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Explain the history of Head-to-Head comparisons method and applications in real life pointing out the importance of mathematics in election methods. Solve the problem 16 on page 43 as well. You can use this problem as an example to show the method we use - Essay Example

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The Head-to-Head comparisons method is simply a subset of Condorcet method as the same procedure is undertaken, except that only two candidates are being evaluated in the former. Stated in another way, the head-to-head comparisons method is a step used in Condorcet method.
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Explain the history of Head-to-Head comparisons method and applications in real life pointing out the importance of mathematics in election methods. Solve the problem 16 on page 43 as well. You can use this problem as an example to show the method we use
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The History and Applications of Head-to-Head Comparisons Method The Head-to-Head comparisons method is simply a subset of Condorcet method as the same procedure is undertaken, except that only two candidates are being evaluated in the former. Stated in another way, the head-to-head comparisons method is a step used in Condorcet method.
Just like Borda’s method, the Condorcet method was discovered independently by two men: Marqui de Condorcet and Ramon Lull. Condorcet (1743 – 1794) was a French mathematician and philosopher born in Ribemont, Aisne, credited for this system of voting (“Condorcet Method,” par. 3). However, documents found in the Vatican Library would prove that Lull discovered it first in 1299 (“Condorcet Elections,” par. 3).
While Borda’s method has found applications outside the realm of elections, Condorcet method has not received much popularity anywhere in the world. In fact, no country has implemented such system in government elections (“Condorcet Method,” par. 3). However, a number of public and private organizations are starting to take interest in the method. Condorcet method is useful in voting systems where voters indicate their preference ranking, or when valid assumptions can be made about the voters’ preference. Although the method requires only simple mathematics, its importance in the electoral process cannot be denied.
The problem below illustrates this method, as well as the other methods previously discussed:
Solution:
a.)
Lincoln = 8 + 23.9 + 1.7 + 0.3 + 5.6 + 0.3 + 0.2 + 0.7 + 2.7 + 0.5 + 0.8 + 1.5 = 46.2%
Douglas = 4.4 + 10.3 + 2.6 + 1.8 + 8 + 2.4 + 0.2 + 3.4 + 10.9 + 0.7 + 3.7 + 5.4 = 53.8%
Therefore Douglas wins by Head-to-Head comparisons method.
b.)
Lincoln = (8 + 23.9 + 1.7 + 0.3 + 5.6 + 0.3)(4) + (4.4 + 10.3 + 0.2 + 0.7 + 0.5 + 0.8)(3) + (2.6 + 8 + 0.2 + 2.7 + 0.7 + 1.5)(2) + (1.8 + 2.4 + 3.4 + 10.9 + 3.7 + 5.4)(1) = 268.9
Douglas = (4.4 + 10.3 + 2.6 + 1.8 + 8 + 2.4)(4) + (8 + 23.9 + 0.2 + 3.4 + 0.7 + 3.7)(3) + (1.7 + 5.6 + 0.2 + 10.9 + 0.5 + 5.4)(2) + (0.3 + 0.3 + 0.7 + 2.7 + 0.8 + 1.5)(1) = 292.6
Breckinridge = (0.2 + 0.7 + 0.2 + 3.4 + 2.7 + 10.9)(4) + (1.7 + 0.3 + 2.6 + 1.8 + 1.5 + 5.4)(3) + (8 + 0.3 + 4.4 + 2.4 + 0.8 + 3.7)(2) + (23.9 + 5.6 + 10.3 + 8 + 0.5 + 0.7)(1) = 200.5
Bell = (0.5 + 0.8 + 0.7 + 3.7 + 1.5 + 5.4)(4) + (5.6 + 0.3 + 8 + 2.4 + 2.7 + 10.9)(3) + (23.9 + 0.3 10.3 + 1.8 + 0.7 + 3.4)(2) + (8 + 1.7 + 4.4 + 2.6 + 0.2 + 0.2)(1) = 238
Therefore, Douglas wins by Borda’s method.
c.)
Lincoln vs. Douglas

8
23.9
1.7
0.3
5.6
0.3
4.4
10.3
2.6
1.8
8
2.4
Lincoln
1
1
1
1
1
1
2
2
3
4
3
4
Douglas
2
2
3
4
3
4
1
1
1
1
1
1

0.2
0.7
0.2
3.4
2.7
10.9
0.5
0.8
0.7
3.7
1.5
5.4
Lincoln
2
2
3
4
3
4
2
2
3
4
3
4
Douglas
3
4
2
2
4
3
3
4
2
2
4
3
Lincoln = 46.2%
Douglas = 53.8%
→ one point for Douglas
Lincoln vs. Breckinridge

8
23.9
1.7
0.3
5.6
0.3
4.4
10.3
2.6
1.8
8
2.4
Lincoln
1
1
1
1
1
1
2
2
3
4
3
4
Breckinridge
3
4
2
2
4
3
3
4
2
2
4
3

0.2
0.7
0.2
3.4
2.7
10.9
0.5
0.8
0.7
3.7
1.5
5.4
Lincoln
2
2
3
4
3
4
2
2
3
4
3
4
Breckinridge
1
1
1
1
1
1
4
3
4
3
2
2
Lincoln = 64.5%
Breckinridge = 35.5%
 one point for Lincoln
Lincoln vs. Bell

8
23.9
1.7
0.3
5.6
0.3
4.4
10.3
2.6
1.8
8
2.4
Lincoln
1
1
1
1
1
1
2
2
3
4
3
4
Bell
4
3
4
3
2
2
4
3
4
3
2
2

0.2
0.7
0.2
3.4
2.7
10.9
0.5
0.8
0.7
3.7
1.5
5.4
Lincoln
2
2
3
4
3
4
2
2
3
4
3
4
Bell
4
3
4
3
2
2
1
1
1
1
1
1
Lincoln = 58.2%
Bell = 41.8%
 one point for Lincoln
Douglas vs. Breckinridge

8
23.9
1.7
0.3
5.6
0.3
4.4
10.3
2.6
1.8
8
2.4
Douglas
2
2
3
4
3
4
1
1
1
1
1
1
Breckinridge
3
4
2
2
4
3
3
4
2
2
4
3

0.2
0.7
0.2
3.4
2.7
10.9
0.5
0.8
0.7
3.7
1.5
5.4
Douglas
3
4
2
2
4
3
3
4
2
2
4
3
Breckinridge
1
1
1
1
1
1
4
3
4
3
2
2
D ouglas= 71.9%
Breckinridge = 28.1%
 one point for Douglas
Douglas vs. Bell

8
23.9
1.7
0.3
5.6
0.3
4.4
10.3
2.6
1.8
8
2.4
Douglas
2
2
3
4
3
4
1
1
1
1
1
1
Bell
4
3
4
3
2
2
4
3
4
3
2
2

0.2
0.7
0.2
3.4
2.7
10.9
0.5
0.8
0.7
3.7
1.5
5.4
Douglas
3
4
2
2
4
3
3
4
2
2
4
3
Bell
4
3
4
3
2
2
1
1
1
1
1
1
Douglas = 66.9%
Bell = 33.1%
→ one point for Douglas
Breckinridge vs. Bell

8
23.9
1.7
0.3
5.6
0.3
4.4
10.3
2.6
1.8
8
2.4
Breckinridge
3
4
2
2
4
3
3
4
2
2
4
3
Bell
4
3
4
3
2
2
4
3
4
3
2
2

0.2
0.7
0.2
3.4
2.7
10.9
0.5
0.8
0.7
3.7
1.5
5.4
Breckinridge
1
1
1
1
1
1
4
3
4
3
2
2
Bell
4
3
4
3
2
2
1
1
1
1
1
1
Breckinridge = 36.9%
Bell = 63.1%
→ one point for Bell
Tally:
Lincoln – II
Douglas – III
Breckinridge -
Bell - I
Therefore, Douglas wins by Condorcet criterion.
Works Cited
“Condorcet Elections” League of Women Voters of Minnesota. 2009. League of Women Voters of Oregon. 14 Sep 2009.
“Condorcet Method” AllExperts. 2009. About.com. 22 Sep 2009. Read More
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