In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. Daniel Ellsberg popularized the paradox in his 1961 paper, "Risk, Ambiguity, and the Savage Axioms". John Maynard Keynes published a version of the paradox in 1921. It is generally taken to be evidence of ambiguity aversion, in which a person tends to prefer choices with quantifiable risks over those with unknown, incalculable risks.
Ellsberg's findings indicate that choices with an underlying level of risk are favored in instances where the likelihood of risk is clear, rather than instances in which the likelihood of risk is unknown. A decision-maker will overwhelmingly favor a choice with a transparent likelihood of risk, even in instances where the unknown alternative will likely produce greater utility. When offered choices with varying risk, people prefer choices with calculable risk, even when they have less utility.
Ellsberg's experimental research involved two separate thought experiments: the 2-urn 2-color scenario and the 1 urn 3-color scenario.
There are two urns each containing 100 balls. It is known that urn A contains 50 red and 50 black, but urn B contains an unknown mix of red and black balls.
The following bets are offered to a participant:
Bet 1A: get 1ifredisdrawnfromurnA,0 otherwise
Bet 2A: get 1ifblackisdrawnfromurnA,0 otherwise
Bet 1B: get 1ifredisdrawnfromurnB,0 otherwise
Bet 2B: get 1ifblackisdrawnfromurnB,0 otherwise
Typically, participants were seen to be indifferent between bet 1A and bet 2A (consistent with expected utility theory) but were seen to strictly prefer Bet 1A to Bet 1B and Bet 2A to 2B. This result is generally interpreted to be a consequence of ambiguity aversion (also known as uncertainty aversion); people intrinsically dislike situations where they cannot attach probabilities to outcomes, in this case favoring the bet in which they know the probability and utility outcome (0.
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In decision theory and economics, ambiguity aversion (also known as uncertainty aversion) is a preference for known risks over unknown risks. An ambiguity-averse individual would rather choose an alternative where the probability distribution of the outcomes is known over one where the probabilities are unknown. This behavior was first introduced through the Ellsberg paradox (people prefer to bet on the outcome of an urn with 50 red and 50 black balls rather than to bet on one with 100 total balls but for which the number of black or red balls is unknown).
The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decision making when the payoff is uncertain. The theory describes which options rational individuals should choose in a situation with uncertainty, based on their risk aversion. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e. the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities).
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environment), often focusing on negative, undesirable consequences. Many different definitions have been proposed. The international standard definition of risk for common understanding in different applications is "effect of uncertainty on objectives".
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