Identifying the median voter Sam, Andrew, and Darnell are roommates who are trying to decide how much money to spend on heat in their apartment each month.

A. Andrew would ideally contribute $15. However, he would prefer contributing $55 to contributing $0 because he does not want to freeze.

B. Sam hates being cold. Therefore, he would ideally like each to contribute $55 to heat, and his utility declines at a constant rate as the roommates decrease the amount of money they spend.

C. Darnell does not care about heat and is on a tight budget. Therefore, he prefers to contribute no money to heat, and his utility declines at a constant rate as the roommates increase the amount of money they spend.

Suppose the three roommates vote on spending either so, $15, or $55 on heat using the Borda count system of voting. That is, each roommate awards three points to his first choice, two points to his second choice, and one point to his third choice

The median voter here is $55 based on the allocated points in order of preference.

This is the vote that avoids the two extremes of 5 and 7

Explanation:

Voting with the Borda count system of voting:          

                        $0          $15        $55

Andrew            1              3            2

Sam                  1              2            3

Darnell             3             2            1

Total points     5             7            6

The median voter is the selection that is based on choosing the median in a spectrum, so that the extremes are avoided.  In this case, the extremes win points 5 and 4, with the median as 6.

The voting was done by using the Borda count system of voting.  With this system, points are allocated based on personal preferences.  The preference that is favored most is given the highest point, and so on.  This implies that the preference that is least favoured is given the lowest point.

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