Let's call a committee of three people a "consumer." (Groups of people often act together as "consumers.") Our committee makes decisions using majority voting. When the committee members compare two alternatives, x and y, they simply take a vote, and the winner is said to be "preferred" by the committee to the loser. Suppose that the preferences of the individuals are as follows: Person 1 likes x best, y second best, and z third best. We write this in the following way: Person 1: x, y, z. Assume the preferences of the other two people are: Person 2: y, z, x; and Person 3: z, x, y. Show that in this example the committee preferences produced by majority voting violate transitivity. (This is the famous "voting paradox" first described by the French philosopher and mathematician Marquis de Condorcet (1743–1794).)

Let's call a committee of three people a "consumer." (Groups of people often act together as "consumers.") Our committee makes decisions using majority voting. When the committee members compare two alternatives, x and y, they simply take a vote, and the winner is said to be "preferred" by the committee to the loser. Suppose that the preferences of the individuals are as follows: Person 1 likes x best, y second best, and z third best. We write this in the following way: Person 1: x, y, z. Assume the preferences of the other two people are: Person 2: y, z, x; and Person 3: z, x, y. Show that in this example the committee preferences produced by majority voting violate transitivity. (This is the famous "voting paradox" first described by the French philosopher and mathematician Marquis de Condorcet (1743–1794).)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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