PS 491/711: Social Choice Theory

Spring 2000 Place/Time: FB B1 T-R 2-3:15

Dr. Matthew Gabel Office: POT 1631

e-mail: mjgabe1@pop.uky.edu Office Hours: Tues. 3:30-4:30

website: www.uky.edu/%7Emjgabe1/ Thurs. 12-2

This course is designed to provide students (particularly graduate students) with the necessary skills to read and evaluate formal models as applied to political science questions. In other words, the goal is for students to achieve a basic literacy in formal models in political science. To this end, the course will introduce students to the basic concepts and tools of game theory and social choice theory and use these tools to examine formal models in international relations, comparative politics, legislative politics, and administrative/policy analysis.

The course is organized around formal theoretical tools. Each section will first introduce the relevant theoretical tool and then examine its application in political science research. The first section focuses on axiomatic social choice theory, which has important (indeed, worthy of a Nobel prize) implications for democratic theory and constitutional design. The second section develops the spatial model, which has applications to electoral competition and legislative bargaining. The third section introduces normal form games and their solutions. This encompasses probably the most common applications of game theory to political scenarios--including the Prisoner's Dilemma. In the fourth section we focus on extensive form games, including signaling games and repeated-play games. These games are commonly applied to issues of international relations.

There are no pre-requisites for the course. However, the language of formal models and their application in political science is often mathematical and symbolic, so a familiarity with mathematical notation is helpful. The appendix to the Morrow book cited below may serve as useful references for students not familiar with technical aspects of formal models. Also, many applications in political science are borrowed from economics. These analogies will obviously be more intuitive if students understand some basic economics. Consequently, students may want to refer to a basic microeconomics text.

Assignments:

The grade for the course will consist of four components.

1. Problem Sets: For each section, students will complete a "problem set" concerning the formal models at issue. In other words, students will need to demonstrate a basic competency in the formal tools by solving formal problems (40%).

2. Article Review: For each section, students will find an article from a political science journal (must gain approval of instructor) and write a review. The article cannot be an article used in the course. The review will have the following components: (1) identify the theoretical question at issue, (2) identify the formal modeling technique used to address this question, (3) assess the applicability of the model to the political question and consider its limitations and possible remedies. The review should be no longer than 1000 words (40%).

3. Class Participation: Students are expected to have completed the reading BEFORE class and participate in course discussion (20%).

Reminders:

Writing Quality: Persuasive writing is an important skill. I expect students to write correctly. Specifically, I will grade written assignments up to the point where I find five writing (including spelling) errors. The first time this happens, I will allow the student to re-write the paper, with a penalty of a letter grade. The second time this happens, I will simply grade based on the material read. Word to the wise: proofread!

Cheating and Plagiarism: According to University Rules, the minimum punishment for

cheating or plagiarism is an "E".

For further information on definitions of cheating and plagiarism and on university policies on grading and absences, see the university document at http://www.uky.edu/StudentAffairs/Code/part2.html .

Books and Readings:

The following books are available in the UK bookstore and at www.bigwords.com , where the B-CODE for this course is B-2BGPGY.

Required books:

1. Dixit, Avinash and Susan Skeath. Games of Strategy. WW Norton.

2. Shepsle, Kenneth and Mark Bonchek. Analyzing Politics. WW Norton.[1]

Recommended books:

3. Dixit, Avinash and Barry Nalebuff. Thinking Strategically. WW Norton.

4. Morton, Rebecca. Methods and Models. Cambridge.

5. Morrow, James. Game Theory for Political Scientists. Princeton.

Articles:

Readings on applications in political science will be made available via the internet or in a box in the graduate student lounge (POT 1643)

Tentative Schedule

Date	Topic	Readings
January 13	Introduction	Two Cheers for Formalism Game Theory D & N, ch. 1 D & S, ch.1 Morton, chs. 1,2, 3, and 5 S & B, ch. 1
January 18	Formalizing Preferences and Social Choice	S & B, chs. 2-3, 7 D & S, ch. 14 (part 1)
January 20-27	Evaluating Social Choice Rules: Binary Choice Rules, The Condorcet Jury Theorem, and Choice Over More Than Two Alternatives	S & B, chs. 4, 6 D & S, ch. 14 (part 2)
Feb. 1	Arrow's Theorem	S & B, ch. 4
Feb. 3	Applications in Political Science	TBA
Feb. 8-10	Utility and Expected Utility Theory	D & N, ch. 1 S & B, ch. 2 Morton, Ch. 4
Feb. 15	Spatial Models of Voting (one dimension)	S & B, ch. 5 Morton, ch. 4 D & N ch. 10 (sections 1-2) D & S, ch. 14 (part 5)
Feb. 17	Spatial Model of Voting (multiple dimensions)	S & B, chs. 3 and 7
Feb. 22	Applications of the Spatial Model to Legislatures	TBA
Feb. 24	Agenda Setting, Strategic Voting and Logrolling	S& B, ch. 6 D & N, ch. 10 D & S, ch. (part 4)
February 29	Games in Normal Form	D & N, ch. 3 D & S, chs. 1-2 S & B, ch. 8
March 2	Dominant Strategy Equilibria and Nash Equilibria	D & N, ch. 3 D & S, ch. 4
March 7	Mixed Strategy Equilibria	D & N, ch. 6-7 D & S, ch. 5
March 9	Games in Extensive Form	D & N, ch. 2 D & S, ch. 3
March 21	Subgame Perfection and Credible Threats	D & N, ch. 6 D & S, ch. 6
March 23	Applications in Political Science	TBA
March 28	Games of Incomplete Information	D & S, ch. 12
March 30	Costly Singalling Games	TBA
April 4	Applications in Political Science	TBA
April 6	Cheap Talk Signalling Games	Austen-Smith (in box)
April 11	Applications in Political Science	TBA
April 13-20	Repeated Play Games (see Smith syllabus)	S & B, ch. 8 N & D, chs. 4-5, 9, 11 D & S, ch. 8
April 25	Applications to Political Science	TBA
April 27	no class (at conference)

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[1] This book has its own website at: http://www.wwnorton.com/college/polisci/analyzing/webbook/home.html