Prospect theory is a theory of
behavioral economics
Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals or institutions, such as how those decisions vary from those implied by classical economic theory. ...
and behavioral finance that was developed by
Daniel Kahneman
Daniel Kahneman (; he, דניאל כהנמן; born March 5, 1934) is an Israeli-American psychologist and economist notable for his work on the psychology of judgment and decision-making, as well as behavioral economics, for which he was award ...
and
Amos Tversky
Amos Nathan Tversky ( he, עמוס טברסקי; March 16, 1937 – June 2, 1996) was an Israeli cognitive and mathematical psychologist and a key figure in the discovery of systematic human cognitive bias and handling of risk.
Much of his ...
in 1979.
The theory was cited in the decision to award Kahneman the 2002
Nobel Memorial Prize in Economics
The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered ...
.
Based on results from
controlled studies, it describes how
individuals
An individual is that which exists as a distinct entity. Individuality (or self-hood) is the state or quality of being an individual; particularly (in the case of humans) of being a person unique from other people and possessing one's own nee ...
assess their loss and gain perspectives in an asymmetric manner (see
loss aversion). For example, for some individuals, the pain from losing $1,000 could only be compensated by the pleasure of earning $2,000. Thus, contrary to the
expected utility theory The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
(which models the decision that perfectly
rational agents
A rational agent or rational being is a person or entity that always aims to perform optimal actions based on given premises and information. A rational agent can be anything that makes decisions, typically a person, firm, machine, or software.
...
would make), prospect theory aims to describe the actual
behavior
Behavior (American English) or behaviour (British English) is the range of actions and mannerisms made by individuals, organisms, systems or artificial entities in some environment. These systems can include other systems or organisms as we ...
of people.
In the original formulation of the theory, the term ''prospect'' referred to the predictable results of a
lottery
A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of ...
. However, prospect theory can also be applied to the prediction of other forms of behaviors and decisions.
Overview
Prospect theory stems from
Loss aversion, where the observation is that agents asymmetrically feel losses greater than that of an equivalent gain. It centralises around the idea that people conclude their utility from "gains" and "losses" relative to a certain reference point. This "reference point" is different for each person and relative to their individual situation. Thus, rather than making decisions like a rational agent (i.e using
expected utility theory The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
and choosing the maximum value), decisions are made in relativity not in absolutes.
Consider two scenarios;
# 100% chance to gain $450 or 50% chance to gain $1000
# 100% chance to lose $500 or 50% chance to lose $1100
Prospect theory suggests that;
* When faced with a risky choice leading to gains agents are
''risk averse'', preferring the certain outcome with a lower expected utility (
concave
Concave or concavity may refer to:
Science and technology
* Concave lens
* Concave mirror
Mathematics
* Concave function, the negative of a convex function
* Concave polygon, a polygon which is not convex
* Concave set
In geometry, a subset o ...
value function).
** ''Agents will choose the certain $450 even though the expected utility of the risky gain is higher''
* When faced with a risky choice leading to losses agents are
''risk seeking'', preferring the outcome that has a lower expected utility but the potential to avoid losses (
convex
Convex or convexity may refer to:
Science and technology
* Convex lens, in optics
Mathematics
* Convex set, containing the whole line segment that joins points
** Convex polygon, a polygon which encloses a convex set of points
** Convex polytop ...
value function).
** ''Agents will choose the 50% chance to lose $1100 even though the expected utility is lower, due to the chance that they lose nothing at all''
These two examples are thus in contradiction with the expected utility theory, which only considers choices with the maximum utility. Also, the concavity for gains and convexity for losses implies diminishing marginal utility with increasing gains/losses. In other words, someone who has more money has a lower desire for a fixed amount of gain (and lower aversion to a fixed amount of loss) than someone who has less money.
The theory continues with a second concept, based on the observation that people attribute excessive weight to events with low probabilities and insufficient weight to events with high probability. For example, individuals may unconsciously treat an outcome with a probability of 99% as if its probability were 95%, and an outcome with probability of 1% as if it had a probability of 5%. Under- and over-weighting of probabilities is importantly distinct from under- and over-estimating probabilities, a different type of
cognitive bias
A cognitive bias is a systematic pattern of deviation from norm (philosophy), norm or rationality in judgment. Individuals create their own "subjective reality" from their perception of the input. An individual's construction of reality, not the ...
observed for example in the
overconfidence effect.
Model
The theory describes the decision processes in two stages:
*During an initial phase termed ''editing'', outcomes of a decision are ordered according to a certain
heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate ...
. In particular, people decide which outcomes they consider equivalent, set a reference point and then consider lesser outcomes as losses and greater ones as gains. The editing phase aims to alleviate any
framing effects.
It also aims to resolve isolation effects stemming from individuals' propensity to often isolate consecutive probabilities instead of treating them together. The editing process can be viewed as composed of coding, combination, segregation, cancellation, simplification and detection of dominance.
*In the subsequent ''evaluation'' phase, people behave as if they would compute a value (
utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophe ...
), based on the potential outcomes and their respective probabilities, and then choose the alternative having a higher utility.
The formula that Kahneman and Tversky assume for the evaluation phase is (in its simplest form) given by:
:
where
is the overall or expected utility of the outcomes to the individual making the decision,
are the potential outcomes and
their respective probabilities and
is a function that assigns a value to an outcome. The value function that passes through the reference point is s-shaped and asymmetrical. Losses hurt more than gains feel good (loss aversion). This differs from
expected utility theory The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
, in which a rational agent is indifferent to the reference point. In expected utility theory, the individual does not care how the outcome of losses and gains are framed. The function
is a probability weighting function and captures the idea that people tend to overreact to small probability events, but underreact to large probabilities. Let
denote a prospect with outcome
with probability
and outcome
with probability
and nothing with probability
. If
is a regular prospect (i.e., either
, or
, or
), then:
However, if
and either
or