COL866: Special Topics in Algorithms, Fall Semester 2023
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 a strong grasp of algorithms and computational complexity (in particular, concepts such as linear programming duality, greedy algorithms, NP-completeness). The relevant prerequisites at IIT Delhi are COL202 (Discrete Mathematical Structures) and COL351 (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+venueTue+Fri 3:30-5PM IST, Venue LH 606.
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 project 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 registerSend an email to Rohit with information about your prior coursework and relevant research experience.
Date | Topic | References | |
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Part I: Matching | |||
Lecture 1 July 25 (Tue) |
The Stable Matching Problem Introduction to the course and basics of the stable matching problem. |
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Lecture 2 July 28 (Fri) |
Structure of Stable Matchings The lattice of stable matchings, and the story of consensus and conflict. |
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Lecture 3 Aug 01 (Tue) |
Manipulation in Stable Matching Problem The conflict between stability and truthfulness (and some workarounds). |
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Lecture 4 Aug 04 (Fri) |
Fairness in Stable Matching Problem Using linear programming to find a median stable matching. |
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Aug 08 (Tue) |
No lecture |
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Lecture 5 Aug 11 (Fri) |
Many-To-One Stable Matchings Reduction to canonical one-to-one problem, Rural hospitals theorem, and manipulation via capacity modification. |
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Assignment 1 |
PDF, .tex file, and solutions. |
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Lecture 6 Aug 18 (Fri) |
House Allocation and Kidney Exchange Top-trading cycle algorithm and its application to kidney exchange. |
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Part II: Fair Division | |||
Aug 19 (Sat) Friday timetable |
No lecture |
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Aug 22 (Tue) |
No lecture |
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Lecture 7 Aug 25 (Fri) |
Cake Cutting Algorithms for proportional and envy-free cake division. |
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Lecture 8 Aug 29 (Tue) |
Fair Allocation of Indivisible Goods Algorithms for achieving envy-freeness up to one good. |
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Assignment 2 |
PDF, .tex file, and solutions. |
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Lecture 9 Sep 01 (Fri) |
Fairness and Efficiency Simultaneously achieving approximate envy-freeness and Pareto optimality. |
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Lecture 10 Sep 05 (Tue) |
Towards Stronger Fairness Guarantees Achieving envy-freeness up to any good by discarding some of the resources. |
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Lecture 11 Sep 08 (Fri) |
Mid-Term Project Presentations |
Project Groups Omkar Shitole Dominant Resource Fairness: Fair Allocation of Multiple Resource Types Vedant Mukesh Deo and Jatin Yadav A Size-Popularity Tradeoff in the Stable Matching Problem Divyansh Mittal and Vaibhav Agarwal How to Cut a Cake Before the Party Ends Era Sarda Fair Division of a Graph Tanish Agarwal and Utsav Krishna Jaiswal Scarf’s Algorithm and Stable Marriages Shivam Kanojia Centralized Admissions for Engineering Colleges in India Mayank Mangla and Ramanuj Goel Fair Division of Time: Multi-Layered Cake Cutting |
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Lecture 12 Sep 19 (Tue) |
Fair Allocation of Indivisible Chores Approximately envy-free allocation of undesirable indivisible resources: Top-trading cycle strikes back! |
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Lecture 13 Sep 26 (Tue) |
Rent Division Using Sperner's lemma to achieve rental harmony. |
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Lecture 14 Sep 29 (Fri) |
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 15 Oct 10 (Tue) |
Voting Rules Introduction to voting rules and their axiomatic properties. |
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Lecture 16 Oct 13 (Fri) |
Manipulation in Voting Gibbard-Satterthwaite and Arrow's theorems. |
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Oct 14 (Sat) Friday timetable |
No lecture |
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Assignment 3 |
PDF, .tex file, and solutions. |
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Lecture 17 Oct 17 (Tue) |
Computational Barriers to Manipulation Or why NP-hardness isn't always a bad thing. |
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Lecture 18 Oct 20 (Fri) |
Voting with Structured Preferences Circumventing impossibility results under single-peaked preferences. |
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Lecture 19 Oct 27 (Fri) |
Rank Aggregation Computational aspects of Kemeny rule. |
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Lecture 20 Oct 31 (Tue) |
Distortion of Voting Rules A quantitative approach to voting. |
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Part IV: Modern Paradigms | |||
Lecture 21 Nov 03 (Fri) |
Multiwinner Voting - I |
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Assignment 4 |
PDF, .tex file, and solutions. |
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Nov 07 (Tue) |
No lecture: Office hours |
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Lecture 22 Nov 10 (Fri) |
Multiwinner Voting - II |
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Lecture 23 Nov 14 (Tue) |
Final Project Presentations |
Project Groups Divyansh Mittal and Vaibhav Agarwal How to Cut a Cake Before the Party Ends Mayank Mangla and Ramanuj Goel Fair Division of Time: Multi-Layered Cake Cutting Shivam Kanojia Centralized Admissions for Engineering Colleges in India |
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Lecture 24 Nov 17 (Fri) |
Final Project Presentations |
Project Groups Vedant Mukesh Deo and Jatin Yadav A Size-Popularity Tradeoff in the Stable Matching Problem Tanish Agarwal and Utsav Krishna Jaiswal Scarf’s Algorithm and Stable Marriages Era Sarda Fair Division of a Graph Omkar Shitole Dominant Resource Fairness: Fair Allocation of Multiple Resource Types |