<p>It means what Herr K. has guessed: there are acts $f$ and $g$ that the decision maker does not deem equivalent from the preference standpoint. In other words, the DM expresses a strong preference in at least one comparison he makes. a preference that does <strong>not</strong> satisfy it is a AA subjective expected utility with a constant index $u$ (i.e. such that the representation is $\int u dp$ for an arbitrary belief $p$). On the other hand if at least for one comparison the DM says $f$ is strictly better than $g$ then you satisfy it. </p>

CC BY-SA 3.0
2017-07-15T15:03:55.303Z
I might add: the reason for this assumption is so that $u(x) = c$ for some constant $c$ does not rationalize the preference. This state of affairs is both boring and destroys any uniqueness results (since beliefs no longer play any role they can be arbitrary).
201p
CC BY-SA 3.0
2017-07-05T11:56:57.160Z
2017-07-05T11:56:57.160Z
Enrico
<p>I saw a non-degeneracy assumption in Gilboa and Schmeidler's paper (maxmin expected utility with non-unique prior).</p>

<p>The statement is "Not for all $f$ and $g$ in $L$, $f \geq g$".</p>

<p>So can you explain the intuition for this assumption and give some example so that I can understand the "non-degeneracy" property better?</p>

CC BY-SA 3.0
2017-05-13T05:56:02.947Z
My first guess would be something related to a [degenerate probability distribution](https://en.wikipedia.org/wiki/Degenerate_distribution). But please provide a bit more details: a link to the paper or the full statement of the assumption.
Herr K.
CC BY-SA 3.0
2017-05-13T06:54:18.520Z
Hi, here is a link:
 https://www.researchgate.net/publication/4902609_Maxmin_Expected_Utility_With_Non-Unique_Prior. The non-degeneracy assumption is on page 144 of the original paper, under the name of A.6.
ask
CC BY-SA 3.0
2017-05-13T08:11:29.947Z
Perhaps it is easier to understand non-degeneracy if we look at the contrapositive of the statement: 
**There exist (horse lotteries) $f,g\in L$ such that $f>g$.**
In other words, $\geq$ is not a preference relation that treats all horse lotteries in $L$ equally; it strictly prefers some $f$ to some $g$. Unfortunately I can't produce examples to help elucidate this, as I'm not that familiar with this field. Maybe looking up Anscombe-Aumann's definition of subjective probability will help.
Herr K.
<microeconomics><mathematical-economics><preferences><decision-theory>
What does non degeneracy mean for a preference?
ask
# What does non degeneracy mean for a preference?

(Asked by: username_0 on 2017-05-13)

I saw a non-degeneracy assumption in Gilboa and Schmeidler's paper (maxmin expected utility with non-unique prior).

The statement is "Not for all $f$ and $g$ in $L$, $f \geq g$".

So can you explain the intuition for this assumption and give some example so that I can understand the "non-degeneracy" property better?

**Tags:** microeconomics, mathematical-economics, preferences, decision-theory

> **Comments:**
> **username_1**: My first guess would be something related to a [degenerate probability distribution](https://en.wikipedia.org/wiki/Degenerate_distribution). But please provide a bit more details: a link to the paper or the full statement of the assumption.  
> **username_0**: Hi, here is a link:  https://www.researchgate.net/publication/4902609_Maxmin_Expected_Utility_With_Non-Unique_Prior. The non-degeneracy assumption is on page 144 of the original paper, under the name of A.6.  
> **username_1**: Perhaps it is easier to understand non-degeneracy if we look at the contrapositive of the statement:  **There exist (horse lotteries) $f,g\in L$ such that $f>g$.** In other words, $\geq$ is not a preference relation that treats all horse lotteries in $L$ equally; it strictly prefers some $f$ to some $g$. Unfortunately I can't produce examples to help elucidate this, as I'm not that familiar with this field. Maybe looking up Anscombe-Aumann's definition of subjective probability will help.  

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## 1 answers

### Answer by username_2 on 2017-07-05. Score: 1

It means what username_1 has guessed: there are acts $f$ and $g$ that the decision maker does not deem equivalent from the preference standpoint. In other words, the DM expresses a strong preference in at least one comparison he makes. a preference that does **not** satisfy it is a AA subjective expected utility with a constant index $u$ (i.e. such that the representation is $\int u dp$ for an arbitrary belief $p$). On the other hand if at least for one comparison the DM says $f$ is strictly better than $g$ then you satisfy it.

> **Comments:**
> **username_3**: I might add: the reason for this assumption is so that $u(x) = c$ for some constant $c$ does not rationalize the preference. This state of affairs is both boring and destroys any uniqueness results (since beliefs no longer play any role they can be arbitrary).  

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