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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.
-How many board members would vote for B based on ideal points?

Question

Quizplus · Accepted Answer

We can use the Euclidean distance formula to calculate the distance between each board member's ideal point and the policy positions announced by A and B. Then, we can determine which policy position results in the smaller distance for each board member. Here are the results:

Board member 1: Distance to A = 3.1623, distance to B = 5.6569, would vote for A
Board member 2: Distance to A = 2.2361, distance to B = 2.2361, could go either way
Board member 3: Distance to A = 4.1231, distance to B = 3, would vote for B
Board member 4: Distance to A = 5.0990, distance to B = 0.4472, would vote for B
Board member 5: Distance to A = 7.0711, distance to B = 3.1623, would vote for B
Board member 6: Distance to A = 3.1623, distance to B = 2.2361, would vote for B
Board member 7: Distance to A = 2.8284, distance to B = 1.4142, would vote for B

Therefore, board members 3, 4, 5, 6, and 7 would vote for B based on ideal points, a total of 5 members.

The best choice for the company would be to choose candidate B for the position, as they have the support of the majority of the board members based on their ideal points.

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