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Make Sense? In Exercises 49-52, determine whether each statement makes sense or does not make sense, and explain your reasoning. A candidate has a majority of the vote, yet lost the election using the plurality method.

Short Answer

Expert verified
The statement does not make sense because if a candidate with a majority (more than half) of the votes, it means they also possess a plurality (highest number of votes) and hence, cannot lose the election using the plurality system.

Step by step solution

01

Understanding the Terminology

Look at the definition of majority and plurality in context of an election. Majority means more than half of all votes while plurality means having the highest number of votes, which might not be more than half of all votes.
02

Apply the Definitions to the Statement

Consider the statement. If a candidate has a majority of the vote, it means they have received more than half of all the votes. On the other hand, to lose under the plurality method, another candidate would need to have more votes.
03

Contradiction in Context

Recognize the contradiction. If a candidate has over half the votes, it also means they would have the highest number of votes (a plurality). Therefore, if a candidate has a majority, they couldn't have lost according to the plurality method because they would be the candidate with the most votes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Majority Vote
In the context of elections, a majority vote means that a candidate receives more than half of all the votes cast. This is a clear threshold because to win by majority, one must attain over 50% of the votes. For example, if there are 100 votes in total, a candidate needs at least 51 votes to secure a majority.
It's important to remember that in scenarios where there are only two candidates, the candidate with the majority vote always wins. However, in elections with more than two candidates, winning a majority becomes challenging as votes are divided among more people.
When discussing majority votes, always think about the simple benchmark of crossing the 50% line to ensure a win. Understanding majority is key when analyzing different voting system outcomes.
Plurality Method
The plurality method is one of the simplest and most used voting systems. In this method, the candidate who receives the most votes wins, regardless of whether or not they have a majority.
For example, if there are three candidates and the votes are divided as 40, 35, and 25, the candidate with 40 votes wins because they have more than any other candidate, despite not having over half of the votes.
The plurality method is straightforward but can sometimes lead to winners who a majority of voters did not prefer. This often occurs in elections with several candidates running, as the winning candidate may only need a small fraction of the total votes compared to achieving a majority.
Voting Systems
Various voting systems exist to elect leaders or make decisions, and each has its own rules and implications.
  • First-Past-the-Post (FPTP): This is synonymous with the plurality method, where the candidate with the most votes wins.
  • Ranked Voting: Voters rank candidates in order of preference. If no candidate receives a majority, the candidate with the fewest votes is eliminated, and votes are redistributed until one achieves a majority.
  • Proportional Representation: Aims to allocate seats in proportion to the votes each party receives, often leading to coalition governments.
Different methods suit different cultural and political contexts, impacting who gets elected and how representative the result is. Understanding these systems helps us look beyond simple vote counts and consider broader electoral fairness and representation.
Election Terminology
Election terminology can sometimes be confusing, but it's essential for understanding how voting systems work. Here are a few key terms:
  • Majority: More than half of the votes.
  • Plurality: The largest number of votes, but not necessarily a majority.
  • Electorate: All the qualified voters in a given election.
  • Ballot: The method by which a voter registers their choice.
By familiarizing oneself with these terms, the complex processes of elections and the implications of different voting outcomes become clearer. This knowledge is crucial for participating in democratic processes and debating proposed changes to voting laws and methods.

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Most popular questions from this chapter

Describe the plurality method. Why is ranking not necessary when using this method?

Voters in a small town are considering four proposals, A, B, \(C\), and D, for the design of affordable housing. The winning design is to be determined by the Borda count method. The preference table for the election is shown. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & 300 & 120 & 90 & 60 \\ \hline \text { First Choice } & \text { D } & \text { C } & \text { C } & \text { A } \\ \hline \text { Second Choice } & \text { A } & \text { A } & \text { A } & \text { D } \\ \hline \text { Third Choice } & \text { B } & \text { B } & \text { D } & \text { B } \\ \hline \text { Fourth Choice } & \text { C } & \text { D } & \text { B } & \text { C } \\ \hline \end{array} $$ a. Which design has a majority of first-place votes? b. Using the Borda count method, which design will be used for the affordable housing? c. Is the majority criterion satisfied? Explain your answer.

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’s method. b. Use Hamilton’s method to determine if the Alabama paradox occurs if the number of teaching assistants is increased from 30 to 31. Explain your answer.

How is the lower quota found from a standard quota?

A country has 200 seats in the congress, divided among the five states according to their respective populations. The table shows each state’s population, in thousands, before and after the country’s population increase. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { Total } \\ \hline \begin{array}{l} \text { Original } \\ \text { Population } \\ \text { (in thousands) } \end{array} & 2224 & 2236 & 2640 & 3030 & 9870 & 20,000 \\ \hline \begin{array}{l} \text { New Population } \\ \text { (in thousands) } \end{array} & 2424 & 2436 & 2740 & 3130 & 10,070 & 20,800 \\ \hline \end{array} $$ n thousands) 2424 2436 2740 3130 10,070 20,800 a. Use Hamilton’s method to apportion the 200 congressional seats using the original population. b. Find the percent increase, to the nearest tenth of a percent, in the population of each state. c. Use Hamilton’s method to apportion the 200 congressional seats using the new population. What do you observe about the percent increases for states A and B and their respective changes in apportioned seats? Is this the population paradox?

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