Better think twice about established theories, especially in economy. For the bias between theories and reality check out the paper **Prospect Theory: An Analysis of Decision under Risk** (1979) by **Nobel Prize winner Daniel Kahneman** and Amos Tversky.

**How do people actually make decisions?** In brief, Kahneman & Tversky test the by-then established theory of **expected utility** against empirically obtained data. In result, **the theory fails**. For an illustration of their work, consider the options 1. or 2. with

*50% chance to win 1,000 Euro and 50% chance to win nothing*

*450 Euro for sure*

**what would you choose?**

Consider that the *expected value* **is larger** for 1. than for 2.. (For each option, multiply the amount that you can win with the chance that you win it and sum over all amounts. This is the *expected value*. Check that the total of the chances yields 100% per option.) However, **human mind seems to decide differently**.

Kahneman & Tversky give a lot more **entertaining and illustrating examples**, (which are partly based on work of the economist Maurice Allais in 1953). For example:

Consider PETER who wears a red T-shirt. He won som money in the lottery and wants to play a decision-game with you. He asks you to choose option 1. or 2.:

**2500 with 33% and 2400 with 66% and 0 with 0.1%**
**2400 with certainty**

Consider ANNA with a short green skirt and long blond hair. She has also got some money left and asks you to choose option 1. or 2.

*2,500 with 33% and 0 with 67%*
*2,400 with 34% and 0 with 66%*

Apparently, in PETER’s setting, most people choose 2.. In ANNA’s set-up, most people choose 1.. Where is the problem?

(Forget about the short skirt.) Let’s focus on the numbers: In Peter’s case, human cherish the utility to win 2400 with 100% more than to win 2500 with 33% or 2400 with 66%. **Utility theory** would postulate that you can write this in following equation (with multiplication “*” and fixed “utility assignments” u(2400) and u(2500)):

100*u(2400) > 33*u(2500) + 66*u(2400)

Now, **utility theory** would postulate that you can treat this with usual algebra operations and subtract 66*u(2400) at both sides which yields:

**34*u(2400) > 33*u(2500).**

Ok. Hence, whether or not this makes sense depends on the values of u(2400) and u(2500).

Now, consider this operation for Anna’s question. This yields:

**33*u(2500) > 34*u(2400)**

This is just **the opposite. **Apparently, there is some **problem with the theory**. Namely there is a **mismatch** between the mathematical concepts which are used here and the **real world**.

Ok, whatever skirt or T-shirt Anna wears, one can wonder whether there is some **structural deviation** from rational decision-making in the human brain.

**In brief:** People seem to** like high gains with low probability** (think about lotteries) and people seem to **prefer security **with less expected value** over 50/50 chances **with higher expected value (think about the market of assurances).

Kahneman & Tversky propose a **value function** for scaling the gains and losses. (They propose a function which is concave for gains and convex for losses and steeper for gains than for losses). Furthermore, they analyse **weighting functions** for the dealing of probabilities of the human mind. Also, they notice that decision-making depends on which **reference point** you choose. The interesting part is that this reference point can be **influenced by the alternatives** that you have.

**My personal conclusion**: Honestly, **I do not think** that value functions and weighting functions really can take into account the complexity of **human decision-making**.

Assume that we have a decision problem, as above, with two options and two assignments of chances. Assume that we want to estimate how a certain person (or company) decides. Then we need to **assign eight parameters** in order to assess how this agent decides. From my perspective, this is the **fiddler’s game, **which means fitting curves to data. Not really satisfying from theoretical perspective. Furthermore, from my perspective, **the reference point** will have a much larger effect on decision-making than the shape of the scaling functions!

**This is why, honestly**, I think that it is much more important to assess the reference point. Take the individual setting of the decision problem into account. Nevertheless, this **paper is absolutely worth reading**. It is inspiring! **It gives illustrating backbone to the bias between mathematical simplicity and the complex reality. I love it!**

**Enjoy reading!**