<p>I have been looking into different models used to consider decisons under ambiguity. One of the simplest models to use is the &quot;Alpha Max-Min Model&quot; where we think of ambiguity resulting from facing a choice over multiple priors. (An excellent overview of the model is provided in a video by Peter Wakker <a href="https://www.youtube.com/watch?v=MfFMEms4mIY" rel="noreferrer">here</a>. )</p>
<p>The Alpha Max-Min Model is defined as:
<span class="math-container">$$\alpha \min_{p\in P}EU(x)+(1-\alpha) \max_{p\in P}EU(x)$$</span></p>
<p>where:</p>
<ul>
<li><span class="math-container">$p$</span> is a vector of probabilities assigned to outcomes <span class="math-container">$x$</span> from a set of possible priors <span class="math-container">$P$</span></li>
<li><span class="math-container">$\alpha$</span> is said to be the degree of &quot;ambiguity aversion&quot; <strong>(I don't know what this is)</strong>.</li>
</ul>
<p>we say if <span class="math-container">$\alpha=1$</span> we are &quot;model pessimistic&quot; or <strong>ambiguity adverse</strong> (assuming worst case scenario) and if <span class="math-container">$\alpha=0$</span> we are &quot;model optimistic&quot; or <strong>ambiguity seeking</strong> (assuming best case scenario).</p>
<p>What I see from this is that we essentially just think of aversion ambiguity as a degree of confidence we have between our worst case and best case priors.</p>
<p>To summarize: why can we use <span class="math-container">$\alpha$</span> as a measure of ambiguity aversion?</p>

CC BY-SA 4.0
2024-08-16T00:30:08.727Z
This is interesting, but what if the "worst case" and "best case" aren't well defined? This model with $\alpha$ is almost like taking a "uniform distribution" between two priors that we're assuming is continuous. Is there a way of generalizing this sort of idea, but to a distribution of continuous priors? (Typing that sentence makes me feel like a mad scientist.)
Kitsune Cavalry
CC BY-SA 4.0
2024-08-16T00:49:12.263Z
@KitsuneCavalry if the best and worst cases arent well defined we replace max and min with sup and inf.  Im restricting ourselves to priors being discrete ala the anscombe- aumann framing of uncertainty.
EconJohn
CC BY-SA 4.0
2024-08-16T04:10:52.670Z
Take a look at the [handbook chapter](https://econweb.ucsd.edu/~mmachina/papers/Machina-Siniscalchi_Handbook_Chapter_on_Ambig_&_Ambig_Aver.pdf) by Machina and Siniscalchi (2014), particularly [Section 13.5.1](https://econweb.ucsd.edu/~mmachina/papers/Machina-Siniscalchi_Handbook_Chapter_on_Ambig_&_Ambig_Aver.pdf#page=23). Interestingly, it is argued that "the intuitive
interpretation of α as an ambiguity-aversion parameter is not warranted in general".
Herr K.
CC BY-SA 4.0
2024-08-16T20:14:16.517Z
@HerrK. well now, it makes me happy to see that im in good company for being skeptical of using alpha as an ambiguity parameter. (I wish was comfortable using it as it would make my work much easier!).
EconJohn
<decision-theory><behavioral-economics>
What exactly is ambiguity aversion? (in reference to alpha max-min model)
EconJohn
# What exactly is ambiguity aversion? (in reference to alpha max-min model)

(Asked by: username_0 on 2024-08-15)

I have been looking into different models used to consider decisons under ambiguity. One of the simplest models to use is the "Alpha Max-Min Model" where we think of ambiguity resulting from facing a choice over multiple priors. (An excellent overview of the model is provided in a video by Peter Wakker [here](https://www.youtube.com/watch?v=MfFMEms4mIY). )

The Alpha Max-Min Model is defined as:
$$\alpha \min\_{p\in P}EU(x)+(1-\alpha) \max\_{p\in P}EU(x)$$

where:

* $p$ is a vector of probabilities assigned to outcomes $x$ from a set of possible priors $P$
* $\alpha$ is said to be the degree of "ambiguity aversion" **(I don't know what this is)**.

we say if $\alpha=1$ we are "model pessimistic" or **ambiguity adverse** (assuming worst case scenario) and if $\alpha=0$ we are "model optimistic" or **ambiguity seeking** (assuming best case scenario).

What I see from this is that we essentially just think of aversion ambiguity as a degree of confidence we have between our worst case and best case priors.

To summarize: why can we use $\alpha$ as a measure of ambiguity aversion?

**Tags:** decision-theory, behavioral-economics

> **Comments:**
> **username_1**: This is interesting, but what if the "worst case" and "best case" aren't well defined? This model with $\alpha$ is almost like taking a "uniform distribution" between two priors that we're assuming is continuous. Is there a way of generalizing this sort of idea, but to a distribution of continuous priors? (Typing that sentence makes me feel like a mad scientist.)  
> **username_0**: @username_1 if the best and worst cases arent well defined we replace max and min with sup and inf.  Im restricting ourselves to priors being discrete ala the anscombe- aumann framing of uncertainty.  
> **username_2**: Take a look at the [handbook chapter](https://econweb.ucsd.edu/~mmachina/papers/Machina-Siniscalchi_Handbook_Chapter_on_Ambig_&_Ambig_Aver.pdf) by Machina and Siniscalchi (2014), particularly [Section 13.5.1](https://econweb.ucsd.edu/~mmachina/papers/Machina-Siniscalchi_Handbook_Chapter_on_Ambig_&_Ambig_Aver.pdf#page=23). Interestingly, it is argued that "the intuitive interpretation of α as an ambiguity-aversion parameter is not warranted in general".  
> **username_0**: @HerrK. well now, it makes me happy to see that im in good company for being skeptical of using alpha as an ambiguity parameter. (I wish was comfortable using it as it would make my work much easier!).  

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## 0 answers

