Prospect Theory in the Brain

Written by Cheung Ka Yui Anthony

Part I: Prospect Theory

Prospect Theory, introduced by Daniel Kahneman and Amos Tversky in 1979, revolutionized our understanding of decision-making under risk by challenging Expected Utility Theory (EUT). Unlike EUT, which assumes people maximize expected value, Prospect Theory accounts for systematic deviations observed in human choices. For example, when choosing between A) a 50% chance to win $1,000 and B) a certain gain of $450, most people prefer the certain gain, despite the higher expected value of option A ($500 vs $450). This "certainty effect" highlights how psychological factors shape decisions (Kahneman & Tversky, 1979).

The theory posits that decision-making occurs in two phases: editing and evaluation. In the editing phase, individuals simplify complex prospects using heuristics, such as decomposing a prospect into simpler components or rounding probabilities. In the evaluation phase, they assign subjective values to these edited prospects, to make a final decision.

The Value Function

The cornerstone of Prospect Theory is its value function, defined as:

In plain terms, Prospect Theory calculates how much a person values a set of possible outcomes (prospect) by multiplying two elements: the subjective value of each outcome (which may differ from the actual value) and the psychological weight given to each outcome’s probability (which may also differ from the actual probability). For an everyday example, most people don't rigorously treat a 0.01% risk as 10 times less likely than a 0.1% risk - they just consider both to be ‘very unlikely’. To them, π(0. 01%) ≈ π(0. 1%) .

The value function v(x) exhibits three key properties:

1. Reference Dependence: Outcomes are evaluated as gains or losses relative to a reference point, not absolute states of wealth (Tversky & Kahneman, 1991).

   
   

2. Diminishing Sensitivity: The function is concave for gains (v''(x) < 0 for x > 0) and convex for losses (v''(x) > 0 for x < 0). This implies the psychological impact of the same absolute change is smaller at larger magnitudes. For instance, the difference between gaining $10 and $20 feels larger than that between $1,010 and $1,020.

   
   

3. Loss Aversion: The function is steeper for losses than for gains (|v(− x)| > v(x) for x > 0). This implies that losses have a greater psychological impact than equivalent gains, typically by a factor of approximately 2.25 (Tversky & Kahneman, 1992).

The Probability Weighting Function

The probability weighting function π(p) also exhibits distinctive properties:

1. Nonlinear Probability Weighting: Small probabilities are overweighted (π(p) > p for small p), while moderate and high probabilities are underweighted (π(p) < p for moderate to large p).

2. Subcertainty: For all 0 < p < 1, π(p) + π(1 − p) < 1, reflecting a preference for certain outcomes over risky ones.

3. Subadditivity: For small p, π(rp) > rπ(p), where 0 < r < 1, indicating that people are more sensitive to probability changes near impossibility (0%) and certainty (100%).

Fourfold Pattern of Risk Attitudes

Together, the value and probability weighting functions create a fourfold pattern of risk attitudes, which is observed in various settings (Kahneman & Tversky, 1979):

• Risk Aversion for high-probability gains (e.g. preferring a certain $450 over a 50% chance of $1,000).

• Risk Seeking for low-probability gains (e.g. buying lottery tickets).

• Risk Aversion for low-probability losses (e.g. purchasing insurance).

• Risk Seeking for high-probability losses (e.g. holding losing stocks).

While the 1979 model remains foundational, later refinements like Cumulative Prospect Theory (Tversky & Kahneman, 1992) extended the model to uncertain probabilities and continuous outcomes.

Additionally, neuroscientific research, explored in Part II, further validates its neural underpinnings.

Part II: The Neuroscience of Prospect Theory

Recent advances in neuroscience have begun to uncover specific brain regions and neurotransmitter systems underlying Prospect Theory’s behavioral phenomena.

Neural Correlates of the Value Function

The ventral striatum and ventromedial prefrontal cortex (vmPFC) are critical for representing anticipated and experienced gains. vmPFC activation scales with anticipated rewards in a concave pattern, mirroring the diminishing sensitivity of Prospect Theory’s value function for gains (Knutson et al., 2003).

Loss aversion is primarily mediated by the amygdala and anterior insula. Functional magnetic resonance imaging (fMRI) studies indicate that amygdala activation correlates with individual loss aversion coefficients (Tom et al., 2007). The anterior insula, linked to negative emotions and pain processing, exhibits greater activation for losses for equivalent gains, providing a neural basis for loss aversion.

Neural Correlates of the Probability Weighting Function

The nonlinear probability weighting function π(p) is reflected in the brain’s reward anticipation circuits, particularly the ventral striatum and dopaminergic midbrain regions. These areas show exaggerated responses to low-probability rewards, consistent with overweighting small probabilities (Hsu et al., 2009).

Dopamine neurons encode reward prediction errors—the difference between expected and actual outcomes—in a manner that aligns with Prospect Theory’s distorted probability perceptions. For example, a small chance of a large reward elicits a disproportionately strong dopaminergic signal, which explains behaviors like gambling.

The Editing Phase, Executive Function Networks, and Neurotransmitters

The editing phase, where prospects are simplified, engages executive function networks, particularly the dorsolateral prefrontal cortex (DLPFC) and anterior cingulate cortex (ACC). The DLPFC supports cognitive control, enabling framing and mental accounting, while the ACC monitors conflicts between competing options (De Martino et al., 2006). These regions’ activities support the simplification and categorization processes proposed in Prospect Theory.

Finally, neurotransmitter systems also contribute. Examples include:

• Dopamine: Encodes reward valuation and probability weighting in the ventral striatum.

• Serotonin: Modulates temporal discounting and impulsivity, influencing how future gains or losses are weighted.

• Noradrenaline: Contributes to loss aversion through arousal and negative emotion processing.

These neural and neurotransmitter mechanisms collectively illustrate how Prospect Theory’s behavioral principles are rooted in the brain’s architecture, paving the way for deeper neuroscientific exploration of human decision-making.

References

De Martino, B., Kumaran, D., Seymour, B., & Dolan, R. J. (2006). Frames, biases, and rational decision-making in the human brain. Science, 313(5787), 684-687.

Hsu, M., Krajbich, I., Zhao, C., & Camerer, C. F. (2009). Neural response to reward anticipation under risk is nonlinear in probabilities. Journal of Neuroscience, 29(7), 2231-2237.

Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291.

Knutson, B., Fong, G. W., Bennett, S. M., Adams, C. M., & Hommer, D. (2003). A region of mesial prefrontal cortex tracks monetarily rewarding outcomes: Characterization with rapid event-related fMRI. NeuroImage, 18(2), 263-272.

Tom, S. M., Fox, C. R., Trepel, C., & Poldrack, R. A. (2007). The neural basis of loss aversion in decision-making under risk. Science, 315(5811), 515-518.

Trepel, C., Fox, C. R., & Poldrack, R. A. (2005). Prospect theory on the brain? Toward a cognitive neuroscience of decision under risk. Cognitive Brain Research, 23(1), 34-50.

Tversky, A., & Kahneman, D. (1991). Loss aversion in riskless choice: A reference-dependent model. The Quarterly Journal of Economics, 106(4), 1039-1061.

Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297-323.