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Prospect theory is a behavioral economic theory that describes the way people choose between probabilistic alternatives that involve risk, where the probabilities of outcomes are known. The theory states that people make decisions based on the potential value of losses and gains rather than the final outcome, and that people evaluate these losses and gains using certain heuristics. The model is descriptive: it tries to model real-life choices, rather than optimal decisions, as normative models do. The theory was created in 1977 and developed in 1992 by Daniel Kahneman and Amos Tversky as a psychologically more accurate description of decision making, compared to the expected utility theory. In the original formulation, the term ''prospect'' referred to a lottery. The paper "Prospect Theory: An Analysis of Decision under Risk" (1979) has been called a "seminal paper in behavioral economics". ==Model== The theory describes the decision processes in two stages:〔 *〕 *During editing, outcomes of a decision are ordered according to a certain heuristic. 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), 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, in which a rational agent is indifferent to the reference point. In expected utility theory, the individual only cares about absolute wealth, not relative wealth in any given situation. The function π is a probability weighting function and captures the idea that people tend to overreact to small probability events, but underreact to large probabilities. Let (x,p;y,q) denote a prospect with outcome x with probability p and outcome y with probability q and nothing with probability 1-p-q. If (x,p;y,q) is a regular prospect (i.e., either p+q<1, or x≥0≥y, or x≤0≤y), then: However if p+q=1 and either x>y>0 or x It can be deduced from the first equation that υ(y)+υ(-y)>υ(x)+υ(-x) and υ(-y)+υ(-x)>υ(x)+υ(-x). The value function is thus defined on deviations from the reference point, generally concave for gains and commonly convex for losses and steeper for losses than for gains. If (x,p) is equivalent to (y,pq) then (x,pr) is not preferred to (y,pqr), but from the first equation it follows that π(p)υ(x)+π(pq)υ(y)=π(pq)υ(y), which leads to π(pr)υ(x)≤π(pqr)υ(y), therefore: This means that for a fixed ratio of probabilities the decision weights are closer to unity when probabilities are low than when they are high. In prospect theory, π is never linear. In the case that x>y>0, p>p' and p+q=p'+q'<1, prospect (x,p';y,q) dominates prospect (x,p';y,q'), which means that π(p)υ(x)+π(q)υ(y)>π(p')υ(x)+π(q')υ(y), therefore: As y → x, π(p)-π(p') → π(q')-π(q), but since p-p'=q'-q, it would imply that π must be linear, however dominated alternatives are brought to the evaluation phase since they are eliminated in the editing phase. Although direct violations of dominance never happen in prospect theory, it is possible that a prospect A dominates B, B dominates C but C dominates A. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「prospect theory」の詳細全文を読む スポンサード リンク
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