Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 13 - Voting and Apportionment - 13.2 Flaws of Voting Methods - Exercise Set 13.2: 26

Answer

Yes, it is possible to have election results using a particular voting method that satisfy all four fairness criteria. No, this does not violate Arrow's Impossibility Theorem.

Work Step by Step

Yes, it is possible to have election results using a particular voting method that satisfy all four fairness criteria. For example, if one candidate receives all the first-place votes in the election, then that candidate would win using any voting method discussed in this chapter. This result would satisfy all four fairness criteria. No, this does not violate Arrow's Impossibility Theorem. Specific election results may satisfy all four fairness criteria because of the way the votes were cast in that specific election. However, this does not mean that the particular voting method used in that election will always satisfy the four fairness criteria in all elections.
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