Question4 Prospect Theory’s probability weighting function captures the fact that: Both A and B People are more sensitive to changes in probabilities in the high-range domain (i.e., for large probabilities) People are more sensitive to a loss than to a gain of the same magnitude (e.g., losing 4 dollars versus winning 4 dollars) ResetMaximum marks: 1 Flag question undefined

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Question4 Prospect Theory’s probability weighting function captures the fact that: Both A and B  People are more sensitive to changes in probabilities in the high-range domain (i.e., for large probabilities) People are more sensitive to a loss than to a gain of the same magnitude (e.g., losing 4 dollars versus winning 4 dollars) ResetMaximum marks: 1 Flag question undefined

BlackTom AI · Accepted Answer

The probability weighting function (w(p)) in prospect theory maps objective probabilities into decision weights and typically has an inverse‑S shape: small probabilities are often overweighted and large probabilities underweighted. This function therefore captures how sensitivity to changes in objective probability varies across the probability scale.

1) Relevant concepts
- Probability weighting function: w(p) transforms p into a decision weight used in choice.
- Inverse‑S shape: implies non‑linear sensitivity across p (different slopes at different p).
- Loss aversion and the value function are separate concepts: loss aversion concerns asymmetry in the value function for gains vs losses, not the probability weighting function.

2) Step‑by‑step reasoning
- The PWF’s shape means the slope (dw/dp) is not constant: for typical parameterizations the slope is steeper in the high‑probability region than in the mid/low region, so a given absolute change in p near the high end produces a larger change in decision weight than the same absolute change in p in the middle or very low range.
- Example (Prelec weighting function w(p)=exp(−(−ln p)^α) with α=0.4 to illustrate the inverse‑S): compute w(0.9) and w(0.8):
  - −ln(0.9)=0.10536; (0.10536)^0.4 ≈ 0.407; w(0.9)=exp(−0.407)=0.666.
  - −ln(0.8)=0.22314; (0.22314)^0.4 ≈ 0.549; w(0.8)=exp(−0.549)=0.578.
  - Difference w(0.9)−w(0.8)=0.088 (larger than the 0.1 raw p difference effect on choices).
  - For very small probabilities (0.02 vs 0.01) the corresponding w differences are much smaller (≈0.019), showing comparatively less sensitivity for this parameterization in that low range.
- Thus the PWF reflects greater sensitivity to changes in probabilities in the high‑range domain.

3) Why the correct answer is correct
- The weighting function specifically models probability sensitivity; the pattern described in the correct option (greater sensitivity in the high‑range domain) is a phenomenon captured by the PWF.

4) Why other options are incorrect
- “Both A and B” is wrong because option C (loss vs gain sensitivity) is not a property of the probability weighting function.
- “People are more sensitive to a loss than to a gain…” describes loss aversion in the value function, not the probability weighting function.

Conclusion: The correct choice is “People are more sensitive to changes in probabilities in the high-range domain (i.e., for large probabilities),” which matches the provided answer.

类似问题

Prospect Theory can be described as investors and gamblers might behave in a manner consistent with the Expected Utility Theory.[Fill in the blank]

Prospect Theory suggests that...[Fill in the blank]

"The satisfaction level of a new investor who has made a 120% return on their first $10,000 investment is higher than that of a wealthy seasoned investor who made the same $10,000 return, but has experienced many ups and downs over time." This statement refers to _____:

Which of the following are consequences of diminishing sensitivity?

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