<p>In several places I have seen reference to the <em>law of diminishing returns</em> with regard to satisfaction. A common toy example is eating cookies. The first cookie gives some amount of satisfaction, the second some smaller amount, and so on. It follows the satisfaction function  <span class="math-container">$S(n)$</span> is a convex function of the number <span class="math-container">$n$</span> of cookies eaten.</p>
<p>This seems quite reasonable but I wonder how is it backed up experimentally? Are there studies where subjects are given various amounts of <em>something</em> and their satisfaction is somehow measured?</p>
<p>Three follow-up questions:</p>
<ol>
<li><p>Has this been done using some objective measure of satisfaction rather than just asking the subject?</p>
</li>
<li><p>Are there any mathematical models for the shape of the convex function?</p>
</li>
<li><p>How do things change is there are several utilities? So <span class="math-container">$S(n,x)$</span> where <span class="math-container">$n$</span> is the number of cookies and <span class="math-container">$x$</span> describes the quality.</p>
</li>
</ol>

CC BY-SA 4.0
2020-07-22T16:39:50.327Z
This is an interesting question, I wonder if satisfaction can be quantified? Because if it can be mapped out as a function of several factors like no. of cookies and quality ( pertaining to the example already provided) then one can use this model to predict customer satisfaction and be ahead of the Customer, every time. It could have huge impacts to conventional economics.
Ps: sorry I have no answers to as to whether this is possible or not :p
Hosanna Vj
CC BY-SA 4.0
2020-07-22T16:52:18.097Z
Ideally you would quantify it by offering a bunch of combinations of amount and quality, and then analysing what people choose. You could also compare to some fixed resource by having people "buy" their favourite combination.
Daron
CC BY-SA 4.0
2020-07-22T16:53:13.377Z
Though even "rate the following items out of 10" type results would be welcome at this stage.
Daron
CC BY-SA 4.0
2020-07-22T17:04:05.890Z
Yes, I guess that a combination of the methodologies that effectively cover all the aspects that drive satisfaction of said product, when compared to an unchanging model could begin to tell us how to quantify satisfactionw with respect to that particular product. If we catalogue and analyze enough products for the satisfaction they cause we might be able to create a model that could integrate all these results into finally measuring human satisfaction...
Hosanna Vj
<reference-request><experimental-psychology><mathematical-psychology><preferences><model>
Are there mathematical models for multi-utility satisfaction?
Daron
# Are there mathematical models for multi-utility satisfaction?

(Asked by: username_0 on 2020-07-21)

In several places I have seen reference to the *law of diminishing returns* with regard to satisfaction. A common toy example is eating cookies. The first cookie gives some amount of satisfaction, the second some smaller amount, and so on. It follows the satisfaction function $S(n)$ is a convex function of the number $n$ of cookies eaten.

This seems quite reasonable but I wonder how is it backed up experimentally? Are there studies where subjects are given various amounts of *something* and their satisfaction is somehow measured?

Three follow-up questions:

1. Has this been done using some objective measure of satisfaction rather than just asking the subject?
2. Are there any mathematical models for the shape of the convex function?
3. How do things change is there are several utilities? So $S(n,x)$ where $n$ is the number of cookies and $x$ describes the quality.

**Tags:** reference-request, experimental-psychology, mathematical-psychology, preferences, model

> **Comments:**
> **username_1**: This is an interesting question, I wonder if satisfaction can be quantified? Because if it can be mapped out as a function of several factors like no. of cookies and quality ( pertaining to the example already provided) then one can use this model to predict customer satisfaction and be ahead of the Customer, every time. It could have huge impacts to conventional economics. Ps: sorry I have no answers to as to whether this is possible or not :p  
> **username_0**: Ideally you would quantify it by offering a bunch of combinations of amount and quality, and then analysing what people choose. You could also compare to some fixed resource by having people "buy" their favourite combination.  
> **username_0**: Though even "rate the following items out of 10" type results would be welcome at this stage.  
> **username_1**: Yes, I guess that a combination of the methodologies that effectively cover all the aspects that drive satisfaction of said product, when compared to an unchanging model could begin to tell us how to quantify satisfactionw with respect to that particular product. If we catalogue and analyze enough products for the satisfaction they cause we might be able to create a model that could integrate all these results into finally measuring human satisfaction...  

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## 0 answers

