Computational Social Choice (IN2229)
Prof. Dr. Felix Brandt
Patrick Lederer, René Romen
Lecture and Tutorials in WS 22/23
Organization
→ Lecture Livestream and Recordings
Lecture: Tuesdays, 16:15 - 18:45 (first lecture: 18 Oct 2022), HS2 (FMI building)
- Tutorials: We offer four tutorial sessions, all of which cover the same content (first tutorial on 24 Oct 2022):
- Monday, 10:00 - 12:00, Room 03.13.010
- Monday, 12:00 - 14:00, Room 01.10.011
- Tuesday, 10:00 - 12:00, Room 01.10.011
- Tuesday, 12:00 - 14:00, Room 01.10.011
- SWS: 3+2
- Credits: 6
- Registration: Via TUMonline for the lecture and the tutorials
- Classification: "Algorithmen" (ALG)
- Module decription: IN2229
- Language: English
- Exam: Tentative date: 03.03.23 14:15 to 16:15. The exam will take place in person in Garching!
IMPORTANT NOTICE: This is a theory course. It is expected that participants are familiar with formal mathematics and standard proof techniques. Addtionally, basic knowledge about NP-completeness is useful (e.g., Module IN0011).
Content
Social choice theory deals with the aggregation of individual preferences into a collective choice such as in voting. This course focusses on the analysis and comparison of aggregation functions that are based on simple majority rule. After introducing the mathematical and microeconomic foundations of social choice theory, particular attention will be paid to algorithmic aspects.
Tentative list of topics:
- Preferences
- Voting rules
- Rational choice theory (rationalizability, consistency)
- May's theorem
- Arrow's impossibility theorem
- Scoring rules
- Condorcet rules (Top cycle, Uncovered set, Banks set, Minimal covering set, Bipartisan set, Kemeny-Young rule)
- McGarvey's theorem
- Computational complexity of voting rules
- Strategic manipulation (Gibbard-Satterthwaite Theorem)
Exercises
Exercises are voluntary, but highly recommended. Each exercise sheet will contain tutorial exercises (T) and homework exercises (H). If you correctly solve at least 60 per cent of (H) exercises and pass the exam with a grade between 1.3 and 4.0, your final grade will be your exam grade minus 0.3 (for example, the grade 1.7 will be turned into 1.4).
Exercise sheets will be made available each Tuesday. They are due the following Sunday. Submission is possible via Moodle.
Homework exercises are to be solved in teams of three students.
Exam
There will be a written exam at the end of the semester, which will be graded according to the following (tentative) grading scale:
- [0,5) points: 5,0
- [5,11) points: 4,7
- [11,17) points: 4,3
- [17,19] points: 4,0
- (19,22] points: 3,7
- (22,24] points: 3,3
- (24,26] points: 3,0
- (26,28] points: 2,7
- (28,30] points: 2,3
- (30,32] points: 2,0
- (32,34] points: 1,7
- (34,36] points: 1,3
- (36,40] points: 1,0
The only resource you may use during the exam are two hand-written sheets of DIN A4 paper that you prepared yourself (you may write on both sides of each sheet). In particular, electronic devices, books, photocopies, and printouts are disallowed.
The exam will be in English. If need be, answers in German are acceptable, too.
Please remember to bring your student id (or an equivalent photo id).
We will notify you by email when the grades are available in TUMonline.
Literature
There is no textbook that covers all the topics listed above. Lecture slides will be published on a weekly basis. You can learn more about the computational social choice community here.
Available online:
- F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia. Handbook of Computational Social Choice, Cambridge University Press, 2016.
- F. Brandt, V. Conitzer, and U. Endriss. Computational Social Choice. In "Multiagent Systems" (G. Weiss, ed.), MIT Press, 2012.
- Y. Chevaleyre, U. Endriss, J. Lang, and N. Maudet. A Short Introduction to Computational Social Choice. In Proceedings of the 33rd Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM-2007), LNCS 4362, Springer-Verlag, 2007.
- P. Faliszewski, E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. A Richer Understanding of the Complexity of Election Systems. In "Fundamental Problems in Computing: Essays in Honor of Professor Daniel J. Rosenkrantz" (S. Ravi and S. Shukla, eds.), Springer-Verlag, 2007.
Recommended advanced books:
- D. Austen-Smith and J. Banks: Positive Political Theory I, University of Michigan Press, 1999.
- W. Gärtner: A Primer in Social Choice Theory, Oxford University Press, 2009.
- J. Laslier. Tournament Solutions and Majority Voting, Springer-Verlag, 1997.
- H. Moulin. Axioms of Cooperative Decision Making, Cambridge University Press, 1988.
- S. Nitzan. Collective Preference and Choice, Cambridge University Press, 2010
- A. Taylor. Social Choice and the Mathematics of Manipulation, Cambridge University Press, 2005.
Refresher on basic mathematical concepts and proof techniques
You may consult this document by Itzhak Gilboa or this document by Walter Bossert (the latter covers much more than we need in this course). Michael Sipser's book "An Introduction to the Theory of Computation" also contains a good introduction to basic mathematical concepts and proof techniques.
Related courses:
- Computational Social Choice by Ulle Endriss, University of Amsterdam, Netherlands
- Computational Social Choice by Lirong Xia, Rensselaer Polytechnic Institute, USA
- Algorithmische Eigenschaften von Wahlsystemen I by Jörg Rothe, Universität Düsseldorf, Germany