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ORIE 4360/5360: Algorithms for Democracy

Cornell University · Fall 2026

Logistics

Instructor: Paul Gölz (mail@paulgoelz.de)

TA: Gabriel Morete de Azevedo (gm587@cornell.edu)

Lectures: Mon/Wed 2:55–4:10 p.m.

Location: Bard Hall 140

Office Hours: TBD

Links: Canvas, Ed Discussion

Course Description

This course uses mathematics, algorithms, and optimization to understand and improve democratic decision-making, from familiar institutions to novel ones. Topics will most likely include:

  • Arrow's and Gibbard-Satterthwaite impossibilities
  • Domain restrictions
  • Epistemic voting and liquid democracy
  • Multi-winner approval elections and participatory budgeting
  • Cardinal welfarism
  • Implicit utilitarian voting (distortion)
  • Apportionment
  • Power indices
  • Sortition

Technical tools include the axiomatic method, notions of fairness and proportionality, mathematical programming, and social welfare functions.

Resources

Syllabus: PDF (Cornell only)

Prerequisites: Basic probability and algorithms. Mathematical maturity is expected, including following proof sketches in class and writing proofs in homework.

Textbook: The Handbook of Computational Social Choice is the most useful single resource; it is freely downloadable from Cambridge University Press as a password-protected PDF (password: cam1CSC). Much of the course material is recent enough that it only appears in papers; references will be posted with each lecture's slides.

Schedule

Subject to change. Slides will be posted as the semester progresses.

# Date Topic Slides
1 Mon Aug 24 TBA
2 Wed Aug 26 TBA
3 Mon Aug 31 TBA
4 Wed Sep 02 TBA
Mon Sep 07 🛠️ Labor Day — no class
5 Wed Sep 09 TBA
6 Mon Sep 14 TBA
7 Wed Sep 16 TBA
8 Mon Sep 21 TBA
9 Wed Sep 23 TBA
10 Mon Sep 28 TBA
11 Wed Sep 30 TBA
12 Mon Oct 05 TBA
13 Wed Oct 07 TBA
Mon Oct 12 🍂 Fall break — no class
14 Wed Oct 14 TBA
15 Mon Oct 19 TBA
16 Wed Oct 21 TBA
17 Mon Oct 26 TBA
18 Wed Oct 28 TBA
19 Mon Nov 02 TBA
20 Wed Nov 04 TBA
21 Mon Nov 09 TBA
22 Wed Nov 11 TBA
23 Mon Nov 16 TBA
24 Wed Nov 18 TBA
25 Mon Nov 23 TBA
Wed Nov 25 🥧 Thanksgiving break — no class
26 Mon Nov 30 TBA
27 Wed Dec 02 TBA
28 Mon Dec 07 TBA

Grading

Subject to change. Full policies are on the syllabus (Canvas).

ComponentWeight
Problem Sets20%
Prelim 120%
Prelim 220%
Final Exam30%
Participation10%
  • Problem sets are assigned roughly every two weeks. Late submissions are not accepted.
  • You may discuss problem sets with others, but must write up your own solutions, and AI tools are not allowed unless stated otherwise.
  • Two 75-minute in-class prelims plus a cumulative final exam, each closed-book with one handwritten sheet of notes allowed.
  • Participation includes in-class polls (PollEverywhere) and engagement in lecture, office hours, and on Ed.