Probability and Rational Choice
(PHIL 258g, Fall 2019)

Jeff Sanford Russell ()

Jesse Wilson ()

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

Our main textbook for the first half of the course, Reason Better, is a customized electronic textbook available through the Top Hat platform. We will also use Top Hat for in-class quizzes and participation.

This means you will need to register for our Top Hat course. (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.)

An email invitation will be sent to you, but if don’t receive this email, you can register by going to our course website:

Our Course Join Code is 248248.

Your textbook will be applied at checkout for $60 (including your Top Hat subscription). Don’t worry if you don’t see any content in the course right away, I will make it available to you as we progress through the semester.

You can visit the Top Hat Overview within the Top Hat Success Center which outlines how you will register for a Top Hat account, as well as providing a brief overview to get you up and running on the system.

If you need help with Top Hat at any time, you can contact their Support Team directly by email (, the in-app support button (this should be at the top right of the course page), or by calling 1-888-663-5491.


Lecture Tue, Thu 9:30–10:50am VKC 102
Discussion Section Fri 8–8:50am VKC 210
Discussion Section Fri 9–9:50am VKC 210
Jeff’s Office Hours
(one-on-one appointments)
Wed 3–4:30pm STO 227
Jeff’s Office Hours
(open discussion)
Thu 11am–12pm STO 227
Jesse’s Office Hours Tue 11am–12pm MHP B5B
Jesse’s Office Hours Fri 10–11am MHP B5B
Final Exam Thu, Dec 12 11am–1pm VKC 102

For Jeff’s Wednesday office hours, you can reserve a one-on-one appointment using this website:

If you have class conflicts with our scheduled office hours, you can email Jeff to make an appointment for another time.


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% Tue, Nov 5
Modeling project part 2 10% Tue, Nov 26
Midterm 1 15% Tue, Oct 8
Midterm 2 15% Tue, Nov 19
Final exam 20% Thu, Dec 12

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 six problem sets, spread out through the semester (see the class schedule).

Problem sets will be due in class, at the beginning of the class. If you do not turn a problem set in at 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).


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. O&E is Odds and Ends.



Read This

Turn This In

Part 1

Thinking Clearly

Tue 8-27

The true and the good.

RB ch. 1, “Reasoning”

Thu 8-29

Thinking fast and slow. Your mind’s two systems, and why they matter

RB ch. 1, “Reasoning”

Tue 9-3

Mindset. Accuracy, degrees of confidence, confirmation bias

RB sec. 2.1 and 2.2 “Mindset”

Part 2

Responding to Evidence

Thu 9-5

How to change your mind (1). Evidence

RB sec. 2.3 and 5.1

Tue 9-10

How to change your mind (2). Strength factors, odds, updating

RB sec. 8.1 “Updating”

Thu 9-12

How to outsmart doctors, lawyers, and the police. Evidence pitfalls, base rate neglect

RB sec. 8.2 “Updating”

Tue 9-17

Putting ideas together. Theory choice, conjunctions and disjunctions

RB ch. 9 “Theories”

Problem Set: evidence

Thu 9-19

Basic rules of probability.

O&E ch. 5 “Calculating Probabilities”

Tue 9-24

Calculating probabilities, continued

O&E ch. 4 “The Gambler’s Fallacy” and ch. 6 “Conditional Probability”

Thu 9-26


RB ch. 6 “Generalizations”

Tue 10-1

What happens in Vegas. Conditional probability, the gambler’s fallacy

Problem Set: calculating probabilities

Thu 10-3

Seeing the whole picture. Selection effects, media biases

RB sec. 5.2, 5.3 “Evidence”

Tue 10-8

Midterm 1

Midterm 1 (in class)

Thu 10-10

Philosophical Applications

Hume, “Of Miracles”

Part 3

Choosing Well

Tue 10-15

Consider your options. Decision tables and decision trees

RB sec. 10.1 “Decisions”

Thu 10-17

Fall Recess

Tue 10-22

Tell me what you want (what you really really want). Utility and expected utility

O&E ch. 12 “Utility”

Thu 10-24

Mistakes were made. Decision-making pitfalls

RB sec. 10.2 “Decisions”

Part 4

Philosophical Foundations: Choices

Tue 10-29

Why should I? Long run arguments, axiomatic arguments

Decision Theory FAQ, secs. 8–8.6.2

Problem Set: expected utility

Thu 10-31

Is it rational to avoid risk? The independence axiom, the Allais paradox

O&E ch. 13, “Challenges to Expected Utility”

Tue 11-5

When small risks are a big deal. The St. Petersburg paradox, Pascal’s wager, existential risk

O&E ch. 14, “Infinity and Beyond”

Modeling Project Part 1

Thu 11-7


Part 5

Philosophical Foundations: Beliefs

Tue 11-12

Belief and action. Betting rates

O&E ch. 15 and ch. 16

Problem Set: foundations of decision theory

Thu 11-14

Coherence. Sure-loss packages

O&E ch. 17

Tue 11-19

Midterm 2

Midterm 2 (in class)

Part 6

Working Together

Thu 11-21

Sudden but inevitable betrayal. Game theory basics, prisoner’s dilemmas

Peterson, sec. 11.1–11.3

Tue 11-26

Coordination and trust. Nash equilibrium strategies, stag hunts

Peterson, sec. 11.5, 12.1

Modeling Project Part 2

Thu 11-28


Tue 12-3

Democracy is broken. Voting

Peterson, sec. 13.1–13.2

Problem Set: betting rates, game theory

Thu 12-5

Catch-up and Review

Thu 12-12

Final Exam

Final Exam (in class)


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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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