COL866: Special Topics in Algorithms, Fall Semester 2022
Algorithms for Collective Decision-Making
Instructor: Rohit Vaish ()
Teaching Assistant: Nitesh Dohre ()
Course Information
What this course is about
This course will explore the mathematical foundations of collective decision-making problems, i.e., when a group decision is made based on the preferences of individual agents. These problems arise in a variety of settings, including day-to-day tasks such as a group of friends deciding how to fairly split the rent for their shared apartment as well as high-stakes scenarios such as political elections and matching applicants with jobs or organ donors with patients.
We will use tools and techniques from theoretical computer science 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 (so, COL351 or an equivalent course). We will not assume any background in economics.
Reference textFrequent references will be Handbook of Computational Social Choice (available in IITD library) and Trends in Computational Social Choice, although individual lectures will refer to different papers that will be shared in the table below.
Admin
Lecture timings+venueTue,Fri 3:30-5PM at IV LT-1 (Block IV). Location on Google Maps.
Announcements will be made on the Microsoft Teams channel.
By email.
Evaluation policyThe evaluation will be based on four assignments (10% each), class participation (20%), and a research project (40%). Depending on the class size, it may be possible to do the assignments and project in groups.
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 Aug 05 (Fri) |
The Stable Matching Problem Introduction to the course and basics of the stable matching problem. |
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Lecture 2 Aug 06 (Sat) |
Structure of Stable Matchings The lattice of stable matchings, and the story of consensus and conflict. |
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Lecture 3 Aug 12 (Fri) |
Manipulation in Stable Matchings The conflict between stability and truthfulness (and some workarounds). |
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Lecture 4 Aug 16 (Tue) |
A Linear Programming Approach Towards Stability Using linear programs to find a "fair" stable matching. |
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Assignment 1 |
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Lecture 5 Aug 23 (Tue) |
One-Sided Matching Top-trading cycle algorithm and its application to kidney exchange. |
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Part II: Fair Division | |||
Lecture 6 Aug 26 (Fri) |
Cake Cutting Algorithms for proportional and envy-free cake division. |
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Lecture 7 Aug 30 (Tue) |
Rent Division Using Sperner's lemma to achieve rental harmony. |
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Lecture 8 Sep 02 (Fri) |
Indivisible Goods Algorithms for achieving envy-freeness up to one good. |
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Assignment 2 |
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Lecture 9 Sep 06 (Tue) |
Fairness and Efficiency Simultaneously achieving approximate envy-freeness and Pareto optimality. |
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Lecture 10 Sep 09 (Fri) |
Indivisible Chores Fair allocation of undesirable resources (top-trading cycle strikes back!). |
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Lecture 11 Sep 20 (Tue) |
Mid-Term Project Presentations |
Project Groups Parth Gupta, Rayyan Shahid, and Rishi Sarraf Which Is the Fairest (Rent Division) of Them All? Mukku Vamsi Krishna Reddy, Alladi Ajay, and Surbhi Rajput A Little Charity Guarantees Almost Envy-Freeness Gorle Kunal Kaushik, Nallani Sai Venkata Kartheek, and Nalla Khyateeswar Naidu Fair Division of Time: Multi-layered Cake Cutting Chirag Bansal, Lakshay Saggi, and Mohit Sharma Fair Division with Subsidy Sourav Bansal, Manav Bansal, and Dipanshu Patidar On the Stable Matchings that Can be Reached When the Agents Go Marching in One by One Harshavardhan Baheti, Chirag Mohapatra, and Vishal Bindal Proportionality and the Limits of Welfarism Anoushka Barthakur and Shreya Gupta A Bounded and Envy Free Cake Cutting Algorithm/ Computer Aided Methods for Social Choice Theory |
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Part III: Voting | |||
Lecture 12 Sep 23 (Fri) |
Voting Rules Introduction to voting rules and their axiomatic properties. |
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Lecture 13 Oct 07 (Fri) |
Manipulation of Voting Rules Gibbard-Satterthwaite and Arrow's theorems. |
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Lecture 14 Oct 08 (Sat) |
Computational Barriers to Manipulation Or why NP-hardness isn't always a bad thing. |
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Lecture 15 Oct 11 (Tue) |
Structured Preferences Algorithms for restricted preference domains. |
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Assignment 3 |
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Part IV: Modern Paradigms | |||
Lecture 16 Oct 25 (Tue) |
Multiwinner Voting - I |
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Lecture 17 Oct 28 (Fri) |
Multiwinner Voting - II |
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Lecture 18 Nov 01 (Tue) |
Rank Aggregation Computational aspects of Kemeny rule. |
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Lecture 19 Nov 04 (Fri) |
Distortion of Voting Rules A quantitative approach to voting. |
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Assignment 4 |
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Lecture 20 Nov 11 (Fri) |
Final Project Presentations - I |
Project Groups Mukku Vamsi Krishna Reddy, Alladi Ajay, and Surbhi Rajput A Little Charity Guarantees Almost Envy-Freeness Gorle Kunal Kaushik, Nallani Sai Venkata Kartheek, and Nalla Khyateeswar Naidu Fair Division of Time: Multi-layered Cake Cutting Harshavardhan Baheti, Chirag Mohapatra, and Vishal Bindal Proportionality and the Limits of Welfarism Chirag Bansal, Lakshay Saggi, and Mohit Sharma Fair Division with Subsidy |
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Lecture 21 Nov 15 (Tue) |
Final Project Presentations - II |
Project Groups Anoushka Barthakur and Shreya Gupta Computer Aided Methods for Social Choice Theory Sourav Bansal, Manav Bansal, and Dipanshu Patidar On the Stable Matchings that Can be Reached When the Agents Go Marching in One by One Parth Gupta, Rayyan Shahid, and Rishi Sarraf Which Is the Fairest (Rent Division) of Them All? |