Social Choice Theory is the formal analysis of collective decision making. A growing number of logical systems incorporate insights and ideas from this important field. This course will introduce the key results (including proofs) and the main research themes of Social Choice Theory. The primary objective is to introduce the main mathematical methods and conceptual ideas found in the Social Choice literature. I will also pay special attention to recent logical systems that have been developed to reason about group decision making and how social choice-style analyses are being used by logicians.
Specific topics include:
- Proofs of key Social
Choice results (e.g., Arrow’s Impossibility Theorem, Sen’s Impossibility of the Paretian Liberal, Müller-Satterthwaite Theroem, Harsanyi's Utilitarian Theorem, and
the Gibbard-Satterthwaite Theorem)
- Responses to Arrow's Theorem (e.g., Domain Restrictions, such as Sen's Value Restriction and Black's Single-Peakedness Condition)
- Axiomatic characterizations of voting procedures (May’s Characterization of the majority rule, Maskin’s Characterization of majority rule, Fishburn’s
Characterization of Approval Voting, Young’s Characterization of positional voting, Saari’s
characterization of Borda Count)
- Voting paradoxes (e.g., Condorcet’s paradox, Anscombe’s Paradox, the No-Show Paradox)
- Generalizations of the classic framework (e.g., assuming there are infinitely many voters)
- Judgement aggregation (e.g., Dietrich-List impossibility theorem)
- The Condorcet Jury Theorem and its many variants
- Logics for reasoning about
preference aggregation (modal logics for preference aggregation, dependence and independence logic for social choice theory).
The course will not only provide a broad overview of the field of Social Choice from a logicians perspective, but will also discuss key technical results of particular interest to logicians. The main goal is to provide a solid foundation for students that want to incorporate
results and ideas from Social Choice Theory into their field of study. I will also explore the to what extent modal and preference logics can faithfully formalize key results in social choice theory.