Decision-making paradoxes are situations where an individual’s choices appear to be inconsistent or irrational when judged against the principles of classical economic theories, like expected utility theory.
These paradoxes highlight how human behavior often deviates from the predictions of traditional models, revealing the influence of cognitive biases and psychological factors.
Here are some of the most common paradoxes:
1. Allais Paradox
The Allais paradox demonstrates that people’s choices can violate the independence axiom of expected utility theory. This axiom suggests that if you add an identical outcome to two different lotteries, the preference between the two lotteries should not change. The paradox shows this isn’t always true, as people often place a disproportionately high value on a certain outcome, a phenomenon known as the certainty effect.
The Setup: Participants are presented with two pairs of choices.
- Choice 1:
- Option A: A 100% chance of winning $1 million.
- Option B: An 89% chance of winning $1 million, a 10% chance of winning $5 million, and a 1% chance of winning nothing. Most people choose Option A, valuing the certainty of a large sum over the slight chance of a higher payout.
- Choice 2:
- Option C: An 11% chance of winning $1 million and an 89% chance of winning nothing.
- Option D: A 10% chance of winning $5 million and a 90% chance of winning nothing. Most people choose Option D, as the odds are similar for a much larger potential payout.
The Paradox: When you calculate the expected utility for these choices, a person who chose Option A in the first choice should, to be consistent with the independence axiom, also choose Option C in the second choice. The fact that most people choose Option A and Option D shows a preference reversal that contradicts the theory.
2. Ellsberg Paradox
The Ellsberg paradox highlights ambiguity aversion, which is a preference for choices with known probabilities over choices with unknown or ambiguous probabilities. This violates the subjective expected utility theory, which assumes people can assign a subjective probability to any event and make decisions based on that.
The Setup: You have an urn containing 90 balls. You know that 30 are red, and the remaining 60 are a mix of black and yellow in unknown proportions.
- Choice 1:
- Option A: Bet that a red ball is drawn. (Known probability: 30/90 = 1/3)
- Option B: Bet that a black ball is drawn. (Ambiguous probability: between 0/90 and 60/90) Most people choose Option A because the probability is known.
- Choice 2:
- Option C: Bet that a red or yellow ball is drawn.
- Option D: Bet that a black or yellow ball is drawn. The probability of a black or yellow ball is exactly 60/90 (since there are 60 of them in total), while the probability of a red or yellow ball is ambiguous. Most people choose Option D.
The Paradox: In the first choice, people prefer the known probability of a red ball over the ambiguous probability of a black ball. However, in the second choice, people prefer the known probability of a black or yellow ball over the ambiguous probability of a red or yellow ball. The choices demonstrate a general human aversion to situations where probabilities are unknown, even if the expected outcome might be the same.
3. St. Petersburg Paradox
The St. Petersburg paradox shows a disconnect between the mathematical expected value of a game and the amount a person would actually be willing to pay to play it. The paradox challenges the idea that people make decisions by simply maximizing expected monetary value.
The Setup: Imagine a game where a coin is flipped until it lands on heads. The payout is determined by the number of flips it takes.
- If heads is on the 1st flip, you win $2^1 = $2.
- If heads is on the 2nd flip, you win $2^2 = $4.
- If heads is on the 3rd flip, you win $2^3 = $8.
- …and so on. The expected value of this game is calculated as the sum of all possible outcomes multiplied by their probabilities: EV = (1/2 * $2) + (1/4 * $4) + (1/8 * $8) + … EV = $1 + $1 + $1 + … = ∞
The Paradox: The mathematical expected value is infinite. According to a theory that assumes people maximize expected value, a person should be willing to pay an incredibly large, even infinite, amount to play this game. However, in reality, people are only willing to pay a very small, finite amount to play, typically just a few dollars.
The resolution of the paradox, proposed by Daniel Bernoulli, is that people don’t maximize expected value, but rather expected utility. Utility is the subjective value or satisfaction a person gets from something. As your wealth increases, the added utility of an extra dollar decreases (the concept of diminishing marginal utility). So, while the monetary payout can be infinite, the utility of those enormous, but highly improbable, payouts is not. This better explains why people only value the game at a few dollars.
Beyond the classic paradoxes, several other concepts and cognitive biases further illuminate the complexities of human decision-making and highlight the limitations of traditional economic models.
4. The Framing Effect
The framing effect demonstrates that people’s choices are influenced by how a problem is presented or “framed,” even if the underlying options are logically equivalent. This highlights that our decisions are not always based on a rational analysis of objective information.
Example: Imagine a public health crisis is expected to kill 600 people. Two different programs are proposed, each with a different “frame”:
- Positive Frame (Gains):
- Program A: “200 people will be saved.”
- Program B: “There’s a 1/3 probability that 600 people will be saved, and a 2/3 probability that no one will be saved.”
- In this frame, most people choose Program A because they prefer the certain gain of saving lives.
- Negative Frame (Losses):
- Program C: “400 people will die.”
- Program D: “There’s a 1/3 probability that no one will die, and a 2/3 probability that 600 people will die.”
- In this frame, most people choose Program D, as they are willing to take a risk to avoid the certain loss of 400 lives.
The Paradox: Program A and Program C are identical in their outcomes (200 saved, 400 die), as are Program B and Program D. The change in people’s choices simply due to the framing of the problem (gains vs. losses) contradicts the idea that people make rational decisions based on the objective outcomes.
5. Prospect Theory
Developed by Daniel Kahneman and Amos Tversky, prospect theory provides an alternative to expected utility theory by better explaining how people make decisions under uncertainty. It incorporates two key psychological insights:
- Reference Dependence: People evaluate outcomes not in terms of their final wealth, but as gains or losses relative to a reference point (e.g., their current wealth or an expected outcome). This is a foundational concept that explains the framing effect.
- Loss Aversion: The psychological impact of a loss is much greater than the psychological impact of an equivalent gain. A loss of $100 feels more painful than the pleasure of gaining $100. This asymmetry in our response to gains and losses is a central pillar of the theory.
The Prospect Theory Value Function: Prospect theory is often visualized with a value function that is S-shaped. It’s steeper for losses than for gains, illustrating loss aversion. This function is also concave for gains (explaining risk aversion when dealing with gains) and convex for losses (explaining risk-seeking behavior when dealing with losses).
6. The Endowment Effect
The endowment effect is a bias where people place a disproportionately higher value on an item simply because they own it. This contradicts the Coase Theorem in economics, which suggests that in the absence of transaction costs, an item’s value should be independent of who owns it.
The Setup:
- Group 1 (Sellers): Given a coffee mug and asked the minimum price they would sell it for.
- Group 2 (Buyers): Not given a mug and asked the maximum price they would pay for it.
The Paradox: Studies consistently show that the sellers demand a much higher price for the mug than the buyers are willing to pay. The mere fact of owning the mug “endows” it with a higher perceived value. This is a direct consequence of loss aversion from prospect theory: the sellers see giving up the mug as a loss, which feels more significant than the buyers’ potential gain of acquiring it.
These concepts and biases, alongside the classic paradoxes, have profoundly influenced behavioral economics and finance.
They provide a more realistic and psychologically grounded understanding of how people make decisions, revealing that our choices are often shaped by cognitive shortcuts, emotions, and the way information is presented, rather than by pure, objective rationality.