Practical rationality syllabus Course overview This is a course about individual, strategic and social choice. The first, largest section of the course is on individual rationality: decision theory. This is the theory of how one ought to make decisions under uncertainty. Second we look at game theory: the theory of strategic choices. These are cases where an agent is faced with responding to the actions of other agents. Finally we look at social choice: how should preferences of individuals be aggregated into group preferences? The aim throughout is to draw out the philosophical questions raised by these formal theories. Some level of mathematical sophistication is, therefore, required. However, the technical details will be kept to a minimum: you won t be expected to prove any theorems, or to understand the details of the theorems we discuss. Though, of course, engaging with the formal details is encouraged for those who can! It will be useful, however, if you are at least able to read some mathematics. The Mathematical Appendix of Gilboa s book will give you a useful phrasebook for understanding the mathematics we will encounter. Readings Each week there will be one or more core readings that you are expected to read. There will also be a list of supplementary readings. These serve as a starting point for exploring the literature in more depth. If you want to write your essay on a particular topic, the supplementary readings for the relevant week are a good place to start. The readings will be made available on the web. To get access to the readings, you should email me at Seamus.Bradley@lrz.uni-muenchen.de. There is no required textbook for the course. If you would like to have a textbook, the following cover a majority of the material: General textbook: Martin Peterson An Introduction To Decision Theory (Cambridge University Press, 2009). For the mathematical details: David M. Kreps Notes on the Theory of Choice (Westview Press, 1988). The reading list is still under construction. New versions of the syllabus will be made available online as and when it becomes more complete. Assessment The main assessment for the course will be by an essay. In the last week of the semester, every student will present (for 5 10 minutes) on the topic they plan to write their essay on. Essays should be around 15 pages for Masters students and around 10 pages for Bachelors students. Class The class is every week on Thursdays 1400 1600 CT in Ludwigstrasse 31, Room 0.21. Office hours are by appointment. I encourage you to email me to arrange a meeting if there are things you haven t understood. The LMU doesn t allow me to make attendance compulsory, but the course is 1
cumulative, and the readings are difficult, so if you don t come to class, you will fall behind. Summary of topics There are currently fewer weeks listed than we have this term. This is deliberate: this gives us some flexibility to spend more time on a topic that we are particularly interested in, or to come back to issues that we didn t have time to cover properly. Week 1: Basics of decision theory We will start with some simple examples of decision problems and talk about the ways one might think to solve them. We will discuss the various different concepts involved: the objects of belief, objects of value, objects of choice, preference, probability, utility. We discuss dominance, maximin and expected utility. Lara Buchak Decision Theory, in Oxford Handbook of Probability and Philosophy, ed. Christopher Hitchcock and Alan Hájek (Oxford University Press, 2013). Itzhak Gilboa Rational Choice (MIT Press, 2010)., Chapters 1 and 2 (and appendix A) Peterson An Introduction To Decision Theory., Chapters 1 and 2 Sven Ove Hansson Decision Theory, A Brief Introduction, 1994., Chapter 4 James M. Joyce The Foundations of Causal Decision Theory, Cambridge Studies in Probability, Induction and Decision Theory (Cambridge University Press, 1999)., Chapter 2 Jon Elster Introduction, in Rational Choice, ed. Jon Elster (New York University Press, 1986), 1 33. Brian Weatherson Logic of Decision Notes (http://brian.weatherson.org/decisiontheorynotes.pdf, 2011)., Chapters 1 to 4 Week 2: Representation theorems Why should we choose according to the probability-weighted sum of utilities? This method is somewhat intuitive, but can we give more justification? Representation theorems give us a positive answer to this question (sort of). We start with some simple representation theorems and work our way up to Savage s theorem. Stanley S. Stevens On the Theory of Scales of Measurement, Science 103 (1946): 677 680. Kreps Notes on the Theory of Choice., Chapter 4 Patrick Suppes and Joseph L. Zinnes Basic Measurement Theory, in Handbook of Mathematical Psychology, 1963, 1 76., Sections 1 and 2 Simon Grant and Timothy van Zandt Expected Utility Theory, in The Handbook of Rational and Social Choice, ed. Paul Anand, Prasanta K. Pattanaik, and Clemens Puppe (Oxford University Press, 2009), 21 68. Joyce The Foundations of Causal Decision Theory., Chapter 3 Alan Hájek Arguments For or Against probabilism? British Journal for the Philosophy of Science 59 (2008): 793 819. Francis John Anscombe and Robert John Aumann A Definition of Subjective Probability, The Annals of Mathematical Statistics 34 (1963): 199 205. F. P. Ramsey Truth and Probability, in The Foundations of Mathematics and Other Logical Essays (Routledge, 1926), 156 198. Richard Bradley Ramsey s Representation Theorem, Dialectica 58 (2004): 483 498. 2
Leonard J. Savage Difficulties in the Theory of Personal Probability, Philosophy of Science 34 (1967): 305 310. Itzhak Gilboa Theory of Decision Under Uncertainty (Cambridge University Press, 2009)., Chapters 10 and 12 Week 4: Risk and ambiguity This week we look at two possibly distinct kinds of uncertainty and how extensions of EU theory might distinguish them. Week 3: Dimensions of rationality Is expected utility theory a theory of how rational agents actually behave or a theory about how rational agents ought to behave? We will look at reasons to have doubts about either position. We will also discuss how to individuate the elements of decision theory. Amos Tversky and Daniel Kahneman Judgement Under Uncertainty: Heuristics and Biases, Science 185 (1974): 1124 1131. José Luis Bermúdez Decision Theory and Rationality (Oxford University Press, 2009)., Chapter 1 Lara Buchak Risk and Tradeoffs, Erkenntnis (2013). Daniel Ellsberg Risk, Ambiguity and the Savage Axioms, Quarterly Journal of Economics 75 (1961): 643 696. Matthew Rabin and Richard H. Thaler Anomalies: Risk Aversion, Journal of Economic Perspectives 15 (2001): 219 232. Peterson An Introduction To Decision Theory., Chapter 4 Week 5: Weakening the theory The axioms of the representation theorem are typically quite strong. This week we explore some ways of weakening the axioms and what the consequences of doing so are. Christopher Meacham and Jonathan Weisberg Representation Theorems and the Foundations of Decision Theory, Australasian Journal of Philosophy 89 (2011): 641 663. Lyle Zynda Representation Theorems and Realism About Degrees of Belief, Philosophy of Science 67 (2000): 45 69. James Dreier Rational Preference as a Theory of Practical Rationality, Theory and Decision 40 (1996): 249 276. Amartya Sen Behaviour and the Concept of Preference, Economica 40 (1973): 241 259. David Christensen Preference-based Arguments for Probabilism, Philosophy of Science 68 (2001): 356 376. Mark Kaplan Decision Theory as Philosophy, Philosophy of Science 50 (1983): 549 577. Ian Hacking Slightly More Realistic Personal Probability, Philosophy of Science 34 (1967): 311 325. Peter Fishburn Preference Structures and Their Numerical Representation, Theoretical Computer Science 217 (1999): 359 383. Patrick Suppes The Measurement of Belief, Journal of the Royal Statistical Society B 36 (1974): 160 191. 3
Henry E. Kyburg Rational Belief, The Brain and Behavioural Sciences 6 (1983): 231 273. James M. Joyce A Defense of Imprecise Credence, Oxford Studies in Epistemology 4 (2011). Gilboa Theory of Decision Under Uncertainty., Part III Francis Chu and Joseph Y. Halpern Great Expectations. Part I: On the Customizability of General Expected Utility, Theory and Decision 64 (2008): 1 36. and Francis Chu and Joseph Y. Halpern Great Expectations. Part II: Generalized Expected Utility as a Universal Decision Rule, Artificial Intelligence 159 (2004): 207 230. Scott Sturgeon Reason and the Grain of Belief, Noûs 42 (2008): 139 165. Week 6: Alternative approaches to rational choice This week we look at alternatives to standard decision theory. We look at prospect theory, and an approach to rationality built around fast and frugal heuristics. Week 7: Evidential and causal decision theories We will look at the car protection problem and Newcomb s problem. These will help us to highlight the distinctions between evidential and causal decision theory. Peterson An Introduction To Decision Theory., Chapter 9 Weatherson Logic of Decision Notes., Chapter 6 Joyce The Foundations of Causal Decision Theory., Chapter 5 Andy Egan Some Counterexamples To Causal Decision Theory, Philosophical Review 116 (2007): 93 114. Arif Ahmed Push the Button, Philosophy of Science 79 (2012): 386 395. Week 8: Sequential choice This week we look at agents facing sequences of choices. Katie Steele Dynamic Decision Theory, 2013. José Luis Bermúdez Pitfalls for Realistic Decision Theory: An Illustration From Sequential Choice, Synthese 176 (2010): 23 40. Mark J. Machina Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty, Journal of Economic Literature 27 (1989): 1622 1668. Week 9: Game theory This week we move on to game theory. We look at the basic ideas, and some simple, standard games: prisoner s dilemma, coordination, tragedy of the commons. We look at solution concepts : in particular, at Nash equilibria. Don Ross Game Theory, in The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, 2012nd ed., 2012., Sections 1 and 2 David Lewis Prisoners Dilemma Is a Newcomb Problem, Philosophy and Public Affairs 8 (1979): 235 240. 4
Week 10: Repeated games We look at how repeating a game, and allowing the agents to learn from past experiences changes things. We look at evolutionary game theory: we see how cooperation can develop. Week 13: Avoiding Arrow s theorem Various ways around Arrow s result will be discussed. Gaertner A Primer in Social Choice Theory., Chapters 3,6 Robert Axelrod and William D. Hamilton The Evolution of Cooperation, Science 211 (1981): 1390 1396. J. McKenzie Alexander Evolutionary Game Theory, in The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, 2009 ed., 2009. Week 11: Signalling and language We look at how signalling games can give us a how possibly story for the evolution of language. Lewis Convention Skyrms Signals Week 12: Social choice We turn now to how to aggregate individual preferences into a group preference. We look at Condorcet cycles, and other problems with aggregation. We look at Arrow s impossibility theorem. Fabrizio Cariani Judgement Aggregation, Philosophy Compass 6 (2011): 22 32. Wulf Gaertner A Primer in Social Choice Theory (Oxford University Press, 2009)., Chapters 1,2 Peter Fishburn Paradoxes of Voting, The American Political Science Review 68 (1974): 537 546. 5