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Economic Modelling · Rational choice theory and utility

Behavioural Critiques and Prospect Theory Explained

Updated 11 October 2026 · Fact-checked

Behavioural critiques show that people often break the axioms of expected utility theory. Prospect theory models this: outcomes are judged as gains or losses against a reference point, losses hurt more than equal gains (loss aversion), and probabilities are weighted non-linearly. To answer questions, name the axiom or bias, then show the numbers.

Understand Behavioural Critiques and Prospect Theory

Expected utility theory says a rational person ranks risky choices by the expected value of a utility function. It rests on axioms such as completeness, transitivity, continuity and independence. Behavioural critiques test whether real people follow these axioms. Often they do not.

Framing means the same choice gets a different answer when worded differently. Offered a certain programme that saves 200 of 600 people or a gamble, people choose the certain programme when outcomes are worded as lives saved. The identical certain outcome, worded as 400 of 600 people dying, is rejected in favour of the gamble. The outcomes are the same in both wordings. Under rational choice, wording should not matter.

The Allais paradox attacks the independence axiom. People prefer a certain gain to a gamble with a higher expected value. In the classic version, option A (a sure ₹10,00,000) can be written as a 0.11 chance of ₹10,00,000 plus a 0.89 chance of ₹10,00,000. Option B shares the same 0.89 chance of ₹10,00,000, with the other 0.11 split between ₹50,00,000 (0.10) and ₹0 (0.01). When this common 0.89 chance of ₹10,00,000 is replaced by a common ₹0, A and B become C and D, and people then choose D, the riskier option. Expected utility cannot produce both choices together (A over B, and D over C). This is the certainty effect: certainty is overvalued. The Ellsberg paradox is about ambiguity. People prefer bets with known probabilities to bets with unknown probabilities, even when no probability assignment can justify this. This is ambiguity aversion, and it conflicts with subjective expected utility.

Prospect theory (Kahneman and Tversky) replaces utility of final wealth with a value function defined on gains and losses relative to a reference point. The function is concave for gains, convex for losses, and steeper for losses than for gains. So people tend to be risk averse for gains and risk seeking for losses when the probabilities are moderate to high. Probabilities are replaced by decision weights, which overweight small probabilities and underweight moderate to high ones. This gives the fourfold pattern: risk averse for moderate or high probability gains and for small probability losses, and risk seeking for moderate or high probability losses and for small probability gains.

For actuaries, the link is practical. Behavioural effects help explain why customers buy low-value insurance with small deductibles, hold on to losing investments, or react to how a product is framed. They also challenge assumptions behind market efficiency. In exams, you should be able to describe each effect, say which rational-choice assumption it breaks, and do simple calculations.

Key rules to remember

Expected utility
E[U(X)] = Σ p_i × U(x_i)
The rational benchmark. Choose the option with the higher expected utility. Independence axiom is the one the Allais paradox breaks.
Prospect theory value
V = Σ w(p_i) × v(x_i − reference point)
v is defined on gains and losses, not final wealth. w(p) is a decision weight, not the probability itself.
Typical value function form
v(x) = x^α for x ≥ 0; v(x) = −λ(−x)^β for x < 0, with λ > 1
λ is the loss aversion coefficient. Parameters are illustrative and given in the question if needed.
Loss aversion
|v(−x)| > v(x) for x > 0
A loss of a given size feels larger than a gain of the same size.
Independence axiom
If A ≻ B then p·A + (1−p)·C ≻ p·B + (1−p)·C
Mixing both options with the same third option should not reverse the ranking. Allais-type choices violate this.

How to solve Behavioural Critiques and Prospect Theory questions

Use this method for both descriptive and numerical questions on behavioural critiques.

  1. 1Identify what the question tests: framing, certainty effect (Allais), ambiguity (Ellsberg), or prospect theory features.
  2. 2Write down the rational benchmark: the expected utility axiom or result that should apply.
  3. 3Calculate expected values or expected utilities of the options if numbers are given.
  4. 4Compare the stated or observed choices with what expected utility predicts.
  5. 5Name the specific axiom broken, such as independence, or the assumption broken, such as invariance to framing.
  6. 6Explain the behavioural effect in one or two sentences using the correct term: reference point, loss aversion, decision weights, certainty effect or ambiguity aversion.
  7. 7If asked, state the implication for insurance, investment or market efficiency.
  8. 8Check that your conclusion matches the numbers and state any assumptions.

Quickest way: Test the pair of choices

When to use it: Use for MCQs and short questions on Allais-type or framing-type choices.

  1. Write the two choice pairs side by side.
  2. Check whether the second pair is the first pair with a common outcome or probability added to both options.
  3. If yes and the ranking flips, the answer is a violation of the independence axiom.
  4. If the same outcomes are worded as gains versus losses and answers differ, the answer is framing.
  5. If one bet has unknown probabilities and is avoided, the answer is ambiguity aversion.

Common mistakes in Behavioural Critiques and Prospect Theory

  • Mixing up the Allais and Ellsberg paradoxes.

    Both are called paradoxes of choice under uncertainty.

    Fix: Allais is about known probabilities and the certainty effect (independence axiom). Ellsberg is about unknown probabilities and ambiguity aversion.

  • Saying prospect theory is the same as expected utility with a different utility function.

    Both use values and probabilities, so they look alike.

    Fix: State the three differences: reference point, separate treatment of gains and losses with loss aversion, and decision weights replacing probabilities.

  • Saying people are always risk seeking for losses.

    Students over-simplify the convex loss region.

    Fix: State the fourfold pattern. People are risk averse for moderate or high probability gains and for small probability losses. They are risk seeking for moderate or high probability losses and for small probability gains.

  • Measuring outcomes as final wealth in a prospect theory answer.

    Habit from expected utility questions.

    Fix: Subtract the reference point first. Define it explicitly, for example current wealth.

  • Treating decision weights as probabilities that sum to one.

    Students assume w(p) = p.

    Fix: Say that w(p) overweights small p, underweights moderate to high p, and need not sum to one.

  • Claiming behavioural evidence proves markets are inefficient.

    Behaviour that departs from rationality sounds like a market failure.

    Fix: Say it challenges the assumption of rational investors. Whether it affects prices depends on limits to arbitrage.

Worked examples

Example 1

Choice 1: A gives ₹10,00,000 for sure; B gives ₹50,00,000 with probability 0.10, ₹10,00,000 with probability 0.89 and ₹0 with probability 0.01. Choice 2: C gives ₹10,00,000 with probability 0.11 and ₹0 otherwise; D gives ₹50,00,000 with probability 0.10 and ₹0 otherwise. Many people choose A and D. Show this violates expected utility.

Show the solution
  1. Set U(0) = 0 and write u1 = U(10,00,000) and u5 = U(50,00,000).
  2. Choosing A over B means u1 > 0.10 u5 + 0.89 u1 + 0.01 × 0.
  3. Rearrange: 0.11 u1 > 0.10 u5.
  4. Choosing D over C means 0.10 u5 > 0.11 u1.
  5. The two inequalities contradict each other.
  6. A and B share a common 0.89 chance of ₹10,00,000, which is replaced by a common 0.89 chance of ₹0 in C and D, so the independence axiom is violated.

Answer: No utility function can give both choices, so A with D violates expected utility. This is the Allais paradox, driven by the certainty effect.

Example 2

A prospect theory value function is v(x) = x^0.5 for gains and v(x) = −2(−x)^0.5 for losses, with x in ₹ thousands relative to the reference point. Find v(36) and v(−36) and state what the result shows.

Show the solution
  1. For the gain: v(36) = 36^0.5 = 6.
  2. For the loss: v(−36) = −2 × (36)^0.5 = −2 × 6 = −12.
  3. Compare sizes: |−12| = 12, which is twice 6.
  4. The loss of ₹36,000 is felt twice as strongly as a gain of ₹36,000.

Answer: v(36) = 6 and v(−36) = −12. This shows loss aversion with coefficient λ = 2.

Exam tips

  • Learn one-line definitions of framing, certainty effect, ambiguity aversion, reference point and loss aversion. Marks are often for the correct term.
  • In Allais-type questions, set U(0) = 0 and show the two inequalities contradict each other. This is the clean proof.
  • Always state the reference point and use gains and losses, not final wealth, in prospect theory calculations.
  • Link to rational choice: say which assumption or axiom is broken. Examiners reward the link.
  • For discussion questions, give one practical implication, such as product framing in insurance or holding losing investments.

Practice questions from Rational choice theory and utility

Behavioural Critiques and Prospect Theory in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Behavioural Critiques and Prospect Theory: frequently asked questions

What is loss aversion in prospect theory?

Loss aversion means a loss feels larger than a gain of the same size. In the value function this appears as a steeper slope for losses than for gains, often shown with a coefficient λ greater than 1.

What is the difference between the Allais and Ellsberg paradoxes?

The Allais paradox uses known probabilities and shows the certainty effect, breaking the independence axiom. The Ellsberg paradox compares known and unknown probabilities and shows ambiguity aversion.

How does behavioural finance differ from rational choice theory?

Rational choice theory assumes people maximise expected utility using consistent preferences. Behavioural finance uses observed behaviour, such as framing and loss aversion, to describe how people actually decide.

Do I need to memorise prospect theory parameters?

Usually no. Questions normally give the value function and parameters. You need to understand the shape and how to apply it relative to a reference point.