Philosophy 666: Rational Choice Theory

Ben Eggleston—eggleston@ku.edu

- 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, cell phone, computer, or other possible source of aid during the exam, do not leave the room before you are finished taking the exam, and be sure to finish the exam within this 50-minute class period—no credit will be given for any work done after you access any possible source of aid, after you leave the room for any reason, or after the end of this class period.
- 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 15 questions. They may ask you to do some or all of the following:

- Write a decision table for a particular choice situation that will be described.
- Examine part of a proof of the claim that a certain transformation is an ordinal one, and indicate whether all the lines are justified or, if not, which is the smallest-numbered line that is not justified.
- Answer a question of the following form: “Either prove that t(x) = ___ is an ordinal transformation or give a counter-example showing that it’s not,” where the blank is filled in by a simple mathematical expression.
- Generate sets of choices that do one or more of the following: comply with
or violate the the contraction condition, comply with or violate the expansion
condition, and comply with or violate the revelation condition. If there is no
such set, you can just say that. You will be provided with statements of the
three conditions, copied essentially verbatim from the glossary of Allingham’s
*Choice Theory*. - Specify which act(s), of those shown in a decision table with numerical outcomes, would be selected by one or more of the following: the maximin rule, the minimax regret rule, the the optimism-pessimism rule (the agent’s optimism index will be specified), and the principle of insufficient reason.
- Prove an interesting fact (which will be specified) relating to one of the rules just listed.
- Give an example of a transformation having certain characteristics and prove that it has those characteristics.
- State whether two probabilistic events are related in one of the following ways: independence, mutual exclusiveness, and equivalence.
- Use Bayes’s theorem to compute the conditional probability of a certain event, given the occurrence of some other event.

Item 8, above, should read “State whether two probabilistic events (which will be described) stand in one of the following relations (which will be specified): independence, mutual exclusiveness, and equivalence. Also, explain why they do, or why they do not, stand in the specified relation. If you know the definitions, axioms, and theorems that mention the specified relation, then you should have no trouble explaining why the specified relation holds in the given case, or why it does not.”