David and Max purchased raffle tickets together and, to their surprise, won three prizes. Now they must make a fair division of their winnings. Using the adjusted winner procedure, what does David end up with? $$\begin{array} { l l l }
\text { Object } & \text { David's points } & \text { Max's points } \
\text { Fly rod } & 50 & 45 \
\text { Fly-fishing lessons } & 10 & 35 \
100 \text { hand-tied flies } & 40 & 20
\end{array}$$
A) fly rod only
B) flies, fly rod
C) flies, 11/19 of fly rod
D) flies, 8/19 of fly rod

Question

David and Max purchased raffle tickets together and, to their surprise, won three prizes. Now they must make a fair division of their winnings. Using the adjusted winner procedure, what does David end up with? $$\begin{array} { l l l } 
\text { Object } & \text { David's points } & \text { Max's points } \
\text { Fly rod } & 50 & 45 \
\text { Fly-fishing lessons } & 10 & 35 \
100 \text { hand-tied flies } & 40 & 20
\end{array}$$
A) fly rod only 
B) flies, fly rod
C) flies, 11/19 of fly rod
D) flies, 8/19 of fly rod

Quizplus · Accepted Answer

To use the adjusted winner procedure, we need to first calculate each person's total points. David has 50 + 10 + 40 = 100 points, while Max has 45 + 35 + 20 = 100 points as well.

Next, we calculate the average points per prize. Since there are three prizes, that is a total of 200 points to be divided, so the average is 200/3 = 66.67 points per prize.

Now, we calculate the excess points for each person, which is the amount by which their total points exceed the average. David's excess points are 100 - 66.67 = 33.33, while Max's excess points are also 33.33.

Finally, we allocate the prizes to each person based on their excess points. The person with the higher excess points gets their preferred prize, while the person with the lower excess points gets their preferred prize and a fraction of the other prize(s) equal to their excess points divided by the total excess points.

In this case, both David and Max have the same excess points, so we need to use a tiebreaker. One approach is to give the fly rod to the person with the higher points in that category, which is David. Therefore, David gets the fly rod, leaving him with no excess points.

Max now has an excess of 33.33 points, which is allocated as follows:
- For the hand-tied flies, Max gets his preferred 20 points worth of flies.
- For the fly-fishing lessons, Max gets his preferred 35 points worth of lessons.
- For the fly rod, Max gets (33.33/66.67) * 50 = 25 points worth of the rod.

Therefore, Max ends up with the flies and 25/50 = 8/19 of the fly rod, which is answer choice D.

David and Max Purchased Raffle Tickets Together And, to Their