Probability and Rational Choice
(PHIL 258, Fall 2025)
Course website: https://app.tophat.com/e/148715/
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 five parts.
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?
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?
Choosing Well. What should you do when you don’t know how things will turn out?
Philosophical Foundations. What justification is there for the standard rules of decision theory (from part 3), and the standard rules for degrees of belief (from part 2)? Do the standard rules sometimes give the wrong answers?
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 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 algebra. (For example, solve the equation 3p = p + 1 for p.) If you don’t remember how to do those things quickly and reliably, 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.
You will think carefully and critically about what you should believe and what you should do.
You will understand how cognitive biases can lead your beliefs away from the truth, and the habits of mind that can help compensate for them.
You will use probabilities to understand how beliefs fit together and are supported by evidence. You will use diagrams, numbers, and symbols to determine how strong evidence for a claim is, and when a theory is more likely to be true. You will identify mistakes and confusions in real-life reasoning with probabilities.
You will represent choices using diagrams, numbers, and symbols. You will use these tools to precisely describe difficult decisions, and to work out how to balance risks.
You will apply probability and decision theory to make progress on controversial philosophical questions.
You will precisely explain and evaluate philosophical arguments about what you should do and what you should believe. You will understand and explain the central mathematical ideas that these philosophical arguments rely on. You will clearly distinguish descriptive claims about what will happen from normative claims about what should happen.
You will represent cooperation problems using diagrams, numbers, and symbols. You will use these tools to precisely describe social relationships and explain special problems facing group decision-making.
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.
We will be using Top Hat (https://tophat.com) for class participation. Top Hat is an educational platform that integrates interactive features into learning materials, enhancing class engagement and comprehension.
(This will cost you some money — sorry! — but it’s less than the price of the hard copy textbooks I used to use for this course, for whatever that’s worth.)
For instructions on how to download the Top Hat app, please refer to our Student’s Getting Started Guide online.
If you already have a Top Hat account, go to https://app.tophat.com/e/148715/ to be taken directly to our course. If you are new to Top Hat, follow the link in the email invitation you received or…
Important! You cannot create a Top Hat account using the mobile application. Please first sign-up (using your USC email address) and enroll into your course using a web browser.
For support, visit Top Hat Support or use the contact form here.
Lecture | Mon, Wed | 8:30–9:50am | SOS B2 |
Discussion Section | Tue | 8-8:50am | DMC 161 |
Discussion Section | Tue | 11–11:50am | THH 110 |
Discussion Section | Thu | 8–8:50am | DMC 161 |
Discussion Section | Thu | 11–11:50am | DMC 203 |
Jeff’s Office Hours | Wed | 10–11am or by appointment | MHP 205E (up the stairs near the philosophy office) |
June’s Office Hours | Thu | 9–10am | MHP courtyard |
Yangming’s Office Hours | Fri | 1–2pm | MHP B5B |
Final Exam | Wed, Dec 10 | 8–10am | SOS B2 |
If you have class conflicts with our scheduled office hours, you can email Jeff, June, or Yangming to try to find another appointment time that works.
See the schedule for dates and deadlines.
Reading questions (Top Hat) | 10% |
Check-in quizzes (Top Hat) | 10% |
Discussion activities | 10% |
Problem sets | 20% |
Midterm | 20% |
Final exam | 30% |
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 50% 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.
Each section of the assigned reading on Top Hat has a few review questions at the end. You should answer these when you do the reading before each class. But usually I will give you a grace period to answer reading questions (or change your answers) up to the end of the week. (These deadlines will be posted on Top Hat.) In general, I will not give any extensions for reading questions beyond this grace period.
Normally, half of the credit for a reading question will be based on answering the question at all, and the other half will be based on whether you get it right.
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 quizzes where you only get points for correct answers, and others will be just based on participation.
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 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 in class at the beginning of class on the day of the deadline (8:30am Pacific time). If you do not turn in a problem set at the beginning of class, you will use a late day (see the Late Policies below).
There will be one in-class midterm (see the class schedule).
To help you consolidate your understanding so far
To evaluate your knowledge and understanding of the main ideas
To evaluate your ability to apply core skills
There will be a comprehensive in-class final exam.
To give you an opportunity to reflect on what you have learned through the whole semester, and put all the pieces together.
To evaluate your understanding of ideas and mastery of skills from the entire class, and your ability to apply them.
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, 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 problem set two days 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 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, which may affect assignment deadlines or the midterm date. 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 Aug 25 | The true and the good. | RB ch. 1.1 (“Reasoning”) | |
W Aug 27 | Thinking fast and slow. Your mind’s two systems, and why they matter | RB ch. 1.2 and 1.3 (“Reasoning”) | |
M Sep 1 | Labor Day | ||
W Sep 3 | Mindset. Accuracy, degrees of confidence, bias | RB sec. 2.1 and 2.2 (“Mindset”) | |
Part 2 | Responding to Evidence | ||
M Sep 8 | Evidence. The evidence test. | RB sec. 2.3 (“Mindset”) and 5.1 (“Evidence”) | |
W Sep 10 | How to change your mind. Strength factors, odds, updating | RB sec. 8.1 “Updating” | |
M Sep 15 | How to outsmart doctors, lawyers, and the police. Updating pitfalls, prior neglect | RB sec. 8.2 and 8.3. Optional: Jemisin, “Non-Zero Probabilities” | |
W Sep 17 | Ifs, ands, ors. Probability of conjunctions and disjunctions | O&E ch 5 “Calculating Probabilities” | |
M Sep 22 | What if? Calculating conditional probabilities | O&E ch. 6 “Conditional Probability” | Problem set 1: evidence |
W Sep 24 | Calculating probabilities | O&E ch. 7 “Calculating Probabilities, Part 2” | |
M Sep 29 | Looking at the whole picture. Selection effects, media biases | RB sec. 5.2, 5.3 “Evidence” | |
Part 3 | Choosing Well | ||
W Oct 1 | Consider your options. Decision tables and decision trees | RB sec. 9.1 (“Decisions”) | |
M Oct 6 | Tell me what you want (what you really really want). Utility and expected utility | O&E ch. 12 “Utility” | Problem set 2: calculating probabilities |
W Oct 8 | Mistakes were made. Decision-making pitfalls | RB sec. 9.2 (“Decisions”) | |
M Oct 13 | Is voting pointless? A decision theory application | Barnett, “Why You Should Vote to Change the Outcome”, sections 1–4 | |
W Oct 15 | Catch-up | ||
M Oct 20 | Midterm | Midterm (in class) | |
W Oct 22 | Long shots. Extreme decision theory. | Bostrom, “Pascal’s Mugging”. Optional: Bostrom, “Astronomical Waste” | |
Part 4 | Philosophical Foundations | ||
M Oct 27 | Why should I? Long run arguments, axiomatic arguments | Decision Theory FAQ, secs. 8–8.6.2 | Problem Set 3: expected utility |
W Oct 29 | Risk and rationality The independence axiom, the Allais paradox | O&E sec. 13.1–13.3, “Challenges to Expected Utility” | |
M Nov 3 | Belief and action. Betting rates | O&E ch. 16 (“Beliefs and Betting Rates”) | |
W Nov 5 | Coherence. Dutch books | O&E ch. 17 (“Dutch Books”) | |
M Nov 10 | Close to the truth. Accuracy | Pettigrew, selections from Accuracy and the Laws of Credence | |
W Nov 12 | TBD | ||
Part 5 | Working Together | ||
M Nov 17 | Sudden but inevitable betrayal. Game theory basics, prisoner’s dilemmas | Peterson, sec. 11.1–11.3 | Problem set 4: philosophical foundations |
W Nov 19 | Coordination and trust. Nash equilibrium strategies, stag hunts | Peterson, sec. 11.5, 12.1 | |
M Nov 24 | Continued | ||
W Nov 26 | Thanksgiving break | ||
M Dec 1 | Game theory applications. | ||
W Dec 3 | Catch-up and review | Problem set 5: game theory | |
W Dec 10 | Final exam | Final exam 8–10am |
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This course follows the expectations for academic integrity as stated in the USC Student Handbook. All students are expected to submit assignments that are original work and prepared specifically for the course/section in this academic term. Students may not submit work written by others or “recycle” work prepared for other courses without obtaining written permission from the instructor(s). Students suspected of academic misconduct will be reported to the Office of Academic Integrity.
Academic dishonesty has a far-reaching impact and is considered a serious offense against the university. Violations will result in a grade penalty, such as a failing grade on the assignment or in the course, and disciplinary action from the university, such as suspension or expulsion.
For more information about academic integrity see the Student Handbook, the Office of Academic Integrity’s website, and university policies on Research and Scholarship Misconduct.
Please ask your instructor if you are unsure what constitutes unauthorized assistance on an exam or assignment or what information requires citation and/or attribution.
You can use AI to help you study, but never to do your homework for you.
Here is a good rule of thumb: you may use generative AI (such as ChatGPT, Copilot, Claude, Gemini, Grammarly, …) in the same way you might use a classmate or a tutor — to ask questions, to check your understanding, or to talk through ideas. You may not use AI to generate problem set answers, write up solutions or reflections, answer reading questions, or otherwise do the work the assignments are meant to teach you. That will be considered plagiarism in the same way as if you had turned in another person’s work as your own.
This restriction is for your benefit. The point of the class assignments is to practice and develop the skills yourself; if you outsource the work, you won’t learn the skills, you won’t do well on the exams, and you won’t gain much of value from this class.
Also, remember that generative AI often hallucinates, makes errors in reasoning, and even fails at simple arithmetic. Relying on it to produce answers is risky as well as inappropriate.
If you are unsure whether a particular use of AI is acceptable, ask me in advance.
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