Prospect theory
Based on Wikipedia: Prospect theory
The Pain of Losing
Here is a question that reveals something uncomfortable about how your mind works: Would you accept a coin flip where heads wins you $1,000 and tails loses you $1,000?
Most people say no.
This is strange. The expected value is exactly zero. A perfectly rational person, one who treats gains and losses symmetrically, should be indifferent. Yet something in us recoils. The potential loss looms larger than the potential gain, casting a shadow over what should be an even bet.
This asymmetry sits at the heart of prospect theory, a framework developed by psychologists Daniel Kahneman and Amos Tversky in 1979 that fundamentally reshaped our understanding of human decision-making. The theory earned Kahneman the Nobel Prize in Economics in 2002. Tversky, who died in 1996, would almost certainly have shared it; Nobel Prizes are not awarded posthumously.
What makes prospect theory revolutionary is not that it describes how people should make decisions. Economists had plenty of those theories. Instead, it describes how people actually make decisions, warts and all, and it does so using controlled experiments rather than armchair theorizing.
The Expected Utility Problem
Before Kahneman and Tversky, the dominant framework for understanding decision-making was expected utility theory, developed by mathematician John von Neumann and economist Oskar Morgenstern in 1944. Their approach was elegant and logical: a rational person should calculate the expected value of each option and choose the highest one.
Expected utility works like this. Say you can choose between a guaranteed $450 or a 50% chance of winning $1,000. The expected value of the gamble is $500 (half of $1,000). A rational agent should prefer the gamble because $500 exceeds $450.
But people don't behave this way.
In study after study, Kahneman and Tversky found that most people prefer the guaranteed $450. They are willing to sacrifice expected value for certainty. Economists call this risk aversion, and while it was known before prospect theory, the deeper patterns that Kahneman and Tversky uncovered were not.
The Reflection Effect
Now consider the mirror image of that choice. You must either lose $500 for certain or accept a 50% chance of losing $1,100.
Expected utility theory says you should prefer the certain loss. After all, the expected loss of the gamble is $550 (half of $1,100), which is worse than losing $500. A rational agent minimizes expected losses just as they maximize expected gains.
But here the pattern flips. Most people prefer the gamble. They become risk-seeking, willing to accept a worse expected outcome for the chance of avoiding any loss at all.
This is the reflection effect, and it is bizarre. The same person who plays it safe when winning becomes a gambler when losing. The reference point matters more than the absolute outcome.
Kahneman and Tversky quantified this asymmetry. On average, losses hurt about twice as much as equivalent gains feel good. The pain from losing $1,000 can only be compensated by the pleasure of earning $2,000. This is loss aversion, and it permeates human behavior far beyond the laboratory.
A Theory Named for Nothing
An amusing footnote: the name "prospect theory" is essentially meaningless. In an early draft circulated to economist Richard Thaler in 1976, Kahneman and Tversky called it "Value Theory." They changed the name to avoid confusion with other value theories in philosophy and economics. Kahneman later admitted the new title was deliberately chosen to mean nothing, ensuring that no one would confuse it with anything else.
The word "prospect" originally referred to a lottery or gamble with predictable outcomes. But the theory's applications have expanded far beyond gambling into negotiations, insurance, investment, medical decisions, and any domain where humans must choose among uncertain options.
The Reference Point
Prospect theory's central insight is that people do not evaluate outcomes in absolute terms. Instead, they evaluate them relative to a reference point, typically their current situation.
This seems obvious until you consider its implications.
Imagine two people who each have $3 million in net worth. Person A started the day with $1 million and gained $2 million. Person B started with $5 million and lost $2 million. They are equally wealthy, but they are not equally happy. Person A feels elated. Person B feels devastated.
Expected utility theory cannot explain this. If utility depends only on final wealth, both people should feel the same. But prospect theory predicts exactly the asymmetry we observe. Gains and losses are evaluated relative to where you started, not where you ended up.
This reference dependence creates strange situations. A bonus that would have thrilled you last year might disappoint you this year if your reference point has shifted upward. A salary cut that would have devastated you at your first job barely registers after you've grown accustomed to fluctuating income. The reference point moves, and our emotional responses move with it.
The Value Function
Kahneman and Tversky proposed that people evaluate prospects using a value function with specific properties. Picture a graph where the horizontal axis shows gains to the right and losses to the left, while the vertical axis shows psychological value, positive above and negative below.
The function is S-shaped, but not symmetrically so.
For gains, the curve is concave, meaning it bends downward. The difference between winning nothing and winning $100 feels larger than the difference between winning $1,000 and winning $1,100. This is diminishing sensitivity. Each additional dollar of gain produces less additional happiness.
For losses, the curve is convex, bending upward. The difference between losing nothing and losing $100 feels larger than the difference between losing $1,000 and losing $1,100. Diminishing sensitivity again, but now applied to pain.
Critically, the loss side is steeper. The curve drops more sharply for losses than it rises for gains. This is the mathematical expression of loss aversion. Moving from zero to negative $100 produces more psychological pain than moving from zero to positive $100 produces pleasure.
Probability Weighting
Prospect theory's second major contribution concerns how people perceive probabilities. We do not treat them linearly.
Consider a 1% chance of winning $10,000. Expected utility theory says this is worth $100. But many people would pay considerably more than $100 for such a ticket. We overweight small probabilities, treating a 1% chance as though it were larger, perhaps 5%.
Now consider a 99% chance of winning $10,000. Expected utility theory says this is worth $9,900. But many people would accept less than $9,900 as a certain payment to forgo the gamble. We underweight high probabilities, treating 99% as though it were smaller, perhaps 95%.
This probability weighting function explains several puzzling behaviors. People simultaneously buy lottery tickets (overweighting the small chance of winning) and insurance (overweighting the small chance of disaster). A purely rational agent would not do both, since lotteries have negative expected value and insurance companies profit precisely because the expected payout is less than the premium.
The weighting is not about miscalculating probabilities. People can accurately state that a lottery offers a one-in-ten-million chance. The distortion occurs in how that probability translates into decisions. It is a weighting, not an estimate.
Two Stages of Choice
Kahneman and Tversky proposed that decision-making occurs in two phases.
First comes the editing phase. Here, people organize and simplify their options. They decide which outcomes to treat as equivalent, establish a reference point, and frame outcomes as gains or losses. They may combine probabilities, separate certain outcomes from risky ones, or eliminate options that are clearly dominated by others.
This editing is not always rational. How a choice is presented, what economists call framing, can dramatically change how people edit it. The same medical treatment described as having a "90% survival rate" or a "10% mortality rate" produces different choices, even though the information is identical.
Second comes the evaluation phase. Here, people compute something like expected utility, but using the distorted value function and probability weights rather than objective values and probabilities. They then choose the option with the highest weighted value.
The editing phase explains why presentation matters so much. The evaluation phase explains why even after editing, our choices diverge from what pure logic would recommend.
Diminishing Sensitivity and the Rich
One implication of the curved value function deserves special attention: the richer you are, the less you care about fixed amounts of money.
Someone with $1,000 in savings experiences an extra $100 as a significant gain. Someone with $1,000,000 barely notices. The value function's concavity means that additional gains matter less as you accumulate more. This is diminishing marginal utility, an old idea, but prospect theory gives it a precise mathematical form.
The same applies to losses. A wealthy person experiences a $100 loss as a minor annoyance. A poor person experiences it as a real setback. This is not just about practical consequences, though those matter too. It is about psychological impact, about how the loss registers emotionally.
This asymmetry has implications for policy. A flat tax takes the same percentage from everyone, but the psychological burden falls disproportionately on those with less. Progressive taxation, whatever its political merits or drawbacks, aligns with how people actually experience money.
Applications Beyond the Laboratory
Prospect theory has illuminated behavior across domains.
In investing, it explains the disposition effect: people sell winning stocks too early (to lock in gains) and hold losing stocks too long (hoping to avoid realizing the loss). This is exactly backwards from tax-optimal behavior, where you should realize losses to offset gains. But it follows directly from loss aversion and the reflection effect.
In negotiations, it explains why people often fight harder to avoid concessions than to obtain gains. A negotiator who has anchored on a particular outcome experiences anything less as a loss, triggering risk-seeking behavior that can lead to impasse or worse outcomes.
In medicine, it explains why framing matters so much for treatment decisions. Patients respond differently to "this surgery has a 95% survival rate" versus "this surgery has a 5% mortality rate," even though these statements are logically equivalent.
In consumer behavior, it explains why free shipping feels disproportionately valuable. Paying $50 for an item plus $5 shipping feels worse than paying $55 for an item with free shipping, even though the outcome is identical. The shipping fee registers as a separate loss.
The Endowment Effect
Loss aversion produces a striking phenomenon called the endowment effect. People value things more once they own them.
In a classic experiment, some participants received a coffee mug and were asked the minimum price at which they would sell it. Others were given nothing and asked the maximum price at which they would buy the same mug. Sellers demanded roughly twice what buyers would pay.
This is irrational from the standpoint of expected utility. The mug has objective characteristics. Its value should not depend on whether you currently possess it. But giving up the mug feels like a loss, and losses loom larger than gains. So sellers demand compensation not just for the mug's value, but for the pain of parting with it.
The endowment effect has practical consequences for everything from salary negotiations to real estate transactions to international diplomacy. Once something becomes "ours," we treat giving it up as a loss to be avoided rather than a trade to be evaluated.
Cumulative Prospect Theory
In 1992, Kahneman and Tversky published an updated version called cumulative prospect theory. The revision addressed several technical problems with the original formulation, particularly around how probability weights were applied to outcomes.
In the original theory, probability weights were applied independently to each outcome. This could produce violations of first-order stochastic dominance, a fancy way of saying the theory sometimes preferred options that were worse in every possible state of the world. Cumulative prospect theory fixes this by applying weights to cumulative probabilities, ensuring that unambiguously better options are always preferred.
The updated theory also handled uncertain reference points more elegantly and aligned better with other models in decision theory. But the core insights, loss aversion, diminishing sensitivity, and probability weighting, remained intact.
Critics and Limits
Prospect theory is not without critics. Some economists argue that it sacrifices too much parsimony. Expected utility theory, despite its failures at predicting behavior, offers a clean normative benchmark: this is how people should decide if they want to maximize their outcomes. Prospect theory describes what people do, but is that description stable enough to build on?
Others point out that prospect theory was primarily developed using small-stakes gambles with explicit probabilities. How well does it generalize to high-stakes decisions, to ambiguous probabilities, to repeated choices, to group decisions? The evidence is mixed.
The reference point, so central to the theory, is not always well-defined. What is your reference point when buying a house? When choosing a career? When deciding whether to marry? The theory assumes a reference point exists but does not always specify how it forms or changes.
Still, prospect theory remains the most influential alternative to expected utility. Its insights have permeated behavioral economics, finance, public policy, and marketing. When academics and practitioners want to understand why people make "irrational" choices, prospect theory is typically where they start.
The Rationality Question
Are the biases documented by prospect theory truly irrational? Or do they represent evolved adaptations that served our ancestors well?
Loss aversion may have survival value. In ancestral environments, losing resources could mean death, while gaining equivalent resources merely improved comfort. The asymmetric response, treating losses as twice as painful as equivalent gains, may have been calibrated to these asymmetric consequences.
Similarly, overweighting small probabilities may reflect appropriate caution about catastrophic risks. If a 1% chance of death is treated as though it were 5%, that might lead to excess caution, but it might also keep you alive long enough to pass on your genes.
This evolutionary perspective does not make these biases any less troublesome in modern contexts. Evolution optimized for survival and reproduction on the African savanna, not for maximizing returns in financial markets or making optimal medical decisions. Our inherited psychology may be poorly suited to the choices we now face.
The Kahneman-Tversky Partnership
The collaboration between Daniel Kahneman and Amos Tversky was one of the most productive in the history of social science. They worked together from 1969 until Tversky's death in 1996, producing a body of work that transformed multiple fields.
Their partnership was unusual. Academic collaborations typically involve clear divisions of labor. With Kahneman and Tversky, the ideas emerged from intense conversation, neither could afterward say who had contributed what. They wrote by passing drafts back and forth, sometimes sentence by sentence, until they could not remember who had written which words.
Kahneman later wrote about the collaboration with evident grief. Tversky was the more confident personality, the one who believed they were doing important work when Kahneman had doubts. Kahneman was the more cautious, the one who worried about errors and limitations. Together, they balanced each other.
When Kahneman received the Nobel Prize, he spoke of the award as honoring work done jointly. The committee, bound by rules against posthumous awards, could only name him. But the work was never just his.
A Theory of Human Nature
Prospect theory began as a technical correction to expected utility theory, but it became something larger: a statement about human nature.
We are not the rational calculators that classical economics imagined. We do not weigh gains and losses symmetrically. We do not treat probabilities as they mathematically deserve to be treated. We are swayed by how choices are framed, by what we already possess, by where we started rather than where we might end up.
These are not minor quirks to be corrected through education. They are deep features of human psychology, consistent across cultures and resistant to training. Even experts who understand prospect theory fall prey to its documented biases.
The practical question becomes not how to eliminate these biases, but how to design systems that account for them. If we know that people overweight small probabilities, we can structure choices to harness or counteract that tendency. If we know that framing matters, we can present information in ways that support good decisions. If we know that losses loom larger than gains, we can reframe choices to feel less like losses.
This is the domain of behavioral economics and nudge theory, fields that prospect theory helped create. The recognition that humans are predictably irrational opens possibilities for improving decisions without restricting choice.
The Pain and the Pleasure
Return to that coin flip: heads wins $1,000, tails loses $1,000. You now understand why most people refuse it. The expected pain of losing exceeds the expected pleasure of winning, even though the expected monetary values are equal.
But understanding the bias does not eliminate it. Even knowing about loss aversion, the coin flip still feels like a bad deal. The knowledge is intellectual; the aversion is visceral.
This gap between knowing and feeling is perhaps prospect theory's deepest lesson. We are not minds that happen to have emotions. We are emotional beings who happen to have developed the capacity for abstract reasoning. When the two conflict, emotion usually wins.
Kahneman and Tversky gave us a map of this conflict. They showed where reason and feeling diverge, and by how much. They did not resolve the conflict or tell us which side to favor. But they made it possible to see, with mathematical precision, exactly what we are up against when we try to think clearly about uncertain futures.
The pain of losing still hurts more than equivalent gains feel good. It probably always will. But at least now we know why.