Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Expected utility
- Part II Nonexpected utility for Risk
- 5 Heuristic arguments for probabilistic sensitivity and rank dependence
- 6 Probabilistic sensitivity and rank dependence analyzed
- 7 Applications and extensions of rank dependence
- 8 Where prospect theory deviates from rank-dependent utility and expected utility: reference dependence versus asset integration
- 9 Prospect theory for decision under risk
- Part III Nonexpected utility for uncertainty
- 13 Conclusion
- Appendices
- References
- Author index
- Subject index
7 - Applications and extensions of rank dependence
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Expected utility
- Part II Nonexpected utility for Risk
- 5 Heuristic arguments for probabilistic sensitivity and rank dependence
- 6 Probabilistic sensitivity and rank dependence analyzed
- 7 Applications and extensions of rank dependence
- 8 Where prospect theory deviates from rank-dependent utility and expected utility: reference dependence versus asset integration
- 9 Prospect theory for decision under risk
- Part III Nonexpected utility for uncertainty
- 13 Conclusion
- Appendices
- References
- Author index
- Subject index
Summary
In the preceding chapter we saw how rank dependence can be used to model pessimism and optimism. Another important component of probability weighting, orthogonal to the optimism–pessimism component, and cognitive rather than motivational, concerns likelihood sensitivity. This component is introduced informally in the following section, and is presented formally in §7.7. Several other extensions and applications of rank dependence are given.
Likelihood insensitivity and pessimism as two components of probabilistic risk attitudes
Figures 7.1.1–3 illustrate how two kinds of deviations from additive probabilities combine to create the probability weighting functions commonly found. Fig. 7.1.1a depicts traditional EU with probabilities weighted linearly; i.e., w(p) = p. Fig. 1b depicts pessimism as discussed in the preceding chapter.
Fig. 2a shows another psychological phenomenon. It reflects “diminishing sensitivity” for probabilities, which we will call likelihood insensitivity. Relative to EU, the weighting function is too shallow in the middle region, and too steep near both endpoints. An extreme case is shown in Fig. 3a. Here w is extremely steep at 0 and 1, and completely shallow in the middle. Such behavior is typically found if people distinguish only between “sure to happen,” “sure not to happen,” and “don't know.” An example of such a crude distinction is in Shackle (1949b p. 8). The expression 50–50 is commonly used to express such crude perceptions of uncertainty. “Either it happens or it won't; you can't say more about it.” is another way of expressing such beliefs. No distinction is made between different levels of likelihood.
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- Information
- Prospect TheoryFor Risk and Ambiguity, pp. 203 - 233Publisher: Cambridge University PressPrint publication year: 2010