Philosophy 666: Rational Choice Theory

Ben Eggleston—eggleston@ku.edu

- Please put away everything except for something to write with.
- This exam may be graded on a curve.
- Please number each of your 22 answers conspicuously.

The instructions at the top of the exam will read as follows:

- Answer all of the following questions on the answer sheets provided. You can write on this sheet of questions, but credit will be awarded only for answers written on answer sheets.
- Do not access any book, notebook, newspaper, calculator, computer, cell phone, or other possible source of inappropriate aid during the exam, do not leave the room before you are finished taking the exam, and be sure to finish the exam within the 90 minutes allotted—no credit will be given for any work done after you access any possible source of inappropriate aid, after you leave the room for any reason, or after the end of the 90 minutes allotted.
- When you are finished, be sure your name is written on each of your answer sheets, and turn them in. You do not need to turn in this sheet of questions.

Then there will be eight 10-point questions and fourteen 5-point questions. One of the 10-point questions and three of the 5-point questions will be questions for which you can prepare by consulting the preview of the mid-term exam. The remaining questions, which will pertain to material we’ve covered since the mid-term exam, may ask you to do some or all of the following:

- Compute actions’ expected monetary values (EMVs) and, given information about actions’ EMVs, solve for variables on which those EMVs depend (such as outcomes’ monetary values and/or states’ probabilities).
- Compute the value of additional information in situations of choice under risk with perfectly reliable and/or imperfectly reliable sources of information.
- Describe the St. Petersburg game and explain how it can have an infinite EMV even though any prize ever awarded in the game is finite.
- State what propositions one should bet for and/or against in order to make a Dutch Book against someone with certain specified probability assignments and, given a table of payoffs and a particular betting strategy, explain why that strategy is a way of making a Dutch Book against someone.
- Compute the chances at particular prizes that certain specified lotteries yield and, given information about the chances at particular prizes that certain specified lotteries yield, solve for variables on which those chances depend (such as prizes’ probabilities).
- Give sets of preferences that comply with or violate one or more of the
rationality conditions of expected-utility theory. (You will
*not*be provided with statements of the conditions.) - Write fairly simple proofs based on the rationality conditions. (Again, you will not be provided with statements of the conditions.)
- Provide a positive linear transformation that converts one utility scale into another.
- Provide a scale of a certain specified kind (ratio, interval, or ordinal) that can be used to represent certain specified preferences.
- Answer questions about what can and/or cannot justifiably be said, about an agent’s preferences, based on the possibility of representing those preferences with a scale of a certain specified kind (ratio, interval, or ordinal).
- Compute the range within which the utility assigned to a particular dollar amount must fall, given utilities assigned to some other dollar amounts and the attitude towards risk (averse or seeking) of the agent whose preferences are being represented.
- Compute the range within which the utility assigned to a certain prize must fall, or compute the inequality that the utility assigned to a certain prize must satisfy, given certain preferences that an agent has and given the assumption that the agent is an expected-utility maximizer.
- Explain why it is possible, or why it is impossible, for an agent with certain preferences to be an expected-utility maximizer.
- Explain how certain specified principles of choice bear on Newcomb’s problem (also called the predictor paradox).

If you would like to have your exam returned to you after grading, please bring to the final exam a 9-by-12-inch envelope bearing your address and adequate postage. (You should be fine with $1.06 cents of postage—for which three 37-cent stamps would suffice—unless you might use more than 17 answer sheets, in which case your envelope will probably end up weighing more than the 4 ounces for which $1.06 is adequate. Add 23 cents for each additional five answer sheets or so.) If you have a mailbox in the philosophy department office and you do not provide me with an envelope, I will put your graded exam in your mailbox. Exams can also be picked up during the spring semester; any exams I still have in my possession as of July 1, 2006 may be discarded then or afterwards.