Prospect Theory
"Whenever you form a global evaluation of a complex object — a car you may buy, your son-in-law, or an uncertain situation — you assign weights to its characteristics. [..] The assignment of weights is sometimes conscious and deliberate. Most often, however, you are just an observer to a global evaluation that your System 1 delivers. [...] The decision weights that people assign to outcomes are not identical to the probabilities of these outcomes, contrary to the expectation principle. Improbable outcomes are overweighted - this is the possibility effect. Outcomes that are almost certain are underweighted relative to actual certainty.[...]Two insights are the essence of prospect theory:
- In mixed gambles, where both a gain and a loss are possible, loss aversion causes extremely risk-averse choices.
- In bad choices, where a sure loss is compared to a larger loss that is merely probable, diminishing sensitivity causes risk seeking.[...]
- Evaluation is relative to a neutral reference point, which is sometimes referred to as an “adaptation level”. Outcomes that are better than the reference points are gains. Below the reference point they are losses.
- A principle of diminishing sensitivity applies to both sensory dimensions and the evaluation of changes of wealth.
- The third principle is loss aversion. When directly compared or weighted against each other, losses loom larger than gains. This asymmetry between the power of positive and negative expectations or experiences has an evolutionary history.
Fig 1 - Graph of Prospect Theory
The graph (fig. 1) shows the psychological value of gains and losses, which are the “carriers” of value in prospect theory (unlike Bernoulli’s model, in which states of wealth are the carriers of value). The graph has two distinct parts, to the right and to the left of a neutral reference point. A salient feature is that it is S-shaped, which represents diminishing sensitivity for both gains and losses. Finally, the two curves of the S are not symmetrical. The slope of the function changes abruptly at the reference point: the response to losses is stronger than the response to corresponding gains. This is loss aversion. [...]
Blind Spots of Prospect Theory
- Relative to your expectations, winning nothing will be experienced as a large loss. Prospect theory cannot cope with this fact, because it does not allow the value of an outcome (in this case, winning nothing) to change when it is highly unlikely, or when the alternative is very valuable. In simple words, prospect theory cannot deal with disappointment.
- Prospect theory and utility theory also fail to allow for regret. The two theories share the assumption that available options in a choice are evaluated separately and independently, and that the option with the highest value is selected."
The Fourfold Pattern
Fig. 2 - The Fourfold Pattern
The top row in each cell shows an illustrative prospect (see fig, 2).
The second row characterizes the focal emotion that the prospect evokes.
The third row indicates how most people behave when offered a choice between a gamble and a sure gain (or loss) that corresponds to its expected value (for example, between “95% chance to win $10,000” and “$9,500 with certainty”). Choices are said to be risk averse if the sure thing is preferred, risk seeking if the gamble is preferred.
The fourth row describes the expected attitudes of a defendant and a plaintiff as they discuss a settlement of a civil suit.
The top left is the one that Bernoulli discussed: people are averse to risk when they consider prospects with a substantial chance to achieve a large gain. They are willing to accept less than the expected value of a gamble to lock in a sure gain.
The possibility effect in the bottom left cell explains why lotteries are popular. When the top prize is very large, ticket buyers appear indifferent to the fact that their chance of winning is minuscule. [...]
The bottom right cell is where insurance is bought. People are willing to pay much more for insurance than expected value. [...]
The results for the top right cell initially surprised us. We were accustomed to think in terms of risk aversion except for the bottom left cell, where lotteries are preferred. When we looked at our choices for bad options, we quickly realized that we were just as risk seeking in the domain of losses as we were risk averse in the domain of gains. [...] Indeed, we identified two reasons for this effect. First, there is diminishing sensitivity. The sure loss is very aversive because the reaction to a loss of $900 is more than 90% as intense as the reaction to a loss of $1,000. The second factor may be even more powerful: the decision weight that corresponds to a probability of 90% is only about 71, much lower than the probability. The result is that when you consider a choice between a sure loss and a gamble with a high probability of a larger loss, diminishing sensitivity makes the sure loss more aversive, and the certainty effect reduces the aversiveness of the gamble. The same two factors enhance the attractiveness of the sure thing and reduce the attractiveness of the gamble when the outcomes are positive.
In the bottom row, however, the two factors operate in opposite directions: diminishing sensitivity continues to favor risk aversion for gains and risk seeking for losses, but the overweighting of low probabilities overcomes this effect and produces the observed pattern of gambling for gains and caution for losses.
Many unfortunate human situations unfold in the top right cell. This is where people who face very bad options take desperate gambles, accepting a high probability of making things worse in exchange for a small hope of avoiding a large loss."
(from "Thinking, Fast and Slow" by Daniel Kahneman - winner of the Nobel Prize in Economics.)
