- Jin wants to buy a $90 keg of beer and $90 worth of pizza. Therefore, he would ideally like each to contribute $60 to the function, but if the others are unwilling to contribute that much, he would settle for buying just the pizza (and contributing $30 each) and asking guests to bring their own beer. - Diego does not care about the function and is on a tight budget. Therefore, he prefers to contribute no money to the function, and his utility declines at a constant rate as the roommates increase the amount of money they spend. - Adrian would ideally contribute $30 because he only wants to buy pizza. However, he would prefer contributing $60 to contributing $0 and not having a party at all. Suppose the three housemates vote on spending either $0,$30, or $60 on the function using the Borda count system of voting. That is, each housemate 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 housemate 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 If, instead, the housemates were to hold a two-phase election (such that they first voted between two options, then voted be the contest and the final option), the winner would be . (Hint: Determine the outcome if the roommates first voted between $60 and $0, and then voted between the winner of that contest and $30.) The median voter in this situation is