Hubert, Manuel, and Shen are roommates who are trying to decide how much money each should contribute to a party they are throwing.

Shen does not care about the party and is on a tight budget. Therefore, he prefers to contribute no money to the party, and his utility is constantly declining as they increase the amount of money they spend. Manuel would ideally contribute $15 because he only wants to buy pizza. However, he would prefer contributing $55 to contributing $0 and not having a party at all. Hubert wants to buy a $120 keg of beer and $45 worth of pizza. Therefore, he would ideally like each to contribute $55 to the party, but if the others are unwilling to contribute that much, he would settle for buying just the pizza (and contributing $15 each) and asking guests to bring beer.

Suppose the three roommates vote on spending either $0, $15, or $55 on the party 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.

Complete the following table by indicating the number of points each roommate awards to each option and then summing the scores of each option to obtain a final ranking.

Under a system of Borda count, the winning option is (0, 15, 55).

If, instead, the roommates were to hold a two-phase election (such that they first voted between two options, then voted between the winner of that contest and the final option), the winner would be (0, 15, 55). (Hint: Determine the outcome if the roommates first voted between $55 and $0, and then voted between the winner of that contest and $15.)

The median voter in this situation is(Hubert/Manuel/ Shen).

Borda Count For Spending... HubertManuelShenTotal$55 Borda Count For Spending... HubertManuelShenTotal$55