<p>Starting from the textbook, I would highly recommend any textbook for <strong>stochastic dynamic optimization</strong>. Then I would recommend you to get acquainted with <strong>markov chains</strong>, because it is <em>relatively good introduction to how states might work</em>. If you want something more from economics side, a good read might be anything on <strong>Savage framework</strong>. Either his original work (1954) or following works from different authors.</p>
<p>What concerns the difference between state-dependence and state-independence, it all comes from how states and preferences work. State of the world might be depicted as binary raining/sunny dichotomy. Ordering of (rational = transitive + complete) preferences is captured by the utility function. Then:</p>
<ul>
<li><strong>State Dependent preferences:</strong> Ordering of preferences depends on the state of the world. For example, consumer who can buy ice cream or steak, might prefer steak over ice cream if it is raining, and ice cream over steak if it is sunny.</li>
<li><strong>State Independent preferences:</strong> This is the opposite. Your ordering of preferences is always the same, whatever happens. If you prefer steak over ice cream when it is sunny, you will prefer it also when it is raining.</li>
</ul>
<p>Explaining this more robustly, you have a utility function <span class="math-container">$U$</span>, for which it holds either <span class="math-container">$U = U(\boldsymbol{x})$</span> in case of state-independent preferences (<span class="math-container">$\boldsymbol{x}$</span> being choices) or <span class="math-container">$U = U(\boldsymbol{x}, \boldsymbol{\psi})$</span> in case of state-dependence (<span class="math-container">$\boldsymbol{\psi}$</span> being the states indicator).</p>
<p>What concerns some critical distinction between these two, state-dependence causes <strong>dynamic inconsistency</strong> by itself (stronger factor than discounting function which is not logarithmically linear).</p>

CC BY-SA 4.0
2023-01-12T19:30:07.953Z
States in Markov chains and in decision theory have pretty much nothing to do with each other.
Michael Greinecker
CC BY-SA 4.0
2023-01-12T23:01:57.740Z
@MichaelGreinecker Would you not consider markov decision process as a prime example of connection between markov chains and decision theory?
Athaeneus
CC BY-SA 4.0
2023-01-12T23:07:38.947Z
I would see this as part of optimization theory, but I'm fine with seeing it as part of decision theory. But it has nothing to do with the "states of the world" Savage and others were talking about.
Michael Greinecker
CC BY-SA 4.0
2023-01-12T23:18:21.913Z
It is possible I misunderstood it. I always understood the Savage's states of the world as some random variable: Healthy/Sick ; Sunny/Raining; or even some quantitative continuous ones... That, however, seems to me as close as possible to the Markov interpretation of states. If I have some lottery (for example: health while insured), some realization of this random variable would change my ordering of preferences, which seems to be in harmony with Savage's framework, but to me it is also similar to the case in which my utility function depends on, for example, current mood...
Athaeneus
CC BY-SA 4.0
2023-01-12T23:46:33.630Z
A random variable is actually a function on a probability space, and the points of the probability space would be what the states are. But I don't think reading books on probability spaces would help in relation to conceptual discussions about states such as [this](https://research.upjohn.org/cgi/viewcontent.cgi?filename=2&article=1176&context=up_press&type=additional), [this](https://faculty.econ.ucdavis.edu/faculty/schipper/notestates.pdf), or [this](http://wrap.warwick.ac.uk/91834/1/WRAP-states-nature-Karni-2017.pdf).
Michael Greinecker
CC BY-SA 4.0
2023-01-12T23:55:04.793Z
I would oppose this perception. I just opened the recommended links, skimmed through, and I have seen just discrete random variables, conditional probability, expected value, variance... Personally, I would say that good understanding of probability theory is the necessary condition for grasping the concept behind economic decision theory under uncertainty.
Athaeneus
CC BY-SA 4.0
2023-01-12T23:58:05.140Z
I said "probability spaces," positive, totally finite, normed measure spaces- not elementary probability theory.
Michael Greinecker
CC BY-SA 4.0
2023-01-13T00:04:53.870Z
To me this just sounds as a non-necessary mathematical purism. Well, how are probability spaces **in general** that different from elementary probability theory? Of course, you don't need the robust math behind it, but I am definitely not advocating in its favor. What I do advocate in favor of, instead, is to understand probability theory up to Markov chains because it helps to develop the probabilistic intuition which then helps in those more problematic cases... Excuse me, but what are we **really** arguing about right now?
Athaeneus
CC BY-SA 4.0
2023-01-12T08:01:24.363Z
2023-01-12T08:57:11.920Z
2023-01-12T08:57:11.920Z
Athaeneus
<p>I am working on changes in preferences and found papers on state-independent preference. What is the difference between state-dependent and state-independent preferences and utility functions? What are the assumptions change between the two? What is a textbook reference to understand the basics of two?</p>

CC BY-SA 4.0
2023-01-11T12:26:07.137Z
Do you mean state-dependent expected utility? It would be helpful to narrow it down.
Michael Greinecker
CC BY-SA 4.0
2023-01-14T16:50:34.813Z
I read state-dependent utility functions actually in literature.
desi arthshastri
CC BY-SA 4.0
2023-01-14T17:31:30.357Z
It would be helpful if you wrote which literature.
Michael Greinecker
<microeconomics><utility><preferences><choice-theory><measuring-utility>
State dependent preferences vs state independent preferences in utility theory
desi arthshastri
# State dependent preferences vs state independent preferences in utility theory

(Asked by: username_0 on 2023-01-11)

I am working on changes in preferences and found papers on state-independent preference. What is the difference between state-dependent and state-independent preferences and utility functions? What are the assumptions change between the two? What is a textbook reference to understand the basics of two?

**Tags:** microeconomics, utility, preferences, choice-theory, measuring-utility
> **Comments:**
> **username_1**: Do you mean state-dependent expected utility? It would be helpful to narrow it down.  
> **username_0**: I read state-dependent utility functions actually in literature.  
> **username_1**: It would be helpful if you wrote which literature.  

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## 1 answers

### Answer by username_2 on 2023-01-12. Score: 3 | Accepted answer

Starting from the textbook, I would highly recommend any textbook for **stochastic dynamic optimization**. Then I would recommend you to get acquainted with **markov chains**, because it is *relatively good introduction to how states might work*. If you want something more from economics side, a good read might be anything on **Savage framework**. Either his original work (1954) or following works from different authors.

What concerns the difference between state-dependence and state-independence, it all comes from how states and preferences work. State of the world might be depicted as binary raining/sunny dichotomy. Ordering of (rational = transitive + complete) preferences is captured by the utility function. Then:

* **State Dependent preferences:** Ordering of preferences depends on the state of the world. For example, consumer who can buy ice cream or steak, might prefer steak over ice cream if it is raining, and ice cream over steak if it is sunny.
* **State Independent preferences:** This is the opposite. Your ordering of preferences is always the same, whatever happens. If you prefer steak over ice cream when it is sunny, you will prefer it also when it is raining.

Explaining this more robustly, you have a utility function $U$, for which it holds either $U = U(\boldsymbol{x})$ in case of state-independent preferences ($\boldsymbol{x}$ being choices) or $U = U(\boldsymbol{x}, \boldsymbol{\psi})$ in case of state-dependence ($\boldsymbol{\psi}$ being the states indicator).

What concerns some critical distinction between these two, state-dependence causes **dynamic inconsistency** by itself (stronger factor than discounting function which is not logarithmically linear).

> **Comments:**
> **username_1**: States in Markov chains and in decision theory have pretty much nothing to do with each other.  
> **username_2**: @MichaelGreinecker Would you not consider markov decision process as a prime example of connection between markov chains and decision theory?  
> **username_1**: I would see this as part of optimization theory, but I'm fine with seeing it as part of decision theory. But it has nothing to do with the "states of the world" Savage and others were talking about.  
> **username_2**: It is possible I misunderstood it. I always understood the Savage's states of the world as some random variable: Healthy/Sick ; Sunny/Raining; or even some quantitative continuous ones... That, however, seems to me as close as possible to the Markov interpretation of states. If I have some lottery (for example: health while insured), some realization of this random variable would change my ordering of preferences, which seems to be in harmony with Savage's framework, but to me it is also similar to the case in which my utility function depends on, for example, current mood...  
> **username_1**: A random variable is actually a function on a probability space, and the points of the probability space would be what the states are. But I don't think reading books on probability spaces would help in relation to conceptual discussions about states such as [this](https://research.upjohn.org/cgi/viewcontent.cgi?filename=2&article=1176&context=up_press&type=additional), [this](https://faculty.econ.ucdavis.edu/faculty/schipper/notestates.pdf), or [this](http://wrap.warwick.ac.uk/91834/1/WRAP-states-nature-Karni-2017.pdf).  
> **username_2**: I would oppose this perception. I just opened the recommended links, skimmed through, and I have seen just discrete random variables, conditional probability, expected value, variance... Personally, I would say that good understanding of probability theory is the necessary condition for grasping the concept behind economic decision theory under uncertainty.  
> **username_1**: I said "probability spaces," positive, totally finite, normed measure spaces- not elementary probability theory.  
> **username_2**: To me this just sounds as a non-necessary mathematical purism. Well, how are probability spaces **in general** that different from elementary probability theory? Of course, you don't need the robust math behind it, but I am definitely not advocating in its favor. What I do advocate in favor of, instead, is to understand probability theory up to Markov chains because it helps to develop the probabilistic intuition which then helps in those more problematic cases... Excuse me, but what are we **really** arguing about right now?  

---

