The MC Raffle A case study for MA115

The MC Raffle As a promotion, MC decides to give a free raffle ticket to every student who is planning on returning next semester. All kinds of good MC prizes will be given away.

The MC Raffle You and a friend decide to combine your chances – you put your raffle tickets together, and if either of them wins anything, you agree to share the winnings equally. You don’t even pay attention to which ticket was originally yours and which was your friend’s – they both now belong equally to both of you.

The MC Raffle Congratulations, you won! One of the tickets was called when they announced the 3rd prize winner – a $20 gift certificate to the bookstore.

The MC Raffle How do you honor your agreement to split the prize equally?

The MC Raffle No – wait – you actually won the 2nd prize, which is much better. It is a scholarship that covers the cost of in-County tuition and fees for a 3 credit course. How can you divide the prize fairly this time?

The MC Raffle “Welcome to Montgomery College – home of [your name] !” Amazingly, your other ticket was also called– you just won the 1st prize! A giant LED screen will be erected on the corner of 355 and Mannakee, and will show a 20-foot tall image of you smiling and waving, with the caption “Welcome to Montgomery College – home of [your name] !”

The MC Raffle Unlike the previous examples, different people may value this prize differently, so it becomes harder to split evenly.

The MC Raffle You think the novelty would be nice, but wouldn’t pay a lot for that honor. You decide that the prize is worth about $100 to you. Your friend, on the other hand, has an enormous ego and would LOVE to have her face on that huge screen – it is worth $1000 to her.

The MC Raffle How can you both get your fair share now, when you have such different ideas of the total value to be split (again, you think there is a $100 prize to be split, your friend thinks it is a $1000 prize?)

The MC Raffle The Grand Prize consists of: All 3 of the other prizes ($20 credit at the bookstore, a $500 scholarship, and a smiling face over Rockville Pike) PLUS A 1-week all expenses paid trip to Cleveland!

The MC Raffle Your friend thinks “Cleveland? Really? Why would I want to go there? A week’s vacation is worth $500 to me no matter where it is, so that’s what I consider this prize to be worth.” You, on the other hand, have always dreamed of going to Cleveland, and now you can! You’ll take full advantage of all the sightseeing opportunities, and have a great time - this trip is worth $1300 to you.

The MC Raffle Find a fair division for the grand prize: Bookstore credit ($20) Scholarship ($500) Sign ($100- you, $1000 – friend) Trip ($1300 – you, $500 – friend)

The MC Raffle Bookstore credit ($20) One of you gets the credit, and pays $10 The other takes the $10 Scholarship ($500) One of you gets the scholarship and pays $250 The other takes the $250 Sign ($100- you, $1000 – friend) Your friend gets the sign, and pays $500 You take $50 (the other $450 is left for now) Trip ($1300 – you, $500 – friend) You take the trip and pay $650 Your friend takes $250. The remaining $400 is left.

The MC Raffle At this point, the division might be: You Friend Bookstore credit, $-10 $10 $250 Scholarship, $-250 $50 Sign, $-500 Trip, $-650 $250 ----------- ------------- Bookstore, Trip Scholarship, Sign, Pay $660 Pay $750 Receive back $300 Receive back $260

The MC Raffle You Friend Bookstore, Trip Scholarship, Sign, Pay $660 Pay $750 Receive back $300 Receive back $260 Notice that between you and your friend, you have paid a combined $1410, but only taken back $560. Even though you have both received your fair shares already, an additional $850 remains unclaimed and can be split evenly between you two! So you each take an additional ½ of $850, or $425 in the final settlement.

The MC Raffle You Friend Bookstore, Trip Scholarship, Sign, Pay $660 Pay $750 Receive back $300 Receive back $260 +$425 in final settlement +$425 ------------- --------------- Bookstore, Trip, Scholarship, Sign, Receive $65 Pay $65 (Notice that in the end the money balances out, as it must – there should never be any money leftover, or more money taken than was paid)

The MC Raffle Summary of the method of sealed bids used: Divide up the goods, giving each to whichever person values it the most. The person who receives the good pays into a pot the excess of the good’s value over their fair share. Everyone else takes from that pot an amount equal to their fair share based on the value they assigned to the good. At the end, there will be money left over in the pot – divide it evenly among the players. Make sure all goods have been distributed, and the sum of all monetary payments exactly balances the sum of all moneys received.

The MC Raffle A slightly more efficient way to do the same thing is as follows: Each player determines the total value, to them, of all of the goods together. They can then determine what the value of their fair share of the collection is by dividing this value by the total number of players. Give each good to whichever player values it the most. Each person then compares the value of the goods they receive to the value they are entitled to (from step 1). Everyone who has received too much value then pays the excess to a pot of money to be used to make sure everyone gets their fair share. Everyone who received too little value takes enough money from the pot to make their share fair. After everyone has paid/taken money to make their share fair, there will be leftover money – divide that evenly among all of the players.