Probability and Rational Choice
(PHIL 258g, Spring 2021)

Jeff Sanford Russell ()

Levy Wang ()

This course is about how to live with uncertainty. How should our beliefs be shaped by evidence about the world? How should we make decisions when our actions have risky outcomes? How can we trust other people in shared projects?

This course has six parts.

  1. Thinking Clearly. How is your mind vulnerable to biases that lead you away from the truth? What skills and habits will help you have beliefs that aim at what is true and make choices that aim at what is good? Why bother with tables and numbers when it comes to real life questions?

  2. Responding to Evidence. How should you change your mind as you learn new things? How can you have coherent beliefs even when you aren’t sure what is true?

  3. Choosing Well. What should you do when you don’t know how things will turn out?

  4. Philosophical Foundations: Decisions. What justification is there for the standard rules of decision theory (from part 3)? Do the standard rules sometimes give the wrong answers?

  5. Philosophical Foundations: Beliefs. What justification is there for the standard rules for degrees of belief (from part 2)?

  6. Working Together. Why is it hard to solve social problems together? What factors make it easier or harder to cooperate?

This is a philosophy class, but we will also use tools and ideas from psychology, math, and economics.

This class fills a quantitative reasoning general education requirement (GE-F). In some ways it will be like a math class. It involves some numbers and equations, and there will be problem sets. But our main emphasis won’t be on calculation, but rather on conceptual understanding. How can we use probabilities to understand an uncertain world? What do they mean?

You will be evaluated not just on your ability to calculate correct answers, but also on your ability to think critically and write clearly.

This class does not assume you have any background in college-level math. But you will need to do some arithmetic. (For example, what is 2/3 of 3/5? What is 20% of 80?) And you will need to do some basic algebra. (For example, solve the equation 3p = p + 1 for p.) If you don’t remember how to do those things, you will need to do some review to brush up. This might be a helpful resource:

This class does not assume you have any background in philosophy. But you will need to think carefully, and you will need to write clearly and directly. If you need help with your writing, the USC Writing Center might be a helpful resource:



We have two main textbooks for this class:

Reason Better is only available through the Top Hat platform, which is described below. Odds and Ends is available for free online, here:

We will also use some short selections from other books and articles, which I will distribute through the course Top Hat site.

Top Hat

We will be using Top Hat Pro ( to access the digital interactive textbook, Reason Better, that we will be using in this class. We will also use Top Hat for in-class quizzes.

(This will cost you some money, but it’s quite a bit less than the price of the hard copy textbooks I used to use for this course, so I think it’s a fair deal.)

For instructions on how to create a Top Hat account and enroll in our Top Hat Pro course, please refer to one of the following resources:

  1. The invitation sent to your school email address OR
  2. Consult Top Hat’s Getting Started Guide OR
  3. Get started with this 2 minute video walkthrough

If you already have a Top Hat account, go to to be taken directly to our course. If you are new to Top Hat, follow the link in the email invitation you received or

  1. Go to
  2. Click “Search by school” and input the name of our school
  3. Search for our course with the following join code: 066344

The cost of the textbook will be applied at checkout when enrolling in our Top Hat course. Bear in mind that textbook material will be made available in our course throughout the semester once your professor assigns it to the class, so do not panic if you do not see any content in the course upon entry.

Should you require assistance with Top Hat at any time please contact their Support Team directly by way of email (, the in-app support button, or by calling 1-888-663-5491. Specific user information may be required by their technical support team when troubleshooting issues.


Lecture Mon, Wed 8:30–9:50am online
Discussion Section Tue 8–8:50am CPA 154 & online
Discussion Section Tue 9–9:50am CPA 154 & online
Jeff’s Office Hours Mon 10–11:30am online
Levy’s Office Hours Tue 10–11am online
Final Exam Mon, May 10 11am–1pm TBD

You can reserve a one-on-one appointment during Jeff’s office hours using this link:

You’ll get a Zoom link automatically after you sign up for a time.

If you have class conflicts with our scheduled office hours, you can email Jeff to try to find another appointment time that works.

Levy will give you instructions by email for how to attend her office hours.


Assignment deadlines and midterm dates are provisional: I may adjust these dates if necessary. Watch for updates.

Reading questions (Top Hat) 5% Every meeting
Check-in quizzes (Top Hat) 10% Every meeting
Discussion activities 5% Weekly
Problem sets 15% See schedule
Modeling project part 1 5% Wed, Mar 31
Modeling project part 2 10% Wed, Apr 28
Midterm 1 15% Wed, Mar 10
Midterm 2 15% Mon, Apr 19
Final exam 20% Mon, May 10 11am–1pm

The grade break-down is structured to reward consistent work through the whole semester. No one component is worth a huge portion of your grade. Make sure to keep up with the reading questions, check-in quizzes, discussion activities, and problem sets. No single one of them is worth very much on its own, but all together they are worth almost a third of your grade.

The later parts of this class will build on the skills you develop early on, so if you don’t keep up with the work consistently week by week, you may find yourself lost later on.

Reading questions


Each section of the assigned reading on Top Hat has a few review questions at the end. Normally, your answers to reading questions will be due at midnight before the class meeting for that reading. These deadlines will be posted on Top Hat. Normally, half of the credit for this will be based on answering the question at all, and the other half will be based on whether you get it right.

Check-in quizzes


We will use Top Hat for frequent short in-class quizzes. Usually these quizzes will just be one or two questions. We will have one of them (or sometimes more than one) in almost every class. Some of these will be standard quizzes, in which you only get points for correct answers, and some of them will be purely participation-based.

Discussion activities


Discussion section is a required part of this class. Be present, be prepared, and be on time. Ask questions, contribute to discussions, and participate in activities. Be helpful and respectful to others.

Problem sets


Problem sets will include calculations, drawing diagrams, as well as short written reflections about philosophical questions. There will be five problem sets, spread out through the semester (see the class schedule).

Problem sets will be due by the beginning of class on the day of the deadline (8:30am Pacific time). If you do not turn a problem set in by the beginning of class, you will use a late day (see the Late Policies below).

Modeling project


You will write an analytical essay applying tools from probability and decision theory to a philosophical or practical problem. This will have two parts. The first part is a detailed proposal, which will give you a chance to get feedback on your ideas and approach. The second part is the final essay, describing a specific philosophical problem, and explaining how we can use ideas from probability and decision theory to investigate it. See the class schedule for deadlines.

I will distribute separate handouts describing this project in more detail.


There will be two in-class midterms (see the class schedule).

Note: I am still figuring out what an “in-class exam” means for an online class. I’ll update you on the protocol when the first midterm gets closer.


Final Exam

There will be a comprehensive in-class final exam.


Late Policies

Problem Sets and Modeling Project

Life is messy, and sometimes you just can’t reasonably get homework done on time. Instead of dealing with all of these problems case by case, everyone gets ten “late days” to use on any problem set or either part of the modeling project, no questions asked.

You can split up your late days however you want: for example, you can spend all your late days on one assignment and turn it in ten days late, or you can turn in every assignment one day late. (You can’t use just half a late day, though: if the assignment is a few hours late, that uses up a whole late day. Days when we don’t have class meetings still count, including weekends and holidays.)

There is no grade penalty for spending a late day. But after you have spent all of your late days, you will not get any more credit for late work. So don’t spend all your late days on the first assignment! Save them for real emergencies when you need them.

Late work can be turned into Jeff’s mailbox in the main philosophy office (MHP 113). Make sure to write the date and time that you turn it in at the top.

Reading Quizzes, Check-in Quizzes, and Discussion Activities

Reading questions, check-in quizzes, and discussion activities cannot be made up or turned in late. This is because these assignments are difficult to fairly administer at alternative times, and each particular one of them is worth a very small fraction of your overall grade.


The following schedule is provisional. I will make adjustments through the semester. Watch for updates.

RB is Reason Better (available through Top Hat). O&E is Odds and Ends (available free online). Other readings besides these will also be distributed through Top Hat.

Date Topic Read This Turn This In
Part 1 Thinking Clearly
M Jan 18 Martin Luther King Jr. Day
W Jan 20 The true and the good. RB ch. 1, “Reasoning”
M Jan 25 Thinking fast and slow. Your mind’s two systems, and why they matter RB ch. 1, “Reasoning”
W Jan 27 Mindset. Accuracy, degrees of confidence, confirmation bias RB sec. 2.1 and 2.2 “Mindset”
Part 2 Responding to Evidence
M Feb 1 Evidence RB sec. 2.3 and 5.1
W Feb 3 Looking at the whole picture. Selection effects, media biases RB sec. 5.2, 5.3 “Evidence”
M Feb 8 How to change your mind. Strength factors, odds, updating RB sec. 8.1 “Updating”
W Feb 10 How to outsmart doctors, lawyers, and the police. Evidence pitfalls, base rate neglect RB sec. 8.2 “Updating”
M Feb 15 President’s Day
W Feb 17 Putting ideas together. Theory choice, conjunctions and disjunctions RB ch. 9 “Theories” Problem Set: evidence
M Feb 22 What happens in Vegas. The gambler’s fallacy and independence, basic rules O&E ch. 4 “The Gambler’s Fallacy” and ch. 5 “Calculating Probabilities”
W Feb 24 What if? Calculating conditional probabilities O&E ch. 6 “Conditional Probability”
M Mar 1 Calculating probabilities, continued O&E ch. 7 “Calculating Probabilities, Part 2”
W Mar 3 Philosophical Applications Hume, “Of Miracles” Problem Set: calculating probabilities
M Mar 8 review
W Mar 10 Midterm 1 Midterm 1 (in class)
Part 3 Choosing Well
M Mar 15 Consider your options. Decision tables and decision trees RB sec. 10.1 “Decisions”
W Mar 17 Tell me what you want (what you really really want). Utility and expected utility O&E ch. 12 “Utility”
M Mar 22 Mistakes were made. Decision-making pitfalls RB sec. 10.2 “Decisions”
Part 4 Philosophical Foundations: Choices
W Mar 24 Modeling overview Problem Set: expected utility
M Mar 29 Why should I? Long run arguments, axiomatic arguments Decision Theory FAQ, secs. 8–8.6.2
W Mar 31 Risk and rationality The independence axiom, the Allais paradox O&E sec. 13.1–13.3, “Challenges to Expected Utility” Modeling Project Part 1
Part 5 Philosophical Foundations: Beliefs
M Apr 5 Belief and action. Betting rates O&E 16.1 (“Measuring Personal Probabilities”) and 16.2 (“Things to Watch Out For”)
W Apr 7 Wellness Day
M Apr 12 Coherence. Dutch books O&E ch. 17 (“Dutch Books”) Problem set: foundations of decision theory
W Apr 14 Midterm review
M Apr 19 Midterm 2 Midterm 2 (in class)
Part 6 Working Together
W Apr 21 Sudden but inevitable betrayal. Game theory basics, prisoner’s dilemmas Peterson, sec. 11.1–11.3
M Apr 26 Coordination and trust. Nash equilibrium strategies, stag hunts Peterson, sec. 11.5, 12.1
W Apr 28 Catch-up and Review Modeling Project Part 2
M May 10 Final Exam Final Exam 11am–1pm


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Plagiarism – presenting someone else’s ideas as your own, either verbatim or recast in your own words – is a serious academic offense with serious consequences. Please familiarize yourself with the discussion of plagiarism in SCampus in Part B, Section 11, “Behavior Violating University Standards” <>. Other forms of academic dishonesty are equally unacceptable.  See additional information in SCampus and university policies on scientific misconduct,

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