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.

Who is this course aimed at

Students interested in research on algorithmic aspects of economics and game theory should find the course relevant.

Prerequisites

This 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 text

Frequent 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+venue

Mon+Thurs 3:30-5:00 PM IST, Venue TBA.
Announcements will be made on the Microsoft Teams channel.

Office hours

By email.

Evaluation policy

The 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 register

Email Rohit with information about your prior coursework and relevant research experience.

Date Topic References
Part I: Matching
Lecture 1
Jan 02 (Thurs)
The Stable Matching Problem
Introduction to the course and basics of the stable matching problem.
Lecture 2
Jan 06 (Mon)
Structure of Stable Matchings
The lattice of stable matchings, and the story of consensus and conflict.
    
  • Slides (TBA)
  • Gale and Sotomayor (1985)
  • Chapter 3 in the book by Roth and Sotomayor (1990); IITD library has a copy.
  • Sec 1.4 of market design book
Lecture 3
Jan 09 (Thurs)
Manipulation in Stable Matching Problem
The conflict between stability and truthfulness (and some workarounds).
Lecture 4
Jan 13 (Mon)
Fairness in Stable Matching Problem
Using linear programming to find a median stable matching.
Assignment 1
PDF, .tex file, and solutions.
  • Announced: Jan 19 (tentative)
  • Due: Jan 28 (tentative)
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.
Lecture 6
Jan 23 (Thurs)
House Allocation and Kidney Exchange
Top-trading cycle algorithm and its application to kidney exchange.
Part II: Fair Division
Lecture 7
Jan 27 (Mon)
Cake Cutting
Algorithms for proportional and envy-free cake division.
Lecture 8
Jan 30 (Thurs)
Fair Allocation of Indivisible Goods
Algorithms for achieving envy-freeness up to one good.
Lecture 9
Feb 03 (Mon)
Fairness and Efficiency
Simultaneously achieving approximate envy-freeness and Pareto optimality.
Assignment 2
PDF, .tex file, and solutions.
  • Announced: Feb 06 (tentative)
  • Due: Feb 15 (tentative)
Lecture 10
Feb 06 (Thurs)
Towards Stronger Fairness Guarantees
Achieving envy-freeness up to any good by discarding some of the resources.
Lecture 11
Feb 10 (Mon)
Mid-Term Project Presentations

Lecture 12
Feb 13 (Thurs)
Fair Allocation of Indivisible Chores
Approximately envy-free allocation of undesirable indivisible resources: Top-trading cycle strikes back!
Lecture 13
Feb 17 (Mon)
Rent Division
Using Sperner's lemma to achieve rental harmony.
Lecture 14
Feb 20 (Thurs)
Fairness for a Mixture of Resources
Fairly dividing a mixture of divisible and indivisible resources. (Envy-cycle strikes back!)
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.
Part III: Voting
Lecture 16
Mar 06 (Thurs)
Voting Rules
Introduction to voting rules and their axiomatic properties.
Lecture 17
Mar 17 (Mon)
Manipulation in Voting
Gibbard-Satterthwaite and Arrow's theorems.
Assignment 3
PDF, .tex file, and solutions.
  • Announced: Mar 17 (tentative)
  • Due: Mar 26 (tentative)
Lecture 18
Mar 20 (Thurs)
Computational Barriers to Manipulation
Or why NP-hardness isn't always a bad thing.
Lecture 19
Mar 24 (Mon)
Voting with Structured Preferences
Circumventing impossibility results under single-peaked preferences.
Lecture 20
Mar 27 (Thurs)
Rank Aggregation
Computational aspects of Kemeny rule.
Lecture 21
Apr 03 (Thurs)
Distortion of Voting Rules
A quantitative approach to voting.
Part IV: Modern Paradigms
Lecture 22
Apr 07 (Mon)
Multiwinner Voting I
How to elect a representative committee?
Assignment 4
PDF, .tex file, and solutions.
  • Announced: Apr 11 (tentative)
  • Due: Apr 20 (tentative)
Lecture 23
Apr 12 (Sat)
Thursday timetable
Multiwinner Voting II
More ABC rules and more axioms.
Lecture 24
Apr 14 (Mon)
Participatory Budgeting
Lecture 25
Apr 17 (Thurs)
SAT Solving I: Introduction
  • Slides (TBA)
Lecture 26
Apr 21 (Mon)
SAT Solving II: Applications in COMSOC
  • Slides (TBA)
Lecture 27
Apr 24 (Thurs)
Final Project Presentations
Lecture 28
Apr 28 (Mon)
Final Project Presentations
Project Suggestions
Voting
Matching
Fair Division