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.

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 a strong grasp of algorithms and computational complexity (so, COL351 or an equivalent course). We will not assume any background in economics.

Reference text

Frequent 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+venue

Tue,Fri 3:30-5PM at IV LT-1 (Block IV). Location on Google Maps.
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), 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 register

Send an email to Rohit with information about your prior coursework and relevant research experience.

Date Topic References
Part I: Matching
Lecture 1
Aug 05 (Fri)
The Stable Matching Problem
Introduction to the course and basics of the stable matching problem.
Lecture 2
Aug 06 (Sat)
Structure of Stable Matchings
The lattice of stable matchings, and the story of consensus and conflict.
Lecture 3
Aug 12 (Fri)
Manipulation in Stable Matchings
The conflict between stability and truthfulness (and some workarounds).
Lecture 4
Aug 16 (Tue)
A Linear Programming Approach Towards Stability
Using linear programs to find a "fair" stable matching.
Assignment 1
  • Announced: Aug 17, 2022 (Wed)
  • Due: Aug 26, 2022 (Fri)
Lecture 5
Aug 23 (Tue)
One-Sided Matching
Top-trading cycle algorithm and its application to kidney exchange.
Part II: Fair Division
Lecture 6
Aug 26 (Fri)
Cake Cutting
Algorithms for proportional and envy-free cake division.
Lecture 7
Aug 30 (Tue)
Rent Division
Using Sperner's lemma to achieve rental harmony.
Lecture 8
Sep 02 (Fri)
Indivisible Goods
Algorithms for achieving envy-freeness up to one good.
Assignment 2
  • Announced: Sep 05, 2022 (Tue)
  • Due: Sep 17, 2022 (Sat)
Lecture 9
Sep 06 (Tue)
Fairness and Efficiency
Simultaneously achieving approximate envy-freeness and Pareto optimality.
Lecture 10
Sep 09 (Fri)
Indivisible Chores
Fair allocation of undesirable resources (top-trading cycle strikes back!).
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

Part III: Voting
Lecture 12
Sep 23 (Fri)
Voting Rules
Introduction to voting rules and their axiomatic properties.
Lecture 13
Oct 07 (Fri)
Manipulation of Voting Rules
Gibbard-Satterthwaite and Arrow's theorems.
Lecture 14
Oct 08 (Sat)
Computational Barriers to Manipulation
Or why NP-hardness isn't always a bad thing.
Lecture 15
Oct 11 (Tue)
Structured Preferences
Algorithms for restricted preference domains.
Assignment 3
  • Announced: Oct 12, 2022 (Wed)
  • Due: Oct 21, 2022 (Fri)
Part IV: Modern Paradigms
Lecture 16
Oct 25 (Tue)
Multiwinner Voting - I
Lecture 17
Oct 28 (Fri)
Multiwinner Voting - II
Lecture 18
Nov 01 (Tue)
Rank Aggregation
Computational aspects of Kemeny rule.
Lecture 19
Nov 04 (Fri)
Distortion of Voting Rules
A quantitative approach to voting.
Assignment 4
  • Announced: Nov 05, 2022 (Sat)
  • Due: Nov 17, 2022 (Thu)
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

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?
Project Suggestions
Voting
Matching
Fair Division