COL749, Fall Semester 2024
Computational Social Choice
How to make group decisions, and what's computation got to do with it.
Instructor: Rohit Vaish ()
Course Information
What this course is about
This course will explore the mathematical foundations of social choice or collective decision-making problems. These are problems that involve making a group decision based on the preferences of individuals. Such problems arise in a variety of settings; for example, when a group of friends want to decide how to fairly split the rent for their shared apartment or a shared cab ride, or in high-stakes scenarios such as political elections, matching applicants with jobs, matching organ donors with patients, fairly dividing an inheritance, the list goes on.
We will use tools and techniques from theoretical computer science, economic theory, and artificial intelligence to design and analyze algorithms for collective decision-making problems. The narrative will center around economic issues such as fairness, efficiency, and incentives and how they interact with computation.
Students interested in research on algorithmic aspects of economics and game theory should find the course relevant.
PrerequisitesThis is a theoretical course that will require mathematical maturity (in particular, the ability to understand and write formal mathematical proofs) and familiarity with algorithms and NP-completeness. The relevant prerequisites at IIT Delhi are COL202/MTL180 (Discrete Mathematical Structures) and COL351/MTL342 (Analysis and Design of Algorithms). The course does not require any background in economics. Please get in touch with Rohit before the start of the course if you have any questions about the prerequisites.
Reference textFrequent references will be Handbook of Computational Social Choice (available in IITD library), Trends in Computational Social Choice (available in IITD library), and Online and Matching-Based Market Design (password:OMBMD_CUP), although individual lectures will refer to different books and papers that will be shared in the table below.
Admin
Lecture timings+venueMon+Thurs 3:30-5:00 PM IST, Venue TBA.
Announcements will be made on the Microsoft Teams channel.
By email.
Evaluation policyThe evaluation will be based on four assignments (10% each), in-class quizzes (30%), and a research project (30%). Depending on the class size, it may be possible to do the assignments and projects in groups. For quizzes, the three worst scores will be dropped.
For the project, you will be expected to read a paper (or a set of closely related papers); a suggestive list is here. The deliverables will include a presentation and a report. There will also be a mid-term project update meeting.
Your final presentation and report should clearly convey the problem studied by the paper(s), the status of prior work, the main contribution of the paper(s) and why you think it is novel and interesting, as well as directions for future research. There will be a significant weightage for new observations and insights, so you are strongly encouraged to present those as well.
How to registerEmail Rohit with information about your prior coursework and relevant research experience.
Date | Topic | References | |
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Part I: Matching | |||
Lecture 1 Jan 02 (Thurs) |
The Stable Matching Problem Introduction to the course and basics of the stable matching problem. |
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Lecture 2 Jan 06 (Mon) |
Structure of Stable Matchings The lattice of stable matchings, and the story of consensus and conflict. |
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Lecture 3 Jan 09 (Thurs) |
Manipulation in Stable Matching Problem The conflict between stability and truthfulness (and some workarounds). |
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Lecture 4 Jan 13 (Mon) |
Fairness in Stable Matching Problem Using linear programming to find a median stable matching. |
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Assignment 1 |
PDF, .tex file, and solutions. |
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Lecture 5 Jan 20 (Mon) |
Many-To-One Stable Matchings Reduction to canonical one-to-one problem, Rural hospitals theorem, and manipulation via capacity modification. |
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Lecture 6 Jan 23 (Thurs) |
House Allocation and Kidney Exchange Top-trading cycle algorithm and its application to kidney exchange. |
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Part II: Fair Division | |||
Lecture 7 Jan 27 (Mon) |
Cake Cutting Algorithms for proportional and envy-free cake division. |
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Lecture 8 Jan 30 (Thurs) |
Fair Allocation of Indivisible Goods Algorithms for achieving envy-freeness up to one good. |
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Lecture 9 Feb 03 (Mon) |
Fairness and Efficiency Simultaneously achieving approximate envy-freeness and Pareto optimality. |
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Assignment 2 |
PDF, .tex file, and solutions. |
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Lecture 10 Feb 06 (Thurs) |
Towards Stronger Fairness Guarantees Achieving envy-freeness up to any good by discarding some of the resources. |
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Lecture 11 Feb 10 (Mon) |
Mid-Term Project Presentations |
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Lecture 12 Feb 13 (Thurs) |
Fair Allocation of Indivisible Chores Approximately envy-free allocation of undesirable indivisible resources: Top-trading cycle strikes back! |
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Lecture 13 Feb 17 (Mon) |
Rent Division Using Sperner's lemma to achieve rental harmony. |
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Lecture 14 Feb 20 (Thurs) |
Fairness for a Mixture of Resources Fairly dividing a mixture of divisible and indivisible resources. (Envy-cycle strikes back!) |
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Lecture 15 Mar 03 (Mon) |
Fairness through Randomness Finding a randomized allocation that satisfies best-of-both-worlds (i.e., ex-ante and ex-post) fairness. |
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Part III: Voting | |||
Lecture 16 Mar 06 (Thurs) |
Voting Rules Introduction to voting rules and their axiomatic properties. |
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Lecture 17 Mar 17 (Mon) | Manipulation in Voting Gibbard-Satterthwaite and Arrow's theorems. |
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Assignment 3 |
PDF, .tex file, and solutions. |
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Lecture 18 Mar 20 (Thurs) |
Computational Barriers to Manipulation Or why NP-hardness isn't always a bad thing. |
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Lecture 19 Mar 24 (Mon) |
Voting with Structured Preferences Circumventing impossibility results under single-peaked preferences. |
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Lecture 20 Mar 27 (Thurs) |
Rank Aggregation Computational aspects of Kemeny rule. |
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Lecture 21 Apr 03 (Thurs) |
Distortion of Voting Rules A quantitative approach to voting. |
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Part IV: Modern Paradigms | |||
Lecture 22 Apr 07 (Mon) |
Multiwinner Voting I How to elect a representative committee? |
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Assignment 4 |
PDF, .tex file, and solutions. |
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Lecture 23 Apr 12 (Sat) Thursday timetable |
Multiwinner Voting II More ABC rules and more axioms. |
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Lecture 24 Apr 14 (Mon) |
Participatory Budgeting |
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Lecture 25 Apr 17 (Thurs) |
SAT Solving I: Introduction |
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Lecture 26 Apr 21 (Mon) |
SAT Solving II: Applications in COMSOC |
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Lecture 27 Apr 24 (Thurs) |
Final Project Presentations |
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Lecture 28 Apr 28 (Mon) |
Final Project Presentations |
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