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Chapter 13: Problem 40

Describe what is contained in a preference table. What does the table show?

Short Answer

Expert verified
A preference table is a tool that depicts the ranking or ordering of distinct alternatives or outcomes by different individuals. It's a graphical representation of ordinal preferences. The way the ranking is arranged in the table represents each individual's preference from the most preferred to the least.

Step by step solution

01

Introduction to Preference Tables

A preference table, as the name hints, is a table that captures people's preferences over a set of alternatives or outcomes. The preference table typically lists the alternatives horizontally, while individuals or groups of individuals are listed vertically, with their preferences represented by ranks.
02

Understanding What a Preference Table Shows

This table presents data about how every person in a group ranks their preferences. Each row represents a person, and each column represents one of the different outcomes or options. The table typically uses a numerical scale to show preference, with a lower number showing a higher preference and a higher number indicating a lower preference. The way the ranking is organized indicates the perceived value or preference of each individual for the alternatives.
03

Example of Preference Table

Consider an example: If there are three coffee shops (A, B, and C) in a city, and five people are asked to rank their preference. You may find the first person places Shop A first, Shop B second, and Shop C third, thus showing they prefer Shop A most and Shop C least. Similarly, another person might rank Shop B first, indicating that they prefer Shop B most. All these individual rankings can be populated in a table, thus forming a preference table.

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Most popular questions from this chapter

What is the quota rule?

Four professors are running for chair of the Natural Science Division: Professors Darwin (D), Einstein (E), Freud (F), and Hawking (H). The votes of the professors in the natural science division are summarized in the following preference table. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Number of Votes } & 30 & 22 & 20 & 12 & 2 \\ \hline \text { First Choice } & \text { D } & \text { E } & \text { F } & \text { H } & \text { H } \\ \hline \text { Second Choice } & \text { H } & \text { F } & \text { E } & \text { E } & \text { F } \\ \hline \text { Third Choice } & \text { F } & \text { H } & \text { H } & \text { F } & \text { D } \\ \hline \text { Fourth Choice } & \text { E } & \text { D } & \text { D } & \text { D } & \text { E } \\ \hline \end{array} $$ Who is declared the new division chair using the plurality method?

A small country is comprised of four states, A, B, C, and D. The population of each state, in thousands, is given in the following table. Congress will have 400 seats, divided among the four states according to their respective populations. Use Jefferson's method with \(d=7.82\) to apportion the 400 congressional seats.$$ \begin{array}{|l|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } \\\ \hline \begin{array}{l} \text { Population } \\ \text { (in thousands) } \end{array} & 424 & 664 & 892 & 1162 \\ \hline \end{array} $$

What is the plurality-with-elimination method? Why is it advantageous to rank the candidates when using this method?

Three people pool their money to buy 30 shares of stock. The amount that each person contributes is shown in the following table. Use Adams's method to apportion the shares of stock. (Hint: Find the standard divisor. A modified divisor that is greater than this standard divisor will work.) $$ \begin{array}{|l|c|c|c|} \hline \text { Person } & \text { A } & \text { B } & \text { C } \\ \hline \text { Amount } & \$ 795 & \$ 705 & \$ 525 \\ \hline \end{array} $$
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