<p>For decision theory:</p>

<ul>
<li>Gilboa, I. (2009). Theory of decision under uncertainty. Cambridge University Press.</li>
<li>Parmigiani, G., &amp; Inoue, L. (2009). Decision theory: Principles and approaches. John Wiley &amp; Sons.</li>
<li>Peterson, M. (2009). An introduction to decision theory. Cambridge University Press.</li>
</ul>

<p>For social choice theory, see my answer to this question : <a href="https://economics.stackexchange.com/questions/34334/good-books-to-learn-social-choice-theory">Good books to learn social choice theory</a>.</p>

CC BY-SA 4.0
2020-03-06T19:58:30.860Z
2020-03-06T20:04:42.710Z
2020-03-06T20:04:42.710Z
Martin Van der Linden
<p><a href="http://rads.stackoverflow.com/amzn/click/0521438837" rel="nofollow noreferrer">Decisions with Multiple Objectives: Preferences and Value Tradeoffs</a>
by Ralph L Keeney</p>

CC BY-SA 3.0
2017-01-16T03:23:05.827Z
2017-01-16T03:23:05.827Z
decision maker
<p>I do not know about social choice, but for utility representations I think the two most cited books are "Convex analysis" by Rockafellar and "Infinite Dimensional Analysis: A Hitchhiker's Guide" by Alliprantis and Border. They contain most (if not all) results on convex analysis and functional analysis used by economists.</p>

CC BY-SA 3.0
2015-10-24T18:55:39.390Z
2015-10-24T18:55:39.390Z
Oliv
<p>I am looking for a set of mathematics books to understand proofs in decision theory. Examples would be proofs of utility representations and social choice (im-)possibility results. I found many textbooks on both decision theory and social choice, some of which contain proofs which contain references to mathematical results.</p>

<p>However, I could not find a collection of mathematical results commonly used in these fields. Usual "Mathematics for Economists" textbooks fall short. What is the standard reference/textbook researchers use to find the results they employ?</p>

<reference-request><decision-theory><social-choice>
What are good mathematics books to learn decision theory?
HRSE
# What are good mathematics books to learn decision theory?

(Asked by: username_0 on 2015-10-23)

I am looking for a set of mathematics books to understand proofs in decision theory. Examples would be proofs of utility representations and social choice (im-)possibility results. I found many textbooks on both decision theory and social choice, some of which contain proofs which contain references to mathematical results.

However, I could not find a collection of mathematical results commonly used in these fields. Usual "Mathematics for Economists" textbooks fall short. What is the standard reference/textbook researchers use to find the results they employ?

**Tags:** reference-request, decision-theory, social-choice

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## 3 answers

### Answer by username_3 on 2015-10-24. Score: 7 | Accepted answer

I do not know about social choice, but for utility representations I think the two most cited books are "Convex analysis" by Rockafellar and "Infinite Dimensional Analysis: A Hitchhiker's Guide" by Alliprantis and Border. They contain most (if not all) results on convex analysis and functional analysis used by economists.


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### Answer by username_1 on 2020-03-06. Score: 2

For decision theory:

* Gilboa, I. (2009). Theory of decision under uncertainty. Cambridge University Press.
* Parmigiani, G., & Inoue, L. (2009). Decision theory: Principles and approaches. John Wiley & Sons.
* Peterson, M. (2009). An introduction to decision theory. Cambridge University Press.

For social choice theory, see my answer to this question : [Good books to learn social choice theory](https://economics.stackexchange.com/questions/34334/good-books-to-learn-social-choice-theory).


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### Answer by username_2 on 2017-01-16. Score: 2

[Decisions with Multiple Objectives: Preferences and Value Tradeoffs](http://rads.stackoverflow.com/amzn/click/0521438837)
by Ralph L Keeney


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