Question

question 8
5 pts
consider the election given by the following preference schedule.
number of voters: 51, 25, 10, 14
1st choice: flagship, phoenix, yuma, tuscor
2nd choice: phoenix, yuma, phoenix, phoeni
3rd choice: tuscon, tuscon, tuscon, yuma
4th choice: yuma, flagship, flagship, flagshi
determine the winner on majority of first-place votes?
options: tuscon, phoenix, there is no winner, flagship

Explanation:

Step1: Calculate total voters

First, find the total number of voters by adding the number of voters in each group: \( 51 + 25 + 10 + 14 = 100 \) voters.

Step2: Determine majority threshold

A majority requires more than half of the total votes. Half of 100 is \( \frac{100}{2}=50 \), so a majority is more than 50 votes (i.e., at least 51 votes).

Step3: Count first - place votes

• Flagship: 51 first - place votes.
• Phoenix: 25 first - place votes.
• Yuma: 10 first - place votes.
• Tuscon: 14 first - place votes.

Step4: Check for majority

Flagship has 51 first - place votes, which is more than 50 (the majority threshold).

Answer:

Flagship