Prospect Theory

Prospect theory is the answer to a question expected utility theory was never designed to ask: not how a rational agent should choose among risks, but how people actually do. Its answer rests on three observations about the mind. People evaluate outcomes as gains and losses from where they stand, not as totals of what they would own. Losses hurt roughly twice as much as equal gains please. And probabilities are not taken at face value: small chances loom too large, near-certainties are trusted too little, and the step from probable to guaranteed carries a weight all its own. From these three ingredients, Daniel Kahneman and Amos Tversky built the most influential descriptive model of risky choice ever proposed, one that explains in a single framework why the same person buys insurance and lottery tickets, refuses favorable coin flips, clings to losing investments, and reverses course when identical options are re-described. This page presents the theory from first principles, follows it through its 1992 cumulative revision, sets out what it explains, and takes its boundaries and critics seriously. Three interactive tools let you bend the value function and watch loss aversion emerge, locate any gamble in the fourfold pattern of risk attitudes, and catch your own preferences reversing between two frames of the same choice.

Prospect theory is the leading descriptive theory of decision making under risk: an account, built from experimental evidence, of how people actually evaluate and choose among risky options, in contrast to the normative account of how an ideally rational agent should (Kahneman & Tversky, 1979). Where expected utility theory values final states of wealth and uses probabilities exactly as given, prospect theory values changes, gains and losses measured from a reference point, weights losses more heavily than gains, and transforms probabilities into decision weights that overweight small chances and prize certainty. The theory was constructed deliberately around the standard model's documented failures, above all the certainty-effect reversals of the Allais paradox, and its 1992 cumulative revision extended it from risk to uncertainty and supplied measured parameters that remain the field's common currency (Tversky & Kahneman, 1992). Three decades of scrutiny have left its status remarkably stable: it is still widely regarded as the best available description of how people evaluate risk in experimental settings, its core patterns have survived a preregistered replication across nineteen countries, and the anomalies it does not capture, from experience-based choice to a contested loss-aversion literature, are mapped precisely because the theory made them visible (Barberis, 2013; Ruggeri et al., 2020). The sections below build the theory from its three revisions to the standard model, develop loss aversion and probability weighting in depth, present framing and the cumulative version, survey what the theory explains, and give its boundaries and critics their full due.

From Rational Standard to Descriptive Science

Prospect theory begins where the rational standard breaks. Expected utility theory, the normative model descended from Bernoulli and axiomatized by von Neumann and Morgenstern, holds that a coherent chooser values a gamble by the probability-weighted average of the utilities of its outcomes, with utility defined over final states of wealth (Bernoulli, 1738/1954). By the 1970s the evidence against it as a description of human choice was systematic rather than scattered: Maurice Allais had shown that the pull of certainty reverses preferences in ways no utility function permits, and the pattern survived reflection, replication, and stakes (Allais, 1953). Kahneman and Tversky's response was a change of scientific posture, not merely of model. Rather than treating each violation as noise around a rational signal, they treated the violations as the signal, collected them, and asked what evaluative machinery would produce exactly those choices. The 1979 theory that resulted was presented as a critique of expected utility theory as a descriptive model and a replacement for it in that role, and it carried a division of labor that the field has largely kept: expected utility theory remains the standard for how choices ought to cohere, while prospect theory models how they in fact are made, with the space between the two defining the research program of behavioral economics (Kahneman & Tversky, 1979; Starmer, 2000). The relationship between the two theories, and their places in the wider cluster that includes game theory, is mapped on the Expected Utility Theory page; this page develops the descriptive side in full.

The Three Revisions

Prospect theory replaces the standard model with three coordinated revisions, each answering a specific body of evidence. The first is reference dependence. The carriers of value are not final states of wealth, as they had been from Bernoulli onward, but changes: gains and losses measured from a reference point, usually the status quo, sometimes an expectation or aspiration. This is a claim about perception as much as preference, made on the model of sensation: just as the eye registers changes in brightness rather than absolute luminance, the evaluative system registers departures from its adaptation level rather than totals (Kahneman & Tversky, 1984). The second revision is the value function defined over those gains and losses, drawn in Figure 1. It is concave for gains and convex for losses, reflecting diminishing sensitivity in both directions: the difference between gaining 100 and 200 feels larger than the difference between 1,100 and 1,200, and the same is true of losses. And it is steeper for losses than for gains, with a kink at the reference point: loss aversion, the property that losses loom larger than corresponding gains. Diminishing sensitivity on both sides produces the reflection effect, in which risk aversion for gains flips to risk seeking for losses of the same size (Kahneman & Tversky, 1979). The third revision is probability weighting: outcomes are weighted not by their stated probabilities but by decision weights that overweight small probabilities, underweight moderate and large ones, and change most sharply near the endpoints of impossibility and certainty, which is where the certainty effect lives. The original theory also described an editing phase that precedes evaluation, a set of mental operations that code outcomes as gains or losses, combine and cancel components, and discard shared elements; the last of these, cancellation, produces the isolation effect, in which decomposing the same prospect differently leads to different choices (Kahneman & Tversky, 1979). Everything the theory explains flows from these parts working together, and the demonstration after the figure lets you take the value function in hand.

Loss Aversion: The Kink That Runs Through Everything

Of the three revisions, loss aversion has traveled farthest, and a lunchtime story explains why. The economist Paul Samuelson once offered a colleague a bet on a fair coin: win 200 dollars on heads, lose 100 on tails. The colleague declined the single bet, saying the 100-dollar loss would be felt more than the 200-dollar gain, an answer that became the informal definition of the phenomenon and, decades later, the opening move of a famous analysis of investment behavior (Benartzi & Thaler, 1995). In cumulative prospect theory's median estimates, the loss limb of the value function is about 2.25 times as steep as the gain limb, so a fifty-fifty gamble must offer to win more than twice what it risks before it becomes attractive (Tversky & Kahneman, 1992). The mechanism matters because the standard theory has no room for it. Within expected utility theory, aversion to small gambles can only come from the curvature of the utility function, and Matthew Rabin proved that any curvature strong enough to explain everyday refusals of modest coin flips implies absurd rejection of enormously favorable large gambles: realistic small-stakes risk aversion cannot be curvature, which leaves the kink at the reference point as the viable explanation (Rabin, 2000). Loss aversion also operates where there is no risk at all. Tversky and Kahneman showed that reference dependence and the steeper loss limb reshape riskless choice, generating the status quo bias and the endowment effect (Tversky & Kahneman, 1991); in the classic demonstration, students given a coffee mug demanded roughly twice as much to sell it as otherwise identical students would pay to buy one, a gap that persisted through real market trading and cut predicted trade volume in half (Kahneman, Knetsch, & Thaler, 1990). The signature even appears in the brain: in people evaluating mixed fifty-fifty gambles, activity in valuation circuitry including the ventral striatum and prefrontal cortex increased with the potential gain and decreased with the potential loss, the loss slope was steeper than the gain slope, and the size of that neural asymmetry predicted each individual's behavioral loss aversion (Tom, Fox, Trepel, & Poldrack, 2007). A single kink, visible in a lunch bet, a mug market, and a brain scanner, is the theory's most consequential export, though, as the criticisms section takes up, also its most contested.

The Weighting of Probability

The value function alone cannot explain why the same person buys a lottery ticket on the way to renewing an insurance policy; for that, prospect theory needs its second nonlinearity. Decision weights are not probabilities. People overweight small probabilities, which makes long shots and rare disasters both loom large; they underweight moderate and high probabilities; and their weights change fastest near the endpoints, so that the move from 99 percent to certain, or from impossible to 1 percent, matters far more than an equal move in the middle. Richard Gonzalez and George Wu gave the resulting inverse-S curve a psychological anatomy with two separable parameters: curvature, which measures how well the decision maker discriminates among probabilities in the middle of the scale, and elevation, which measures how attractive gambling is overall, an analysis that ties the weighting function to the psychophysics of judgment rather than treating it as a curve-fitting convenience (Gonzalez & Wu, 1999). Combined with the value function, the weighting function yields prospect theory's most compact empirical summary, the fourfold pattern of risk attitudes shown in Table 1: risk aversion for probable gains and improbable losses, risk seeking for improbable gains and probable losses (Tversky & Kahneman, 1992). Each cell is a familiar institution. Overweighted small chances of large gains sell lottery tickets; overweighted small chances of large losses sell insurance; the certainty effect makes people lock in probable gains; and diminishing sensitivity plus underweighted high probabilities makes people gamble to escape probable losses, the pattern behind refusing to settle a losing lawsuit and riding a losing investment down. The demonstration below computes the pattern live, so you can find the probabilities at which each attitude flips.

Table 1
The Fourfold Pattern of Risk Attitudes

Note. The pattern combines the value function's diminishing sensitivity with the overweighting of small probabilities and the underweighting of large ones; it was articulated in full, with supporting measurements, in cumulative prospect theory (Tversky & Kahneman, 1992).

Framing and the Construction of Choice

Because value is computed from a reference point, whoever sets the reference point steers the choice, and reference points are set by description. Any theory that values final outcomes obeys description invariance: logically equivalent statements of the same options must yield the same decision. Prospect theory predicts, and experiments confirm, that they do not. In the classic demonstration, a public-health program's identical options were described to different groups in terms of lives saved or lives lost; the gain frame made the majority choose the sure option, the loss frame made the majority choose the gamble, a full reversal produced by wording alone, exactly as reflection around a description-induced reference point requires (Tversky & Kahneman, 1981). The point generalizes far beyond the laboratory. A surcharge for credit is a discount for cash; a medical procedure has a 90 percent survival rate or a 10 percent mortality rate; a fund is up from last year or down from its peak; in each pair the facts are one and the frame decides which side of the value function evaluates them (Kahneman & Tversky, 1984). Framing is prospect theory's most public-facing consequence and has a full treatment on this site's Framing Effects page; here the essential point is architectural: framing effects are not an extra assumption bolted onto the theory but a direct corollary of reference dependence, and their reliability is among the strongest evidence that the reference point is doing real work. The demonstration below runs a framing experiment on you, with both frames of one original scenario, so you can observe the reversal, or your escape from it, firsthand.

Cumulative Prospect Theory

The 1979 theory had a known technical flaw, and its repair produced the version now standard. Because the original applied a weight to each outcome's probability separately, cleverly constructed prospects could receive a higher value than alternatives that dominated them, outcome for outcome, a prediction no one believed and the editing phase's dominance check only patched by hand. Cumulative prospect theory, published by Tversky and Kahneman in 1992, solved the problem by adopting rank-dependent weighting, the device John Quiggin had introduced: weights attach not to individual probabilities but to cumulative ones, transforming the probability of doing at least this well, so that the resulting decision weights respect stochastic dominance by construction (Quiggin, 1982; Tversky & Kahneman, 1992). The revision brought three further gains. Gains and losses received separate weighting functions, an asymmetry the data demanded. The theory extended from risk, where probabilities are stated, to uncertainty, where they must be judged, connecting it to the ambiguity side of decision research. And the paper supplied measured median parameters, a curvature exponent of 0.88 for both limbs of the value function, a loss-aversion coefficient of 2.25, and weighting exponents of 0.61 for gains and 0.69 for losses, that turned the theory into a calculating instrument and remain the field's default calibration (Tversky & Kahneman, 1992). Within the family of non-expected-utility theories that grew up around the same anomalies, surveyed by Chris Starmer, the cumulative version is the member that has functioned as the working consensus: not the final word, but the model against which alternatives are measured (Starmer, 2000).

What Prospect Theory Explains

The theory's reach is best seen in Nicholas Barberis's thirtieth-anniversary assessment, which found prospect theory informing established results across finance, insurance, labor, and policy while remaining, in his summary, the best available description of risk evaluation in experimental settings (Barberis, 2013). Three applications show the mechanism at work. The equity premium puzzle is the century-long observation that stocks have outperformed bonds by far more than standard risk aversion can explain; Shlomo Benartzi and Richard Thaler showed that an investor who is loss averse and evaluates a portfolio frequently, a combination they called myopic loss aversion, will experience stocks as a stream of painful losses and demand exactly such a premium to hold them, with the historical premium implying an evaluation horizon of about one year (Benartzi & Thaler, 1995). The endowment effect converts loss aversion into market predictions: because sellers value a good as a loss and buyers as a forgone gain, willingness to accept exceeds willingness to pay and mutually beneficial trades go unmade, which is why the mug experiments observed roughly half the trading volume that standard theory predicts and why instant endowment matters for everything from consumer returns policies to legal entitlements (Kahneman, Knetsch, & Thaler, 1990). And probability weighting organizes the economics of longshots and disasters, from lottery demand to insurance pricing to the reluctance to realize losses in asset markets, patterns Barberis's survey traces through the applied literature (Barberis, 2013). Beneath the applications sits the theory's quieter scientific role: like expected utility theory before it, it is a measuring instrument, and the parameters it defines, curvature, loss aversion, weighting, have become standard dependent variables for studying how risk preferences vary across people, situations, and, as in the neural work above, biological substrates (Tom, Fox, Trepel, & Poldrack, 2007).

Boundaries and Criticisms

A descriptive theory earns its keep at its boundaries, and prospect theory's are well mapped. The first boundary is the reference point itself. The theory requires one but does not say where it comes from, an indeterminacy critics have pressed since 1979; the most influential answer, from Botond Kőszegi and Matthew Rabin, makes reference points expectations, beliefs about outcomes held in the recent past, which endogenizes the theory's free parameter and predicts when endowment-type effects should appear and, importantly, when they should not (Kőszegi & Rabin, 2006). The second boundary is the gap between description and experience. Prospect theory's overweighting of rare events was measured in choices among described prospects; when people instead learn probabilities by sampling outcomes, as in most of life, rare events are underweighted, the reverse of the signature pattern, a description-experience gap that marks the theory as a model of decisions from description rather than of risky choice in general (Hertwig, Barron, Weber, & Erev, 2004). The third is internal: Michael Birnbaum has shown across a long experimental program that both versions of prospect theory fail systematic new tests, eleven paradoxes in his summary, that configural-weight models anticipate, so the cumulative version's status as working consensus should not be mistaken for descriptive finality (Birnbaum, 2008). The fourth is the loss-aversion debate. David Gal and Derek Rucker reviewed the evidence and argued that it does not support losses being, on balance, more impactful than gains, attributing the principle's persistence partly to sociology of science; Kellen Mrkva, Eric Johnson, Simon Gächter, and Andreas Herrmann answered with data showing loss aversion is real but moderated, larger for bigger stakes and older, more knowledgeable choosers, and reports of its death exaggerated (Gal & Rucker, 2018; Mrkva, Johnson, Gächter, & Herrmann, 2020). The fair reading is that the phenomenon exists and matters while its universality and typical size were oversold in popularization. Against these boundaries stands the replication record: a preregistered study reproduced the 1979 paper's choice problems with more than 4,000 participants in nineteen countries and thirteen languages and found the original patterns broadly intact (Ruggeri et al., 2020). And one boundary is a design decision rather than a defect: prospect theory makes no normative claim. No one proposes that choices ought to depend on frames or that dominated combinations are wise; the theory describes the mind, and the normative standard it departs from remains in place precisely so the departures can be measured (Starmer, 2000).

Worked Example

The 1992 parameters make prospect theory a calculator, and one calculation shows the whole machine. Consider a fair coin flip: win 100 on heads, lose 100 on tails, expected value exactly zero. First the value function, with curvature 0.88 and loss aversion 2.25. The gain is worth 100 raised to the power 0.88, about 57.5; the loss is worth minus 2.25 times that same magnitude, about minus 129.5. Next the decision weights at probability one half: the gain weighting function with exponent 0.61 gives a weight of about 0.42, and the loss weighting function with exponent 0.69 gives about 0.45, both below one half, with the loss side weighted slightly more. The prospect's value is then 0.42 times 57.5 plus 0.45 times minus 129.5, roughly 24.2 minus 58.8, or about minus 34.6. A gamble with zero expected value registers as decisively negative, which is why fair coin flips are refused: the loss is amplified by the steeper limb and the weights do nothing to rescue it. Now ask what gain would make the flip acceptable. Setting the weighted value of the gain equal to the weighted value of the loss and solving gives a required gain of about 274, so at these median parameters a fifty-fifty gamble must offer to win roughly 2.7 times what it risks before it breaks even psychologically, the loss-aversion ratio of 2.25 amplified a little further by the weighting asymmetry (Tversky & Kahneman, 1992). The calculation also shows what Rabin's theorem means in practice: no plausible curvature over final wealth produces this refusal of a small fair flip, but a kinked value function over changes produces it immediately, at every wealth level, which is the modern understanding of where everyday risk aversion comes from (Rabin, 2000).

Why It Matters

Prospect theory matters first as the descriptive anchor of an entire field. Behavioral economics is, at its core, the systematic study of departures from the rational standard, and prospect theory supplied both the first major departure model and the template for all that followed; the arc of recognition runs through Kahneman's 2002 Nobel Prize for the joint work with Tversky and Thaler's 2017 prize for carrying reference dependence, loss aversion, and framing into economics proper. It matters second as applied infrastructure: the fourfold pattern organizes the twin industries of lotteries and insurance, myopic loss aversion reframed the largest puzzle in asset pricing, the endowment effect reshaped how law and marketing think about entitlements and defaults, and framing research made choice architecture, the deliberate design of how options are described, a tool of policy (Barberis, 2013; Kahneman & Tversky, 1984). It matters third to cognitive psychology as a bridge between perception and decision: reference dependence and diminishing sensitivity import the logic of psychophysics into choice, the weighting function has a measurable psychological anatomy, and the value function's kink is visible in neural data, making risky choice one of the best-quantified meeting points of mind, brain, and behavior (Gonzalez & Wu, 1999; Tom, Fox, Trepel, & Poldrack, 2007). And it matters as a model of scientific division of labor: the theory never dethroned the rational standard, it partnered with it, one theory saying what coherence requires and the other saying what minds do, with the distance between them now measured across nineteen countries (Ruggeri et al., 2020). The demonstrations on this page put that measured mind under your own fingers.

Key Researchers

Daniel Kahneman (1934–2024). Israeli-American psychologist who created prospect theory with Amos Tversky and received the 2002 Nobel Memorial Prize in Economic Sciences for the work; his later synthesis carried the theory's two-systems psychology to a global audience. Google Scholar · Wikipedia

Amos Tversky (1937–1996). Israeli cognitive psychologist and co-creator of prospect theory and its cumulative revision; his mathematical psychology of similarity, judgment, and preference supplied the theory's formal spine. Wikipedia

Richard H. Thaler. Charles R. Walgreen Distinguished Service Professor of Behavioral Science and Economics at the University of Chicago Booth School of Business and 2017 Nobel laureate; named the endowment effect and, with Benartzi, used myopic loss aversion to address the equity premium puzzle. Google Scholar · Wikipedia

Matthew Rabin. Pershing Square Professor of Behavioral Economics at Harvard University; his calibration theorem showed that utility curvature cannot explain small-stakes risk aversion, and with Kőszegi he made reference points expectations, endogenizing the theory's free parameter. Google Scholar · Wikipedia

Colin F. Camerer. Robert Kirby Professor of Behavioral Economics at the California Institute of Technology; a leading source of field and neuroeconomic evidence on prospect theory and its use in strategic settings. Google Scholar · Wikipedia

Peter P. Wakker. Professor of decision under uncertainty at Erasmus University Rotterdam; the leading measurement theorist of prospect theory, whose axiomatic and empirical work made the theory's components separately observable. Homepage · Wikipedia

Key Terms

Frequently Asked Questions

What is prospect theory?
Prospect theory is the leading descriptive theory of how people actually decide under risk. It holds that people evaluate options as gains and losses from a reference point, feel losses more strongly than equal gains, and weight probabilities nonlinearly, overweighting small chances and prizing certainty (Kahneman & Tversky, 1979).

How does prospect theory differ from expected utility theory?
Expected utility theory is a normative standard: it values final states of wealth and uses probabilities exactly as given. Prospect theory is descriptive: it values changes from a reference point, builds in loss aversion, and replaces probabilities with decision weights, which lets it capture the framing reversals and paradoxes the standard theory forbids (Tversky & Kahneman, 1992).

What is loss aversion?
Loss aversion is the finding that losses have a larger psychological impact than equal gains, with a typical ratio near two to one. It appears in risky choice and in riskless settings such as the endowment effect, where owners demand far more to give up a good than buyers will pay to acquire it (Tversky & Kahneman, 1991).

What is the value function in prospect theory?
The value function assigns subjective value to gains and losses rather than to total wealth. It is concave for gains, convex for losses, and steeper for losses than for gains, producing diminishing sensitivity in both directions and loss aversion at the reference point (Kahneman & Tversky, 1979).

What is probability weighting?
Probability weighting is the transformation of stated probabilities into decision weights. People overweight small probabilities and underweight moderate to large ones, with the steepest changes near impossibility and certainty, a pattern captured by an inverse-S shaped weighting function with separable curvature and elevation (Gonzalez & Wu, 1999).

What is the fourfold pattern of risk attitudes?
It is the prediction that people are risk averse for probable gains and improbable losses but risk seeking for improbable gains and probable losses. The pattern explains why the same person can buy both a lottery ticket and an insurance policy (Tversky & Kahneman, 1992).

What is cumulative prospect theory?
Cumulative prospect theory is the 1992 revision in which decision weights apply to cumulative, ranked probabilities rather than to individual outcomes. This repairs cases where the original theory could favor a dominated option, allows separate weighting for gains and losses, and extends the theory from risk to uncertainty (Tversky & Kahneman, 1992).

Is prospect theory still supported by evidence?
Its core patterns are robust: a large preregistered study replicated the original findings across 19 countries and 13 languages. At the same time, research has mapped real boundaries, including moderated loss aversion and the underweighting of rare events when people learn probabilities from experience (Ruggeri et al., 2020).

References

The three interactive tools on this page — the value-function, fourfold-pattern, and framing demonstrations — generate their figures and compute their results live in your browser; no dataset is bundled with the page. The empirical claims in the text are sourced to the references above.