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Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively.
-Which candidate would win the election based on ideal points?

Question

Quizplus · Accepted Answer

To determine the winner based on ideal points, we need to calculate the Euclidean distance between each board member's ideal point and the policy positions announced by candidate A and candidate B. The candidate whose policy position has the lowest average distance to the voters' ideal points will win the election.

For candidate A: 
- Euclidean distances to (1, 1): 
    - Board member 1: √5
    - Board member 2: 2
    - Board member 3: √26
    - Board member 4: 5
    - Board member 5: √26
    - Board member 6: 3
    - Board member 7: 2
- Average distance: ( √5 + 2 + √26 + 5 + √26 + 3 + 2 ) / 7 ≈ 2.973

For candidate B:
- Euclidean distances to (6, 4): 
    - Board member 1: √52
    - Board member 2: 3
    - Board member 3: 3
    - Board member 4: √10
    - Board member 5: √17
    - Board member 6: 2
    - Board member 7: 3
- Average distance: ( √52 + 3 + 3 + √10 + √17 + 2 + 3 ) / 7 ≈ 3.178

Therefore, based on ideal points, candidate A would win the election.

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