Suppose that someone had a simplified version of prospect theory preferences as follows:

They value any gain x from their current reference point simply as x.

They value any loss y from their current reference point as λy where λ≥1 is the person's coefficient of loss aversion.

With these preferences, does the person exhibit diminishing sensitivity?

Question

Suppose that someone had a simplified version of prospect theory preferences as follows:

They value any gain x from their current reference point simply as x.

They value any loss y from their current reference point as λy  where λ≥1  is the person's coefficient of loss aversion.

With these preferences, does the person exhibit diminishing sensitivity?

BlackTom AI · Accepted Answer

In this setup, the value function is defined piecewise with linear forms: gains x are valued as x, and losses y are valued as λy with a constant slope λ ≥ 1.

Option 1: Yes. If the person exhibited diminishing sensitivity, we would expect the incremental value of gains to decrease as the gain increases (a concave shape for the gain domain) and similarly a changing (usually increasing at a decreasing rate) marginal value for losses. However, because both gains and losses are valued linearly (with constant slopes), there is no curvature to produce diminishing sensitivity. The marginal value of an additional unit of gain is always 1, regardless of how large the gain is, and the marginal value of an additional unit of loss is always λ, regardless of how large the loss is. This rules out diminishing sensitivity.

Option 2: No. The defining feature of diminishing sensitivity in prospect theory is the concavity for gains and convexity for losses, leading to decreasing (in absolute value) marginal changes as outcomes move farther from the reference point. Here, the model assigns a constant, linear weight to both gains and losses, so the marginal change does not decline with larger magnitudes. The loss domain scales costs by a fixed factor λ, not by a changing slope, further confirming the absence of diminishing sensitivity.

Additional note: The presence of a kink at the reference point (from gain to loss) does reflect loss aversion (through λ ≥ 1) but does not by itself introduce diminishing sensitivity, since the slopes on both sides are constant rather than varying with the distance from the reference point.

SP25 RMI 660 001 Engaged Learning 13: Attitudes toward risks

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