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Chapter 13: Problem 41

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

Short Answer

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The plurality method is a voting system where each voter is allowed to vote for only one candidate, and the candidate who polls more votes than any other candidate is elected. It does not require ranking because voters only vote for their top preference, and the candidate with the most votes wins, regardless of how voters would have ranked the other candidates.

Step by step solution

01

Understanding the Plurality Method

The plurality method, also known as first-past-the-post or winner-take-all, is a voting system where each voter is allowed to vote for only one candidate, and the candidate who polls more votes than any other candidate is elected. It is used in countries with single-seat electoral divisions, where only one candidate can be selected.
02

The Absence of Ranking

In the plurality method, rank does not matter because you are only voting for one candidate. Other methods that require ranking, like the Borda Count and Instant Runoff Voting, look at voter preferences beyond just the top choice. But in plurality voting, the complexity of understanding voter second preferences or third preferences etc, is avoided. Voters only vote for their top preference, and so the candidate with the most votes wins, regardless of how voters would have ranked the other candidates.

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Key Concepts

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

Voting Systems
A voting system is a method used to aggregate individual preferences and determine the winner in elections. Different voting systems can yield divergent results, even with the same set of votes. They influence not only the outcome but also the strategies candidates use, and voters' participation. Some common types of voting systems include:
  • Plurality method, where the candidate with the most votes wins.
  • Ranked choice, in which voters rank candidates by preference, used in methods like the Borda Count.
  • Proportional representation, seeking to allocate seats based on the proportion of votes received.
Each system has its strengths and challenges. The choice of a system can significantly impact democratic outcomes, such as fair representation and election integrity.
First-Past-The-Post
The term "first-past-the-post" is synonymous with the plurality method of voting. In this context, it resembles a race where the candidate who gets to the 'finish line' first鈥攖he one with the most votes鈥攚ins. Each voter casts a vote for one candidate only. This simplicity is why it's widely used in many democratic elections, especially in single-seat constituencies.
Some key points about first-past-the-post (FPTP) include:
  • Only counts the first preference of each voter.
  • Needs no complex calculations or additional rounds.
  • Can lead to issues like "vote splitting" where similar candidates divide votes, allowing a less popular candidate to win.
Despite these issues, FPTP remains popular due to its straightforward nature and quick results.
Winner-Take-All
The winner-take-all approach is intrinsic to the plurality method. Under this system, the candidate with the majority of votes in an election wins the seat. There's no redistribution or adjustment based on any runner-up performances. A consequence of this system is that it often leads to fewer parties holding power, especially over time.
The winner-take-all system often results in:
  • Clear outcomes with one single winner.
  • A tendency to favor larger, well-established parties and candidates.
  • Less incentive for voters to back smaller or independent candidates, leading to strategic voting.
However, it can also disenfranchise minority opinions and make it difficult for smaller parties to gain a foothold in the political arena.
Electoral Divisions
Electoral divisions, also known as constituencies or districts, are geographic areas that are represented by one or more elected officials in a legislative body. These divisions are crucial in systems like first-past-the-post, where each electoral division elects one representative. Some characteristics of electoral divisions include:
  • Defined boundaries, often based on population data.
  • May be periodic adjustment to reflect changes in population or ensure balanced representation.
  • Can influence election outcomes significantly, often leading to debates on fair and equitable representation.
Electoral divisions are foundational to representative democracy, ensuring that the population's diverse views are somewhat reflected in legislative bodies. However, issues like gerrymandering, where boundaries are manipulated for electoral advantage, can lead to unequal representation.

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Most popular questions from this chapter

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.

Suppose that the pairwise comparison method is used to determine the winner in an election. If there are six candidates, how many comparisons must be made?

In Exercises 28鈥�31, determine whether each statement makes sense or does not make sense, and explain your reasoning. My candidate received a majority of first-place votes and lost the election.

Three candidates, A, B, and \(\mathrm{C}\), are running for mayor. Election rules stipulate that the pairwise comparison method will determine the winner. In the event that the pairwise comparison method leads to a tie, the Borda count method will decide the winner. The election results are summarized in the following preference table. Under these rules, which candidate becomes the new mayor? $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{6 0 , 0 0 0} & \mathbf{4 0 , 0 0 0} & \mathbf{4 0 , 0 0 0} & \mathbf{2 0 , 0 0 0} & \mathbf{2 0 , 0 0 0} \\ \hline \text { First Choice } & \text { A } & \text { C } & \text { B } & \text { A } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { A } & \text { C } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { B } & \text { A } & \text { B } & \text { A } \\ \hline \end{array} $$

Playwright Tom Stoppard wrote, "It's not the voting that's democracy; it's the counting." Explain what he meant by this.
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