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CS6283 Topics in Computer Science IV: Computational Social Choice

CS6283 Topics in Computer Science IV: Computational Social Choice. Instructor: Yair Zick 2017. Markets with Money. Rent Division. Reaching fair solutions in the real world. r = $6000. Room: Verde. Room: Azul. Alice. Claire. Bob. Alice. Claire. Bob. Room: Naranja. Alice. Claire.

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CS6283 Topics in Computer Science IV: Computational Social Choice

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  1. CS6283 Topics in Computer Science IV: Computational Social Choice Instructor: YairZick 2017

  2. Markets with Money Rent Division

  3. Reaching fair solutions in the real world

  4. r = $6000 Room: Verde Room: Azul Alice Claire Bob Alice Claire Bob Room: Naranja Alice Claire Bob

  5. The Problem Fairly distribute rooms and rent amongst roommates.

  6. The Valuations : player ’s value of room such that • Easily Expressable • “how would you divide the rent?” • Not Fully Expressive • “I prefer room 1, but can’t afford to pay more than S$500” • Equal Incomes • All roommates have equal opportunities • External Factors • roommate has more disposable income?

  7. Envy Free (EF) Outcome Outcome such that for all “I do not want your room for the price you’re being charged”

  8. Properties of EF Allocations • Does an EF allocation always exist? • Is it Unique? • Can it be efficiently computed?

  9. Known facts about EF 1st Welfare Theorem: if outcome is EF, then room allocation is optimal. 2nd Welfare Theorem: if outcome is EF, then so is for any optimal room allocation .

  10. General Algorithmic Framework • Compute a socially optimal allocation (max. weighted matching) • Find an EF price vector using linear programming. • From now on we ignore the actual room allocation (assume that assigning room to player is optimal).

  11. Provably Fair Solutions • Can be easily related to the users: “You wouldn’t want room 3 for $847 based on your valuations” • Satisfies fundamental ideas of economic/social justice I object! This outcome is totally unfair! Not true! And I have (mathematical) proof!

  12. Where EF goes wrong Room: Verde Room: Azul Alice Alice Claire Bob Claire Bob Room: Naranja Alice Claire Bob

  13. Equitability (under EF constraint): Maximin (under EF constraint):

  14. Theorem: There is a unique maximin price vector, and it is also equitable (minimizes ) However, there exist equitable price vectors that are not maximin.

  15. Maximin is good in theory.Is it also good in practice?

  16. Fair Division is hard to study in the lab “the goods in the lab are not really distributed among participants, but serve as temporary substitutes for money.” [Herreiner and Puppe 09]

  17. Empirical Studies • Study the practical benefit of the maximin solution • The database included more than 16,000 instances! • Most common instances included 2, 3 and 4 rooms

  18. Motivation

  19. Theoretical Benefits Empirical Benefits Are people willing to accept such solutions in practice?

  20. Participants • Spliddit users who participated in rent division • instances with 2, 3 or 4 players • Invited over email • Offered $10 fixed compensation

  21. Within-Subject Design • The subjects were shown the two solutions — maximin and arbitrary EF for their own instance • The two solution outcomes were shown in sequence, and in random order

  22. Survey • Individual • This question relates to your own allocation. • In other words, we would like you to pay attention only to your own benefit. • How happy are you with getting the room called Verde for $2,382? • Other • This question relates to the allocation for everyone else. • How fair do you rate the allocation for Bob and Claire?

  23. Results

  24. References Gal, Mash, Procaccia and Zick “Which is the Fairest (Rent Division) of Them All?”, EC 2016

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