<p>What you seem to be interested is the subfield of decision theory that goes by the name of "menu choice." The starting point of this literature is the paper</p>

<p>Kreps, David M. "<a href="http://www.isid.ac.in/~dmishra/pap_doc/kreps.pdf" rel="nofollow noreferrer">A representation theorem for preference for flexibility</a>." Econometrica: Journal of the Econometric Society (1979): 565-577.</p>

<p>This paper might be directly relevant to the problem you want to address.</p>

CC BY-SA 3.0
2017-08-17T09:40:01.553Z
Good starting point, from which I found the [Handbook of Utility Theory - Chapter 17: Ranking Sets of Objects](https://doi.org/10.1007/978-1-4020-7964-1_4) which gives a nice overview of different motivations for an agent preferences for flexibility as well.
Winks
CC BY-SA 3.0
2017-08-13T09:36:00.490Z
2017-08-13T09:46:27.007Z
2017-08-13T09:46:27.007Z
Michael Greinecker
<p>I am trying to find if there is some litterature or definition of the concept of the Utility of a <em>set</em> of choices. My google searches return nothing, and I expect it is because I do not know the right word. </p>

<p>Here is an example to illustrate what I am looking for.</p>

<hr>

<p>Consider the following items; a very nice sport car, <code>Car1</code>, the same model of car, only without some options such as no A/C and slightly worse seats, <code>Car2</code>, and a worn off pickup, <code>Truck</code>.</p>

<p>Say that all those vehicles have some associated utility, say</p>

<pre><code>u(Car1) = 500, u(Car2) = 490, u(Truck) = 100
</code></pre>

<p>While <code>Car2</code> is very good in isolation, it is dominated by <code>Car1</code> and very unlikely that anyone would pick <code>Car2</code> over <code>Car1</code>. The <code>Truck</code>, on the other hand, has a low value but might be picked over <code>Car1</code> under some circumstances.</p>

<p>Hence, the utility of the <em>set</em> of choices <code>{Car1, Truck}</code> should be higher than the value of the set <code>{Car1, Car2}</code> even if it contains lower quality items as the truck might actually be helpful.</p>

<hr>

<p>The assumption here is that the single value of utility associated with the item does not tell us exactly how the user makes its choice. We could assume for example that the utility of a vehicle is 2-dimensional and consists of <code>Niceness of the vehicle</code> and <code>Carrying capacity</code>.</p>

<p>The total utility of the vehicle is the sum of the utility provided by those two features, but the decision process might be more complicated and not follow the <a href="https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives" rel="nofollow noreferrer">Independance of Irrelevant Alternatives</a>/<a href="https://en.wikipedia.org/wiki/Luce%27s_choice_axiom" rel="nofollow noreferrer">Luce Choice Axiom</a> and would follow a model where <a href="https://en.wikipedia.org/wiki/Discrete_choice#Multinomial_choice_with_correlation_among_alternatives" rel="nofollow noreferrer">correlation among options</a> is possible.</p>

CC BY-SA 3.0
2017-08-12T20:23:33.290Z
So utility of truck is not fully reflecting the value the truck might have to the indivudual? How are then you defining utility? Seems arbitrary. Or, to put it differently, there is a second dimension of value that you have not made explicit, and that the individual uses to choose. It might be worth clarifying this. In any case, this topic, to my understanding, is related to [discrete choice theory](https://en.wikipedia.org/wiki/Discrete_choice) (in contrast to choosing amounts of continues variables).
luchonacho
<reference-request><choice-theory>
Vocabulary/Name for Utility of a Set of Choices
Winks
# Vocabulary/Name for Utility of a Set of Choices

(Asked by: username_0 on 2017-08-12)

I am trying to find if there is some litterature or definition of the concept of the Utility of a set of choices. My google searches return nothing, and I expect it is because I do not know the right word. 
Here is an example to illustrate what I am looking for.

Consider the following items; a very nice sport car, Car1, the same model of car, only without some options such as no A/C and slightly worse seats, Car2, and a worn off pickup, Truck.
Say that all those vehicles have some associated utility, say
u(Car1) = 500, u(Car2) = 490, u(Truck) = 100

While Car2 is very good in isolation, it is dominated by Car1 and very unlikely that anyone would pick Car2 over Car1. The Truck, on the other hand, has a low value but might be picked over Car1 under some circumstances.
Hence, the utility of the set of choices {Car1, Truck} should be higher than the value of the set {Car1, Car2} even if it contains lower quality items as the truck might actually be helpful.

The assumption here is that the single value of utility associated with the item does not tell us exactly how the user makes its choice. We could assume for example that the utility of a vehicle is 2-dimensional and consists of Niceness of the vehicle and Carrying capacity.
The total utility of the vehicle is the sum of the utility provided by those two features, but the decision process might be more complicated and not follow the Independance of Irrelevant Alternatives/Luce Choice Axiom and would follow a model where correlation among options is possible.

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

> **Comments:**
> **username_1**: So utility of truck is not fully reflecting the value the truck might have to the indivudual? How are then you defining utility? Seems arbitrary. Or, to put it differently, there is a second dimension of value that you have not made explicit, and that the individual uses to choose. It might be worth clarifying this. In any case, this topic, to my understanding, is related to [discrete choice theory](https://en.wikipedia.org/wiki/Discrete_choice) (in contrast to choosing amounts of continues variables).  

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## 1 answers

### Answer by username_2 on 2017-08-13. Score: 4 | Accepted answer

What you seem to be interested is the subfield of decision theory that goes by the name of "menu choice." The starting point of this literature is the paper

Kreps, David M. "[A representation theorem for preference for flexibility](http://www.isid.ac.in/~dmishra/pap_doc/kreps.pdf)." Econometrica: Journal of the Econometric Society (1979): 565-577.

This paper might be directly relevant to the problem you want to address.

> **Comments:**
> **username_0**: Good starting point, from which I found the [Handbook of Utility Theory - Chapter 17: Ranking Sets of Objects](https://doi.org/10.1007/978-1-4020-7964-1_4) which gives a nice overview of different motivations for an agent preferences for flexibility as well.  

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