🧪 This platform is in early beta. Features may change and you might encounter bugs. We appreciate your patience!
allais_paradox
The Allais paradox demonstrates that people systematically violate expected utility theory by switching preferences when the same probability difference is embedded in different contexts — specifically when one option changes from certainty to risk. Most people prefer a certain $1M over a lottery, but also prefer a 10% chance of $5M over an 11% chance of $1M — a combination mathematically inconsistent with any utility function.
Problem 1: Most people prefer A (certain $1M) over B (89% $1M, 10% $5M, 1% $0). Problem 2: Most people prefer D (10% $5M, 90% $0) over C (11% $1M, 89% $0). But preferring A over B and D over C is inconsistent with expected utility theory.
A public health official prefers Policy A (certain 500 lives saved) over Policy B (90% chance of saving 600 lives, 10% chance of saving none). But when the baseline changes so that 500 lives are already guaranteed saved, the same official switches to preferring the gamble — violating consistency in expected utility.
An investor chooses a guaranteed €10,000 bonus over a lottery ticket with 89% chance of €10,000, 10% chance of €50,000, and 1% chance of nothing. Yet when offered a standalone choice between a 10% chance of €50,000 versus an 11% chance of €10,000, the same investor picks the bigger prize — an inconsistency that reveals the certainty effect at work.
Binary (yes/no) questions an LLM must answer to identify this aspect:
Does the argument use expected utility theory to predict choice between risky options?
Type: binaryDoes the presence of a certain option change preferences between two uncertain options in a way that violates the independence axiom?
Type: binaryAre preferences between lotteries consistent across contexts where one option is certain versus risky?
Type: binaryIs the analysis sensitive to framing of outcomes as gains versus relative to a certain baseline?
Type: binaryThe Allais paradox demonstrates that people systematically violate expected utility theory by switching preferences when the same probability difference is embedded in different contexts — specifically when one option changes from certainty to risk. Most people prefer a certain $1M over a lottery, but also prefer a 10% chance of $5M over an 11% chance of $1M — a combination mathematically inconsistent with any utility function.
The presence of certainty in Option 1A creates a disproportionate psychological premium on sure gains. When certainty is removed in Problem 2, this premium disappears and people revert to probability-weighted thinking, creating an inconsistency.
When evaluating risky choices, strip away the certainty premium by framing both options consistently as probabilistic. Use decision analysis frameworks that allow for non-linear probability weighting such as prospect theory.
The Allais paradox is foundational to behavioral economics and prospect theory. It has implications for insurance purchasing, pension choices, and policy design when certainty is used as an anchor.
Use these tools to detect, analyze, or train this aspect.