Ambiguity aversion

Preference of known risks to unknown risks
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). There are two categories of imperfectly predictable events between which choices must be made: risky and ambiguous events (also known as Knightian uncertainty). Risky events have a known probability distribution over outcomes while in ambiguous events the probability distribution is not known. The reaction is behavioral and still being formalized. Ambiguity aversion can be used to explain incomplete contracts, volatility in stock markets, and selective abstention in elections (Ghirardato & Marinacci, 2001). The concept is expressed in the English proverb: "Better the devil you know than the devil you don't."

The distinction between ambiguity aversion and risk aversion is important but subtle. Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation and it is defined by the preference between a risky alternative and its expected value. Ambiguity aversion applies to a situation when the probabilities of outcomes are unknown (Epstein 1999) and it is defined through the preference between risky and ambiguous alternatives, after controlling for preferences over risk. Using the traditional two urn Ellsberg choice, urn A contains 50 red balls and 50 blue balls while urn B contains 100 total balls (either red or blue) but the number of each is unknown. An individual who prefers a certain payoff strictly smaller than $10 over a bet that pays $20 if the color of a ball drawn from urn A is guessed correctly and $0 otherwise is said to be risk averse but nothing can be said about her preferences over ambiguity. On the other hand, an individual who strictly prefers that same bet if the ball is drawn from urn A over the case where the ball is drawn from urn B is said to be ambiguity averse but not necessarily risk averse. A real world consequence of increased ambiguity aversion is the increased demand for insurance because the general public are averse to the unknown events that will affect their lives and property (Alary, Treich, and Gollier 2010).

Unlike risk aversion, which is primarily attributed to decreasing marginal utility, there is no widely accepted main cause for ambiguity aversion. The many possible explanations include different choice mechanisms, behavioral biases and differential treatment of compound lotteries; this in turn explains the lack of a widespread measure of ambiguity aversion.

In their 1989 paper, Gilboa and Schmeidler propose an axiomatic representation of preferences that rationalizes ambiguity aversion. An individual that behaves according to these axioms would act as if having multiple prior subjective probability distributions over the set of outcomes and chooses the alternative that maximizes the minimum expected utility over these distributions. In the Ellsberg example, if an individual has a set of subjective prior probabilities of a ball drawn from urn B being red ranging between, for example, 0.4 and 0.6, and applies a maxmin choice rule, she will strictly prefer a bet on urn A over a bet on urn B since the expected utility she assigns to urn A (based on an assumed 50% probability of the predicted color) is greater than the one she assigns to urn B (based on the worst case 40% probability of the predicted color).

David Schmeidler also developed the Choquet expected utility model. Its axiomatization allows for non additive probabilities and the expected utility of an act is defined using a Choquet integral. This representation also rationalizes ambiguity aversion and has the maxmin expected utility as a particular case.

In Halevy (2007) the experimental results show that ambiguity aversion is related to violations of the Reduction of Compound Lotteries axiom (ROCL). This suggests that the effects attributed to ambiguity aversion may be partially explained by an inability to reduce compound lotteries to their corresponding simple lotteries or some behavioral violation of this axiom.

Women are more risk averse than men. One potential explanation for gender differences is that risk and ambiguity are related to cognitive and noncognitive traits on which men and women differ. Women initially respond to ambiguity much more favorably than men, but as ambiguity increases, men and women show similar marginal valuations of ambiguity. Psychological traits are strongly associated with risk but not to ambiguity. Adjusting for psychological traits explains why a gender difference exists within risk aversion and why these differences are not a part of ambiguity aversion. Since psychological measures are related to risk but not to ambiguity, risk aversion and ambiguity aversion are distinct traits because they depend on different variables (Borghans, Golsteyn, Heckman, Meijers, 2009.)

Given the salience of ambiguity in economic and financial research, it is natural to wonder about its relation with learning and its persistence over time. The long run persistence of ambiguity clearly depends on the way the inter temporal ambiguity is modeled. If the decision maker incorporate new information according to a natural generalization of Bayes' rule entailing a set of priors (rather than a unique prior) on a given prior support; then Massari Newton (2020) and Massari Marinacci (2019) show that long run ambiguity is not a possible outcome of the multiple prior learning models with convex prior support (i. e., positive Lebegue measure) and provide sufficient conditions for ambiguity to fade away when the prior support is not convex, respectively.