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Chapter 13: Problem 42

Describe the Borda count method. Is it possible to use this method without ranking the candidates? Explain.

Short Answer

Expert verified
The Borda count method is an electoral system in which voters rank candidates and points are given to each position. The candidate with the highest point sum wins. It's not possible to use it without ranking the candidates, as the method depends on voters' ranking.

Step by step solution

01

Definition of the Borda Count Method

The Borda count method is a single-winner election method in which voters order the candidates in a preference ranking. Each position in the ranking is assigned a certain number of points. The points corresponding to each position are then added up for each candidate, and the candidate with the highest number of points is declared the winner.
02

Description of the Point Allocation Process

In a typical Borda count, if there are \(n\) candidates, then a candidate would get \(n\) points for a first place vote, \(n-1\) points for a second place vote, and so forth, down to 1 point for a last place vote. All points received from all voters are then totalled for each candidate.
03

Can Borda Count Method be used without Ranking?

It's technically not possible to use the Borda count method without ranking the candidates. The whole methodology of the Borda count is based on ranking since it operates by assigning points based on the position of candidates in each voter's ranking. If voters do not provide a ranking of candidates, the methodology cannot assign points to each candidate, so it cannot be applied.

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Most popular questions from this chapter

A town has five districts in which mail is distributed and 50 mail trucks. The trucks are to be apportioned according to each district鈥檚 population. The table shows these populations before and after the town鈥檚 population increase. Use Hamilton鈥檚 method to show that the population paradox occurs. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { District } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { Total } \\ \hline \begin{array}{l} \text { Original } \\ \text { Population } \end{array} & 780 & 1500 & 1730 & 2040 & 2950 & 9000 \\ \hline \text { New Population } & 780 & 1500 & 1810 & 2040 & 2960 & 9090 \\ \hline \end{array} $$

A university is composed of five schools. The enrollment in each school is given in the following table. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { School } & \begin{array}{c} \text { Human- } \\ \text { ities } \end{array} & \begin{array}{c} \text { Social } \\ \text { Science } \end{array} & \begin{array}{c} \text { Engi- } \\ \text { neering } \end{array} & \text { Business } & \begin{array}{c} \text { Educa- } \\ \text { tion } \end{array} \\ \hline \text { Enrollment } & 1050 & 1410 & 1830 & 2540 & 3580 \\ \hline \end{array} $$ There are 300 new computers to be apportioned among the five schools according to their respective enrollments. Use Hamilton's method to find each school's apportionment of computers.

Is it possible to have election results using a particular voting method that satisfy all four fairness criteria? If so, does this contradict Arrow's Impossibility Theorem?

What is the new-states paradox?

The mathematics department has 30 teaching assistants to be divided among three courses, according to their respective enrollments. The table shows the courses and the number of students enrolled in each course.$$ \begin{array}{|l|c|c|c|c|} \hline \text { Course } & \begin{array}{c} \text { College } \\ \text { Algebra } \end{array} & \text { Statistics } & \begin{array}{c} \text { Liberal Arts } \\ \text { Math } \end{array} & \text { Total } \\ \hline \text { Enrollment } & 978 & 500 & 322 & 1800 \\ \hline \end{array} $$a. Apportion the teaching assistants using Hamilton鈥檚 method. b. Use Hamilton鈥檚 method to determine if the Alabama paradox occurs if the number of teaching assistants is increased from 30 to 31. Explain your answer.
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