# Are there mathematical models for multi-utility satisfaction?

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.

• 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 Jul 22 '20 at 16:39
• 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. Jul 22 '20 at 16:52
• Though even "rate the following items out of 10" type results would be welcome at this stage. Jul 22 '20 at 16:53
• 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... Jul 22 '20 at 17:04