Based on the writings of Kahneman, D. (2011). Thinking Fast and Slow New York, NY: Farrar, Straus, and Giroux. Part 4 – Choices.  Chapter 25: Bernoulli’s Errors (pp. 269 – 277).

 

Daniel Kahneman’s chapter 25, “Bernoulli’s Errors”, was just basically supposed to be an introduction into how Prospect Theory was developed from a realization that the economists’ theories about human decision-making were very different from psychologists’ views of human decision making. Economist think of humans as logical, rational, selfish, and having unchanging tastes. Whereas, psychologists think of humans as basing many of their decisions on information that is readily available and easily comes to mind (cognitively lazy) which makes them feel good and emotionally driven rather than logical or rational; they tend not to be completely selfish or selfless; and their tastes change regularly and often. Economists’ theories have been established for some 300 years and Kahneman built his theory off Daniel Bernoulli’s theory which was based on his older brother, Nicolas Bernoulli’s writings and teachings which were based on the St. Petersburg Paradox – or named the St. Petersburg Paradox because Daniel was working in St. Petersburg when he published it – or something like that.

I’m not going to try to pretend that I’m an economist because I’m not. I’m a psychologist… cognitive, I guess. My degree was in Applied and Experimental Human Factors Psychology which is a multi-disciplinary degree. My background covers a great deal of decision-making and human performance. I’ve also studied physiological psychology and sensory perception. Cognitive perception, emotion, and how various influences in one’s life can impact their motivation and behavior are also large areas of my background. Attention, perception, decision-making, and response is the usual flow. How all these things interact on how real human beings make decisions and behave, is complicated. Psychologists and economists strive to make human behavior predictable through theories and formulas. Now, since I am not an economist and am not currently well versed in all the economic theories that have evolved over the centuries – I cannot easily synopsize all the research on Daniel Bernoulli, Nicolas Bernoulli, Gabriel Cramer, the St. Petersburg Paradox, Expected Utility Theory, and so on and so on here. I will tell you that there are many places on the internet that attempt to do just that and appear to do that fairly well but without deeper knowledge on the matter, I am unable to determine which one is on the money.

Basically, for an extraordinarily brief take on the topic  – economists utilize the expected utility theory, from which the rational-agent model was developed. The rational-agent model was a “logic of choice” model. Kahneman and Tversky decided to look at “rules that govern people’s choices between different simple gambles and between gambles and sure things” (pp. 270). They set out to see “how humans actually make risky choices, without assuming anything about their rationality” (pp. 271). After five years they published “Prospect Theory: An Analyses of Decision under Risk” (pp. 271). Their model differed from utility theory in that it was a descriptive attempt to document when rationality is NOT utilized during decision-making. Prospect Theory was a modification of expected utility theory, predicting violations of the axioms or assumptions – such as rationality and logic in human decision-making during gambles.

Kahneman pointed out that expected utility theory only compared the possible outcomes of a choice, ignoring the perspective of where the decision-maker was originating, financially – their wealth… sort-of. Bernoulli’s contribution to Nicolas and the St. Petersburg Theory seemed to be that one’s wealth aids in predicting how one will behave, such as a poor person is more willing to pay a rich person to insure their ship because they are willing to pay a premium to protect from a large loss. The theory has been proven true and applicable for around 300 years but it didn’t cover all applications.

The original theory used probability to weigh the possible outcomes and stated something along the lines that, if you end up with say 4 million dollars, you should be happy but Prospect Theory points out that, if you started with 9 million you won’t be happy and if you started with one thousand you might be extremely happy. The concept of one’s wealth seems to be in both theories but applied differently. One is willing to pay a premium to protect from a loss and the other is not willing to risk any money even for the chance of ending up with more money. To me… both look at one’s original wealth and one is willing to lose a little money to prevent from loosing a lot of money or their livelihood and the other is not willing to risk loosing any money for the chance to win more money – especially if it means they are possibly going to just be out some money. A guaranteed loss for both but one has more to lose (their livelihood) and the other has no real reason to risk their money in the first place – they are just gambling what they have for fun gains but not for necessary gains or protection.

It seems like both must consider the impact of the status quo to evaluate the proper risk to the decision-maker (i.e., subjective risk). Kahneman refers to Gustav Fechner’s (1801-1887) insights into subjective perception. For example, a dim light in the pitch black is subjectively brighter than that same light in the broad sunlight. Or a loud noise following deep silence can be subjectively more intense than the same noise when it is heard in a noisy club. These subjective perceptions can be translated to one’s perception of risk or wealth.

During this time, Kahneman and Tversky also realized the effect of framing or “framing effects” (pp. 271). That is, “the large changes of preferences that are sometimes caused by inconsequential variations in the wording of a choice problem” (pp. 272). Often a person’s perception of something can be drastically altered by the framing of the information presented. Therefore, one’s perception of a risk can be altered if a question is framed a certain way. Politicians often frame a controversial comment with features that most would generally find agreeable, such as “for our children’s future”, “our history”, “our culture”, or “economics”. These attempts to sway people’s decision-making about policies and changes to the government and the country are framed with things that people approve of which may alter their perception of a complicated or a terrible truth. Remember, from previous posts, we humans tend to be cognitively lazy and readily welcome any information that justifies or simplifies our decisions, especially ones that make us feel good about ourselves.

So, back to Daniel Bernoulli who in 1738 looked at the “psychological value or desirability of money”/utility (pp. 272). Prior to Bernoulli it was assumed that people assessed their risk on the expected value and the probability of the possible outcome, (e.g., 10% chance to win x or 10% chance to lose x). Bernoulli proposed that “the psychological response to a change of wealth is inversely proportional to the initial amount of wealth” (logarithmically – there is a chart). Bernoulli found that most people don’t like to take risk and they prefer a sure thing, even if it results in less money than they might possibly get if they took the risk but there was a “diminishing marginal value of wealth”. That is, if you have a million dollars, the addition of another million has more “utility points” or psychological value than the chance to gain one million if you already have nine million (pp. 274). Therefore, a person is more likely to be” risk averse” if the situation shows “diminishing marginal utility for wealth” (pp. 274). “His utility function explained why poor people buy insurance” (because they are risk averse and are willing to pay a premium for some security) “and why rich people sell it to them” (because they are more likely to just get money and lose nothing and if they did have to pay out, it would only be an amount they are willing to risk loosing in comparison to what they have and have to gain). This is still considered a valuable and useful contribution to economics 300 years later – even though, as Kahneman states, it was “flawed” (pp. 274).

The flaw is what Kahneman noticed because he was looking with fresh eyes at an area in which he hadn’t been indoctrinated. He was a newbie to the filed of economic theory and to decision-making (his partner Amos Tversky’s area) and therefore didn’t think it was an issue to question everything – even something that had been accepted for 300 years in the economics field. Kahneman referred to the fact that Bernoulli’s theory went unchallenged for 300 years as “theory-induced blindness” (i.e., when something is so widely accepted that no one sees its flaws) (pp.277).  The flaw or what Kahneman and Tversky add to the theory is the perspective of personal wealth. Personal wealth is easily overlooked because it was mentioned in the “diminishing marginal utility for wealth” which influences the person’s risk taking or risk aversion behavior. Nevertheless, one’s financial status was not applied to predicting peoples’ decision-making behavior when presented with a gamble. What choice will one make when faced with a chance to gain or lose money, a chance to gain or lose nothing, or a sure gain or loss of money, or some combination thereof? Well, as Bernoulli found – generally, people don’t want to lose money or security.  People are risk averse.

Of course, people’s’ risk aversion may be altered if they value the sacrifice. That is, they are sacrificing money or time or something of value for something they believe in – supporting a good cause, benefitting someone or something that they value (e.g., my loss is their gain). The utility in that case is the positive feeling they get from giving money or time or belongings. Kahneman and Tversky found that the person’s “utility of wealth” or psychological value placed on a possible gain or loss is strongly influenced by the amount of money the person started with (i.e., their baseline wealth).  Kahneman and Tversky asked – are two people who end up with an equal amount of wealth, equally happy? (Do they have the same utility?)”. Does the same resultant amount of money mean the same amount of happiness? If you want to be able to predict human behavior – you need to consider how the person perceives how they will feel after the decision is made and they either gain or lose money based on their action of either taking a risk or a sure thing. Their perception of how they will feel post outcome will influence their risk taking and risk averse behavior.

Bernoulli predicted that people prefer a sure thing to a risk/gamble. Kahneman and Tversky pointed out, that is true unless the sure thing is going to be a sure loss from their baseline wealth. Utility is based on where they began – their baseline wealth. If given two bad choices in which both the gamble and the sure thing result in a loss of wealth from the baseline then they will choose whichever is more likely to lose the least. If there is even a small chance that they won’t lose any of their original wealth, than they are more likely to take that risk. Similar to Bernoulli’s example of preferring to lose some (e.g., insurance payments) and possibly not loosing anything, to any chance of loosing an important percentage of their wealth (i.e., lesser of two evils).

I would agree that you must always consider the individual’s perspective of their individual baseline wealth to predict their behavior but I would add that one must also consider the personal value one may place on a particular loss (e.g., contributing towards something they believe in – altruism,  green investments, or their future). People will take great risks to protect their wealth and others will take great risks to gain wealth – especially if they have nothing to lose because they have so little. Kahneman refers to entrepreneurs and generals faced with two bad options but I think of immigrants and refugees seeking a better life for themselves and their families – risking everything for the possibility of a better life and at the same time feeling like loosing everything they have, all current wealth, would be worth the possible gain of eventual opportunity, safety, security, and well-being. An odd play of Maslow’s hierarchy of Needs, restructuring the perceptual value of wealth.

 

Notes to Self:

• Read “Mathematical Psychology” by Amos – it is on decision making.
• Look up: John von Neumann – giant intellect of 20th century; Oskar Morgenstern – economist who derived theory of logical choice between gambles; Gustav Fechner – “psychologist and mystic” – the subjective perception based on where the previous stimulus was established.
• Check out Econometrica Journal – the journal they published their prospect theory essay and changed their lives. He stated that had they published in a psych journal it would have had little impact on economics. Econometrica is where the best papers on decision-making had been published.