Prospect Theory PDF

Making decisions – Prospect theory: Value function Kahneman Ch. 26 The value function in prospect theory reflects three important properties that distinguish it from the traditional utility function. 1) value is measured in terms of changes in wealth from a reference point whereas a util...

Making decisions – Prospect theory: Value function Kahneman Ch. 26 The value function in prospect theory reflects three important properties that distinguish it from the traditional utility function. 1) value is measured in terms of changes in wealth from a reference point whereas a utility function measures value based on the level of wealth. 2) The value function is convex for losses reflecting risk-taking and concave for gains reflecting risk aversion whereas an individual's utility function evaluates risk aversion, risk neutrality, or risk loving. 3) The value function is steeper for losses than for gains due to loss aversion. The surprising outcome when comparing these two problems: Problem 1) Get $900 for sure OR a 90% chance to get $1’000 Problem 2) Lose $900 for sure OR 90% chance to lose $1’000 1) Most people chose in problem 1 the risk-averse option (Get $900 in this case) no surprise here. 2) Most people chose to gamble in this question -> risk seeking Explanation: The explanation of the risk-seeking choice is the mirror image of the explanation of the risk aversion in problem 1. The negative value of losing $900 is much more than 90% of the negative value of losing $1’000. This is clearer in problems 3 and 4: Problem 3) In addition to whatever you own, you get $1’000 Now you have these options to choose from: 50% chance to win $1’000 OR get $500 for sure Problem 4) In addition to whatever you own, you get $2000 Now you have these options to choose from: 50% chance to lose $1’000 OR lose $500 for sure The final states of wealth (which is all that matters for the Bernoulli theory) are identical for both. Either be richer by $1500 with 100% chance or gamble with equal chances (50%) to be richer by $1000 or by $2000. We expect to see similar preferences therefore according to Bernoulli’s theory Results: 3) A large majority preferred the sure thing 4) A large majority preferred the gamble This is a decisive counterexample of the key idea from Bernoulli’s theory It shows the importance of the reference point that is missing in the Utility function. The reference point is $1000 higher than the current wealth in problem 3 and $2000 higher in problem 4. Being richer by $1500 is a gain of $500 in problem 3 and a loss of $500 in problem 4. For financial outcomes, the usual reference point is the status quo, but it can also be the outcome that we expect. Outcomes that are better than the reference points are seen as gains. Below the reference points, they’re losses. Reference Dependence: Decisionmakers assess the psychological value of outcomes relative to a neutral reference point Loss aversion: When directly compared losses loom larger than gains. A loss of $100 is felt worse than a gain of $100. The absolute psychological value of a loss is greater than that of a gain of equal objective value Diminishing sensitivity: Subjective difference between $900 and $1000 is much smaller than the difference between $100 and $200. The psychological value increases with diminishing sensitivity with increasing deviations from the reference point Losses are subjectively felt worse than gains Asian disease problem: A2 = Program A in condition B B2= Program B in condition B Programs A and A2 are identical, as are programs B and B2. The change in the decision frame between the two groups of participants produced a preference reversal: when the programs were presented in terms of lives saved, the participants preferred the secure program, A. When the programs were presented in terms of expected deaths, participants chose gamble B2. People generally prefer the absolute certainty inherent in a positive framing effect, which offers an assurance of gains. When decision options appear framed as a likely gain, risk-averse choices predominate. A shift toward risk-seeking behavior occurs when a decision-maker frames decisions in negative terms or adopts a negative framing effect. In essence: 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. Blind spots of prospect theory: A. one chance in a million to win $1 million B. 90% chance to win $12 and 10% chance to win nothing C. 90% chance to win $1 million and 10% chance to win nothing Winning nothing is a possible outcome in all three gambles, and prospect theory assigns the same value to that outcome in the three cases. Winning nothing is the reference point and its value is zero. Winning nothing is a nonevent in the first two cases and assigning it a value of zero makes good sense. In contrast, failing to win in the third scenario is intensely disappointing. Like a salary increase that has been promised informally, the high probability of winning the large sum sets up a tentative new reference point. 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. Disappointment and the anticipation of disappointment are real, however, and the failure to acknowledge them is as obvious a flaw as the counterexamples that I invoked to criticize Bernoulli’s theory. 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. This assumption is certainly wrong, as the following example shows: Problem 6: Choose between 90% chance to win $1 million OR $50 with certainty. Problem 7: Choose between 90% chance to win $1 million OR $150,000 with certainty Compare the anticipated pain of choosing the gamble and not winning in the two cases. Failing to win is a disappointment in both, but the potential pain is compounded in problem 7 by knowing that if you choose the gamble and lose you will regret the “greedy” decision you made by spurning a sure gift of $150,000. In regret, the experience of an outcome depends on an option you could have adopted but did not