An Introduction to Decision Theory

Cambridge Introductions to Philosophy

by Martin Peterson

Now revised and updated, this introduction to decision theory is both accessible and comprehensive, covering topics including decision making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, with all concepts and results explained in non-technical and intuitive as well as more formal ways. There are now over 140 exercises with solutions, along with a glossary of key terms and concepts. This second edition includes a new chapter on risk aversion as well as updated discussions of numerous central ideas, including Newcomb's problem, prisoner's dilemmas, and Arrow's impossibility theorem. The book will appeal particularly to philosophy students but also to readers in a range of disciplines, from computer science and psychology to economics and political science.

Genres: Philosophy, Mathematics, Textbooks, Economics, Psychology, Nonfiction, Business

336 pages, Kindle Edition

First published May 1, 2009

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Reviews

[Pablo · Rating 3 out of 5]

3.5ish

I started reading this book because it was featured at MIRI's research guide and decision theory had always seemed as something I would like. The book is mostly not about decision theory though, but rather about the philosophical aspects surrounding decision theory.

Overall I expected a bit more focus on more "practical" questions and not so much on the philosophical part. If you know nothing about decision theory you might like it more though since it presents you with a lot of famous paradoxes that are pretty interesting

The book's structure is roughly as follows:

- The first four chapters deal with the basics of decision theory (ignorance vs. risk, minimax, dominance and maximization of expected utility) and are recommended (the last one also exposes some classical paradoxes).
- Chapter 5 and chapter 8 are about the philosophical questions and the methodological assumptions about preferences and utility and I found them quite dull (they might be your thing if you are interested in that kind of philosopy though).
- Chapter 7 surveys the philosophical aspects of probability (a topic that I do find interesting but didn't expect to find in this book) and does so quite well.
- Chapter 9 is about causal vs evidential decision theory (Newcomb's paradox and the like). I had always deemed Newcomb's paradox as an useless theoretical curiosity but the examples were quite convincing and I must admit this book has changed my mnd about it.
- The last chapters explore fields related to (normative) decision theory: (subjective) Bayesianism, game theory, social choice theory and descriptive decision theory. They do not go into a lot of depth but they are good enough.

[Karl Wärn · Rating 5 out of 5]

I'll keep this review brief. I find decision theory to be a very interesting subject. At its essence decision theory, interpreted from a philosophical lens, boils down to the simple question: "how ought a rational decision maker to act?". This question proves to be far more difficult to answer than one at first glance would think.

I was particularly dazzled by the paradoxical conclusion that in certain cases the best or second best outcomes are only attainable by a irrational agent, rather than a "rational" one, whom is usually stuck with the third best. Although, there is certainly a distinction to be made that what is rational need not be correct, however I found this inference very puzzling.

All in all, An Introduction to Decision Theory is a great textbook that makes a rather challenging subject relatively easily digestible even for a beginner such as myself, thus serves its purpose as a introduction.

[Robert · Rating 5 out of 5]

This book is an excellent introduction to decision theory, in my opinion (not that I have compared it to others). It has a good number of exercises and goes into a good amount of detail.

Before reading it, I had picked up a fair amount decision theory by osmosis. After reading it, I feel like I have a solid understanding the basic framework of decision theory and the basic theoretical questions in the field. For example, not long after reading the book I attended a conference on decision theory and more or less understood what was going on. Reading the book also allowed me to work on a paper about risk aversion. So I think that this is a sign of the book being successful in its aims.

[Daniel Frank · Rating 3 out of 5]

An incredibly dry overview of an important and (should be) fascinating subject.

[Yudhister · Rating 3 out of 5]

good overview. imo not enough thought was put into why the distinctions made are appropriate and/or natural, as opposed to clean, and it shied away from some of the more interesting math. still a decent reference if you want to learn a bunch of vocab and/or concepts in an evening.

he mentions that he doesn't find the Dutch book criterion a satisfying justification of why an agent should use subjective probabilities which satisfy the probability axioms. this is probably true? but the concept of a 'Dutch book' generalizes far beyond coherence in this sense, it can also be relaxed to guarantee logical coherence in a practical sense (Garrabrant et. al. prove that a form of a Dutch book criterion is enough to guarantee nearly all desiderata for reasoning under uncertainty except for Gaifman induction). as for the philosophical justification of translating utilities into money, it's plausible we're packaging a lot of hidden assumptions here? but i don't really know what they are. i should probably think about this

again with the insistence on the absolute divide between ordinal and cardinal utilities!! i argue that, in practice, in the scenarios we care about, they're essentially isomorphic, and that all a reasoner needs is some ordinal utility function / ordering over world states. yes, maybe your environment is countable / discrete and not uncountable / continuous, but even then you can still make a natural mapping and aggregate preferences decently.

also, the book argues against EDT on the basis that an EDT agent can't naturally ascribe probabilities to their own beliefs if it results in epicycles? this is mostly just incorrect (or, there are sane ways of dealing with this), but it is something to worry about, sure. there are much better arguments against EDT (like the Smoking Lesion: https://www.andrew.cmu.edu/user/coest... is a good descriptor here)

chapters 11-14 are good and short overviews of game theory & social choice theory that are well worth it. you quickly get exposed to ~all the major game theoretic settings, as well as stuff like Arrow's impossibility results / Harsanyi's utilitarian theorem(s?). if i had read this part six months ago I'd be in a much better place I think

[Alex Strasser · Rating 5 out of 5]

Fantastic book. Easy to read. Sections off more technical aspects in distinct sections for the interested reader. Each chapter includes exercises as well as all of their solutions (although, if the question was merely about conceptual understanding, the solution was frequently "see Section xx.x [where I talked this already]", which isn't particularly helpful. The explanations provided in the book generally are easy to follow, and, where appropriate, the relevant mathematics is detailed. Any time math is included, an intuitive interpretation of the math is included. Gives helpful additional reading for each chapter (a combination of books and important/influential papers).

It covers decisions where the probabilities are unknown (decisions under ignorance), known (decisions under risk), paradoxes associated with the principle of maximizing expected utility, how to rigorously define utility and construct utility functions using various axioms, the mathematics and philosophy of probability, Bayesian and non-Bayesian decision theory (dealing with money pumps and Dutch books), causal vs evidential decision theory, risk aversion, game theory, social choice theory, and descriptive decision theory.

[Jonathan Harrow · Rating 4 out of 5]

SUMMARY:
-Introduces decision matrices, states, outcomes, acts, formalisation ambiguity.
-Decisions under ignorance: Dominance, Maximin, leximin, Maximax, Minimax regret, randomization
-Decisions under risk: Expected utility, associated paradoxes, von Neumann standardization, scales (ratio, ordinal, cardinal)
-Bayes theorem
-Game theory: all zero-sum games can be solved (2-person). Mixed strategies are often the way to go
-Game theory II: Nash equilibrium, bargaining problem, evolution (cooperate is good), ethics
-Arrow's impossibility, Pareto (80% consequences come from 20% causes)

[Γιάννης Αναγνωστούδης · Rating 5 out of 5]

Not only an invaluable introduction to decision theory, but also a fascinating and intriguing book in its own right. Stopped reading at Chapter 9.1.