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Chapter 13: Problem 21

Describe the head-to-head criterion.

Short Answer

Expert verified
The head-to-head criterion is a concept in voting theory, stating that if an option would win every head-to-head competition against all other options, it should be the overall winner. This criterion, though often associated with fairness, is not always respected in all voting systems.

Step by step solution

01

Understand the Head-to-Head Criterion

Firstly, understand what the head-to-head criterion is. It's a concept used in decision-making processes, most notably elections and voting. Suppose there are various candidates or options to choose from. The head-to-head criterion states that if option A would beat every other option in a one-on-one competition, option A should be the winner even when all options are considered simultaneously.
02

Explain the usage of the Criterion

It's also important to know when and how to use this criterion. The head-to-head criterion is used in different voting systems to determine a winner. Usually, you would list out all possible one-on-one matchups between each pair of candidates, and the candidate who wins in all head-to-head matchups is considered the 'overall' win according to this criterion.
03

Discuss its significance

Lastly, highlight the implication of the head-to-head criterion. This criterion is often associated with the concept of 'fairness' within voting systems. If a candidate or option can beat every other option in a head-to-head contest, most would agree that it makes sense for that option to be the winner. However, not all voting systems respect the head-to-head criterion, which can lead to contentious results

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Most popular questions from this chapter

In your own words, state Arrow's Impossibility Theorem.

The preference table gives the results of a straw vote among three candidates, \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & 14 & 12 & 10 & 6 \\ \hline \text { First Choice } & \text { C } & \text { B } & \text { A } & \text { A } \\ \hline \text { Second Choice } & \text { A } & \text { C } & \text { B } & \text { C } \\ \hline \text { Third Choice } & \text { B } & \text { A } & \text { C } & \text { B } \\ \hline \end{array} $$ a. Using the plurality-with-elimination method, which candidate wins the straw vote? b. In the actual election, the six voters in the last column who voted \(A, C, B\), in that order, change their votes to \(C\), A, B. Using the plurality-with- elimination method, which candidate wins the actual election? c. Is the monotonicity criterion satisfied? Explain your answer.

What is the pairwise comparison method? Is it possible to use this method without ranking the candidates? Explain.

Describe the irrelevant alternatives criterion.

a. Which option is favored over all others using a head-tohead comparison? b. Which option wins the vote using the Borda count method? c. Is the head-to-head criterion satisfied? Explain your answer. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & 200 & 80 & 80 \\ \hline \text { First Choice } & \text { C } & \text { B } & \text { A } \\ \hline \text { Second Choice } & \text { A } & \text { A } & \text { B } \\ \hline \text { Third Choice } & \text { B } & \text { C } & \text { C } \\ \hline \end{array} $$ a. Which option is favored over all others using a head-tohead comparison? b. Which option wins the vote using the Borda count method? c. Is the head-to-head criterion satisfied? Explain your answer.
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