMAD01@GMAIL.COM
0333-6792176