New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Week 7: Fair Division Part 1

by: Amy Brogan

Week 7: Fair Division Part 1 MATH 1014

Marketplace > University of Cincinnati > Mathematics (M) > MATH 1014 > Week 7 Fair Division Part 1
Amy Brogan
GPA 3.7
Mathematics of Social Choice
Mary Koshar

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Explanation and examples of Adjusted Winner Procedure and Adjusted Winner Procedure. Includes definitions of Equitable, Envy-free, and Pareto-optimal.
Mathematics of Social Choice
Mary Koshar
Class Notes
fair division Adjusted Winner Procedure Adjusted Winner Procedure Equitable Envy-free Pareto-optimal
25 ?




Popular in Mathematics of Social Choice

Popular in Mathematics (M)

This page Class Notes was uploaded by Amy Brogan on Saturday February 27, 2016. The Class Notes belongs to MATH 1014 at University of Cincinnati taught by Mary Koshar in Spring 2016. Since its upload, it has received 20 views. For similar materials see Mathematics of Social Choice in Mathematics (M) at University of Cincinnati.


Reviews for Week 7: Fair Division Part 1


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/27/16
Koshar Amy Brogan February 22 24 amp 26 2016 Week 7 Fair Division Dividing Up quotStuffquot Equally o Equitable both players believe that she received the same factorial part of the total value 0 Envyfree neither player would be happier with what the other received 0 Paretooptimal no other allocation arrived at by any means can make one party better off without making the other person worse off 0 Important to property economists Adjusted Winner Procedure Points system where both parties go into separate rooms and give points to items they want more than others Then the thirdperson party uses this system to decide who gets what Example 1 Heather vs Sandy Business Split Heather Sandy Property 40 25 Equipment 10 5 Artwork 25 50 Website 25 20 1 Look at each item and see who has the most points for it Heather Sandy Property 40 25 Equipment 10 5 Artwork 25 50 Website 25 20 2 Add up the total points for awarded items Heather Sandy 40 10 50 25 75 50 3 If the points are not even look to see what item can switch sides based on point value and equal want Property 4025 gt 125 Equipment 105 2 Website 2520 125 closest to 1 In this case just moving the item from side to the other will make them uneven again and no progress can be made 4 Figuring out the portion of divide P1 v1x P2 v2x Starting points value 1 of switching item x some portion Starting points value 2 of itemx 7525x 5020x the values of the switching item is based on the individual value of the object 25 45x x 59 The portion of the item the website moving towards the second party 5 Who gets what Heather property equipment 49 of website Sandy artwork 59 of website Disadvantages of this system 0 Possible an item can t be split 0 Difficulty gauging how much points to give items for the parties Example 2 Equal Valued Items What do we do when the parties have given the same amount of points to the same item The same process as before actually 1 Look at each item and see who has the most points for it 2 Add up the total points for awarded items 3 If the points are not even look to see what item can switch sides based on point value and equal want 4 Figuring out the portion of divide 5 Who gets what Harry Lloyd Dog Van 10 10 Parrot 10 13 Scooter 10 12 Samsonite Case 20 20 Lamborghini 50 45 1 Harry Lloyd Dog Van 10 10 Parrot 10 13 Scooter 10 12 Samsonite Case 20 20 Lamborghini 50 45 In this case we have an extra halfstep For the items that were awarded the same points we are going to give them to one of the two parties Let s give them to Lloyd to make it closer to even Ha Ll 10 13 12 20 50 50 55 3 We can t really make ratios for this problem since the items are weighted the same so we can start moving over items that have the least amount of points Here the Dog Van 4 Our equation will read 50 10x 55 10x 20x 5 x 520 Harry will be gaining of the Dog Van and Lloyd will be keeping of the Dog Van 5 Harry Lamborghini of the Dog Van Lloyd Parrot Scooter Samsonite case and of the Dog Van Knaster Inheritance Procedure What if there are more than two parties And what if there is only one item that can t be split and nobody wants to sell it and split the money There are similar steps as before but without ratios and an equation Again away from each other the parties value the item as to how much they would pay for it Then the person who bids the most begins the act of buying the others shares Example 1 Dan Ed and Bill inheriting their parents house All interior contents are already taken care of 1 How much is each party willing to pay for the item the house Dan Ed Bill 120000 105000 81000 2 Who bid the highest Dan did so at this step he has the house but what about the other two 3 Buying the other shares 3A split each of the bids by the number of parties Dan Ed Bill 120000 105000 81000 Divide by 3 Divide by 3 Divide by 3 40000 35000 27000 3B put n1n shares of the highest bidder into the Kitty 23 in this case two shares out of three people 40000 40000 80000 9 use this to pay for the other shares 3C 80000 35000 27000 18000 3D Split the remaining amount among the parties 18000 3 6000 9 each party including Dan gets 6000 more 4 Who gets what Dan house pays 74000 9 80000 6000 Ed 35000 6000 41000 Bill 27000 6000 33000 Check 41000 33000 74000 Dan s payout Perks o If everyone gives an honest bid everyone will end up better off Drawbacks 0 Income discrepancies one party may make more income than the others and thus be able to bid more cutting out any chance the others have at the item Example 2 Thomas Nikola Benjamin and Alexander look to inherit land in southern Ohio 1 Bids Thomas Nikola Benjamin Alexander 44000 50000 22000 31000 2 Nikola bid the highest 3 Shares of each dividing by 4 in this example Thomas Nikola Benjamin Alexander 44000 50000 22000 31000 Divide by 4 11000 12500 5500 7750 Kitty 12500 12500 12500 37500 37500 11000 5000 7750 13250 9 divide by 4 9 each gets 331250 4 Who gets what Thomas Nikola Benjamin Alexander 11000 331250 50000 331250 5500 331250 7750 331250 1431250 Land pays 3418750 881250 1106250 Check 1431250 881250 1106250 3418750 Practice Adjusted Winner Procedure Joey and Chandler Roommate Split Joey Chandler Foosball Table 20 32 White dog statue 20 10 Duck and chick 25 10 Working recliner 20 30 Entertainment center 15 18 Knaster Inheritance Procedure Mary Sara Marcia Nessa and Diane all look to inherit their grandmother s wedding ring Their bids are as follows Mary Sara Marcia Nessa Diane Ring 1000 500 900 100 1200 AWP 1 Who has the most points for an item Joey Chandler Foosball Table 20 32 White dog statue 20 10 Duck and chick 25 10 Working recliner 20 30 Entertainment center 15 18 2 Add up the points Joey Chandler 32 20 25 30 18 45 80 3 Ratios Foosball 3220 16 3rel Recliner 3020 15 2quot l Center 1815 65 12 closest to 1 Just moving the entertainment center will not even out the points 60 to 62 though it is close 4 Portion of Divide We ll let Joey keep the entertainment center and split the second closest item the working recliner 60 20x 62 30x 50x 2 x 125 04 We knew this would be a small number since they were so close after step 3 5 Who gets what Joey White dog statue duck and chick the entertainment center 4 of the working recliner 2025200415 608 Chandler Foosball table 96 of the working recliner 323096 608 KIP Mary Sara Marcia Nessa Diane Ring 1000 500 900 100 1200 Divide by 5 Mary Sara Marcia Nessa Diane 200 100 180 20 240 Kitty 45 240x4 960 1200 240 960 960 200 100 180 20 460 9 divide by 5 92 Mary Sara Marcia Nessa Diane Ring Bids 1000 500 900 100 1200 200 92 100 92 180 92 20 92 960 92 End Totals 292 192 272 112 Ring Pay 868 Check 292192272112 868


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.