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

  1. 50% chance to win 1,000 Euro and 50% chance to win nothing
  2. 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.:

  1. 2500 with 33% and 2400 with 66% and 0 with 0.1%
  2. 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.

  1. 2,500 with 33% and 0 with 67%
  2. 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!

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