Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - 13.1 Voting Methods - Exercise Set 13.1: 20

Answer

If there are six candidates, 15 comparisons must be made.

Work Step by Step

Suppose that the pairwise comparison method is used to determine the winner in an election. In an election with $n$ candidates, the number of comparisons, C, that must be made is determined by the formula $C = \frac{n~(n-1)}{2}$ We can find how many comparisons must be made if there are six candidates. In this case, $n=6$. $C = \frac{n~(n-1)}{2}$ $C = \frac{6~(6-1)}{2}$ $C = 15$ If there are six candidates, 15 comparisons must be made.
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