More on Gains & Losses
The work of Kahneman and TverskyThe research on Prospect Theory of Daniel Kahneman and the late Amos Tversky stands as among the most important thinking about risk ever performed. You will remember from chapter 2 of FWD that in the psychological "domain of gains" people will generally seek safety, while in the "domain of losses" they will tend to double down their bets in the hope of getting even. This page provides somewhat more detailed explanation than that provided in the book.
The graph at the right displays the domains of gains and losses as curves. Both gains and losses demonstrate "diminishing returns" -- the relative impact of a dollar of benefit or cost decreases as the amount increases. You can also see that losses create greater value intensity (they "hurt" more), and that the curves are shaped differently: gains are "concave down" while losses are "concave up." You will see in a moment why this is important.
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Certainty equivalentsThe explanation is a bit complicated, so bear with me. You might also want to enlarge the picture at the right to study it in detail.
The expected values of the 50/50 bets of $50 are mid-way along the line connecting plus or minus $100 and the zero point. The mid-point is the average of the value of winning (or losing) $100 and zero. They appear as colored dots above or below the values of plus $50 and minus $50 along the x-axis.
The value of a certain gain of $50 appears above this mid-way point on the connecting line (certainty is valued more), while the value of a certain loss appears below the connecting line (gambles are worth more). This arises from the shape of the curves, i.e., whether they face "up" or "down."
The certainty equivalents are the cash amounts that equate to the same degree of pain or pleasure as the gamble. In the domain of losses, gambles hurt less so the numerical loss is smaller; in the domain of gains, gambles provide less pleasure, so the certainty payoff is smaller.
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Click on the picture to see a larger version on a new page.
Note: For pictorial purposes, the upper and lower scales on this graph are not the same. Since losses hurt more than gains, the lower y-axis scale is compressed. You can see the proper proportions in the "Domains of Gains & Losses" graph above. |
Many experiments have shown that these curves are reasonable approximations of how people actually behave when dealing with uncertainty. The Wikipedia entry for Prospect Theory contains further information.
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