Fair Division in Theory and Practice
[CSE/Poli Sci 245A (Spring 2015)]

Overview

You are encouraged to work in groups of up to 3 people on this project. Your group submits just one report, coauthored by all group members.

Data

• Testing: each is 100x100 data points in a CSV file
  • Homogeneous Use this same data set for each player's preferences.
  • 1/2 chcolate, 1/2 vanilla: same cake but two different views
    • chocolate lover One player feels this way
    • vanilla lover The other player feels this way
  • Random
    • player 1's preferences
    • player 2's preferences
• Abstract Israel 1000x1000 CSV file (map)
  • Putative Palestinian preferences
  • Putative Israeli preferences

Procedure

Adjusted Winner

1. In the Massoud piece, the author bundles security and boundaries and shows how the allocation and final pay-offs would differ. What other issues might be bundled, and how would it affect the division and welfare of the two sides?
2. In the real world, two sides are often not aiming for a strictly equitable outcome. A common example is in the settlement of a divorce, the two sides may have to find a 60/40 split. How would the allocation change if, say, Israel has greater bargaining power and the division is not equitable but rather it is predetermined that Israel should fare better and receive 1.5 times the points that Palestine receives (a 60/40 split)?
3. How would you change the adjusted winner algorithm to accommodate a third player? Imagine a separatist Israeli group that has some claim over the contested land was given a seat at the bargaining table. Which axiom(s) would your new algorithm violate (envy-freeness, efficiency, equitability)?
4. How would the algorithm change if the issues were not independent? For example, Palestinians might value allowing Palestinian refugees' right of return, but if Palestine were granted both sovereignty and control of the occupied territory, the issue would be moot. Can the procedure be adjusted to allow for changing preferences as certain issues are won/lost? In other words, how would the algorithm account for non-additive preferences?
5. How does introducing indivisibility into certain issues affect the final outcome? Which axiom(s) might the algorithm violate?
6. Massoud briefly mentions variation in the survey responses across issues. How robust is the final allocation of items to slight variations in the point totals reported by the two sides? You can play with the Massoud example to answer the question.
7. The AW procedure (naively) assumes honesty between the players. If one side has privileged information, what would their best strategy be? What if both sides have a knowledge of how the other player will value issues? What would their optimal strategy be? Is there an equilibrium? To answer this example, try playing with the 2-person, 3-good divorce example given in lecture.

For now, look these over with the idea of picking one that you will think about between now and Wednesday February 4. Look below to see what we would like to get from you in your write-up.

Report (due Feb 4, start of class)

• The names of the people in your group
• Reponses to the following:

  Austin

  For each of the cakes:

  • Homogeneous
  • chocolate/vanilla
  • Random
  • Israel

  describe the results of your application of Austin's algorithm.

  • How close was your solution to being equitable?
  • How dependent was your result on the knife-moving direction?

  Adjusted Winner

  • Which question did your group consider?
  • What approach do you propose to find answers to the question?

    You do not need to have working code yet to obtain answers. We want to see the approach you would take to address the question.