Decision Theory Course

One of the courses I’ll be teaching this semester is 483 – Philosophy of Choice & Decision. Despite the course number starting with ‘4’, which might be interpreted as a sign the course is pitched at 4th year (i.e. senior) students this is basically a grad class that is meant to be accessible to good undergraduates. I was working through the topics I planned to cover in the course and thought this was as good a place as any to record my first ideas on what we will and won’t cover. Although comments are more than welcome, this is of fairly specialised interest, so I’ve put most of it below the fold.

The course consists of 37 50-minute classes. I have the ability (and possibly the obligation) to run a couple more classes at the end of that, so maybe we can go as high as 39 classes. Here’s the plan for what to cover. (The numbers refer to which classes we’ll cover the topics in.)

1. Intro – mostly focus on distinctions between topics we’ll cover

2. Primer on probability theory – probably unnecessary for most, but we can talk about some of the finer points to do with conditional probability to keep them interested.

3-4. Dutch Book Arguments – both pragmatic and ‘de-pragmatised’ arguments that belief functions should be probability functions.

5-6. Joyce’s Error Measurement Argument for Probabilism.

7-9. Axioms for Decision Theory – how they can be used to (yet again) defend probabilism and to construct a utility function.

10-12. Causal vs Evidential Decision Theory – Newcomb’s Paradox and responses to it

13-14. Infinite Utilities – St Petersburg Paradox, Two Envelopes, Pascal, etc. (This might need to be increased, especially if I want to talk about countable vs finite additivity).

15-16. Updating Principles – Arguments for Conditionalisation and Reflection.

17-19. Vague Probabilities – Motivation, discussion of how decision making goes, maybe some discussion of issues about updating.

20-22. Indexical Beliefs – Sleeping Beauty cases and the like. Maybe the ‘forgetful driver’ depending on how we’re doing for time.

23-24. Indifference Principles – Adam Elga’s Dr Evil paper and my reply. (It’s a grad seminar; I’m allowed to slip some of my stuff in.)

25-28. Game Theory – The basic concepts: Nash Equilibrium, Mixed Strategies, stronger equilibrium concepts; evolutionary examples.

29-30. Iterated Prisoners Dilemma – Theoretical issues, focussing on Pettit and Sugden’s paper

31-33. Iterated Prisoners Dilemma – Practical issues, focussing on Axelrod’s experiments and more contemporary follow-ups. Ideally get the class to work on their own strategies.

34-37. Arguments that game theory should be thought of as a special case of decision theory – Looking again at the theoretical issues in IPD, reading through a lot of Stalnaker’s recent material on game theory.

The game theory parts are woolier than the rest, largely because I just don’t know the topics as well. And I haven’t taught 50 minute grad classes before, so I don’t really have a feel for how much you can pack into them.

Here are the big things I’m leaving out.

  • Any discussion of social welfare functions
  • Indeed, any discussion of interpersonal utility comparisons
  • Discussion on whether utility-maximisation is prudential rationality
  • Mostly leaving out evolutionary applications, though I might mention some of these in passing
  • Mostly leaving out discussion of ‘forgetting’, though again there might be some opportunity for getting some of that into the Sleeping Beauty section.

All of the things I’m leaving out could be topics of larger discussions, but I think the course is more coherent as it is than with those topics. But this is a first draft, and it’s very much subject to change.

4 Replies to “Decision Theory Course”

  1. what textbook will you be using for this class?

    the vague probababilities, indexical beliefs, and indifference principles sections seem the most interesting, but that’s probably because those topics were not covered in a decision theory course i took.

    i think it’s probably a good idea to leave out social welfare functions. heh.

  2. Brian,

    Looks like an interesting course.

    I have a question related to Jonas’s. I teach a sophomore-junior level decision/game theory course, and have used Resnik’s book Choices which I like. The only drawback is that it is getting a bit dated (last edition 1987, I think) and I would like to use a book that is similar but that also covers a bit more of the recent literature (including some of the recent work Brian mentions). Does anyone out there know of such a book? Also, does any one know of any good anthologies covering the standard puzzles. I’ve used Campbell and Snowden’s Paradoxes of Rationality and Cooperation but it was published in 1985…

    Thanks,

    Chris

  3. Chris,

    You might want to look at the Gardenfors and Sahlin collection.

    ISBN: 0-521-33658-9 / 0521336589
    Title: Decision, Probability and Utility: Selected Readings
    Author: Peter Gardenfors
    with Nils-Eric Sahlin
    Publisher: Cambridge University Press
    Edition: Softcover

    Cheers,
    Jeff

  4. I’m using the Resnik book as the only textbook, though I’m also using lots of papers as additions, and I’m half thinking of writing up bunches of notes to supplement them. That might be just easier than trying to adapt to a less than ideal textbook.

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