Utility Theory and Just-Noticeable Differences in Measuring Satisfaction

# Function that best describes intensity of human/(group of humans) emotions?


# Function that best describes intensity of human/(group of humans) emotions?












Let me give you couple of examples. You're at a dinner and you order something. You could say:

- "It's OK"

- "It's good"

- "It's great"

- "It's fantastic"

- "I've never ate something this good"

- "Goodlike"

The similar grading can be made for bad food. The next example would be if you won the prize. We could look at the connection between the prize value and the satisfaction that you experience. My assumption is that quality of food vs pleasure would look something like this: If you increase the quality of food the pleasure would rise fast, you would get to a point where you'd be satisfied that you've eaten well, after that there would be dampening of an effect, if you could increase the food quality to infinity, the pleasure would remain constant after one point. The same goes for wining a prize, if you won 1000$ and if you won a million dollars, the difference between satisfaction you would experience would be much larger then the difference if you won 100million vs 101million dollars. Has anybody made measurements of similar examples? How would that function look like, would it be linear and then started bending after some critical point. Would it be exponential at the beginning then get saturated after some critical point? Would it look something like tanh, Fermi-Dirac? What about the bad examples, bad food, paying taxes etc? I assume that it's not symmetric. Any differences in group effects? (Nations, sports, business teams etc?)

## Answer by SRKX (score 7, accepted)

https://quant.stackexchange.com/a/3380

I believe you should look into the field of Utility Theory which aims to model how people actually understand and feel about gains and losses. Usually, the most interesting cases are when the outcomes of the experiment are actually random, or when the payment can occur at different times.

A famous model for the utility function is Risk Aversion. You can start from there.

I would also like to say that this question could be answered more in details in Economics SE because it is a very important aspect of that field.

Besides, there is also some research done in Game Theory aiming to model people's preferences and designing voting mechanisms.

## Answer by Michael Greinecker (score 5)

https://quant.stackexchange.com/a/3381

One can get some kind of absolute measure of satisfaction by working with just noticable differences. The idea is that a decision maker is indifferent between very similar choices but not indifferent between dissimilar choices. Here is an example: A decisonmaker likes sugar, and wants as much sugar as possible- with a caveat. Let $\epsilon>0$ be the just notable difference and $s_1$ and $s_2$ be two amounts of sugar. Then the consumer prefers $s_1$ weakly to $s_2$, in symbols $s_1\succeq s_2$, if $s_1$ isn't noticable smaller than $s_2$. That is, $s_1\succeq s_2$ if and only if $s_2-s_1<\epsilon$. The resulting preference relation is not transitive, but the assymetric part $\succ$, given by $s_1\succ s_2$ iff $s_1\succeq s_2$ and $\neg(s_2\succeq s_2)$, is transitive. With such preferences, one can get an absolute scale of measurement, based on the number of just-notable-differences from zero (if there is a zero).

A discussion of this approach can be found in section 6.4.1. in Theory of Decision under Uncertainty by Itzhak Gilboa.