Bestiary of Behavioral Economics/Ellsberg Paradox

First brought to attention by Daniel Ellsberg, the Ellsberg Paradox represents a class of choice situations in which an uncertainty is weighed against a known probability. In most cases it is observed that this uncertainty is regarded as a risk, while statistically is equally as likely of producing a given outcome as the known probability.

In most cases the failure to realize such conditions is not due to haphazard guessing, as many irrational decisions are themselves deliberately and empirically reasoned, but represent an uncertainty about the nature of information given, where the ambiguity of the information presented to the responder incites probabilistic responses. This suggestion of human activity by Ellsberg is in contradiction to the Savage axioms of choice, which suggest that people will react rationally, assign a relative probability to an uncertain situation, and rely on this perceived probability and expected outcome to make choices.

Examples

Urn with Marbles

Experimental Conditions

Urn I contains 100 red and black balls, at an unknown ratio Urn II contains exactly 50 black and 50 red balls

Experimental Questions

1. If you were to draw a ball from Urn I if you had to bet $100 dollars on drawing either Red_I or Black_I which would you chose?
2. "Which do you prefer to bet on, Red_II or Black_II?"
3. "Which do you prefer to bet on, Red_I or Red_II?"
4. "Which do you prefer to bet on, Black_I or Black_II?"

Experimental responses

To the questions "Which do you prefer to bet on, Red_I or Red_II?" and "Which do you prefer to bet on: Black_I or Black_II?", the majority of responses suggested a preference in Red_II and Black_II over Red_I and Black_I. From these majority preferences it seems that preference is not based on statistical probability as the possibilities are equally as likely with the given characteristics.

Ambiguity

The more ambiguous information seems, the less confident is held with the estimate of that probability despite an ample amount of information. This presence of ambiguity comes from when questions of reliability, relevance, and conflict appears in a set of information. Ellsberg defines ambiguity in Risk, Ambiguity, and the Savage Axioms as: "a quality depending on the amount, type, reliability and "unanimity" of information, and giving rise to one's degree of "confidence" in an estimate of relative likelihoods." (Ellsberg, p. 657)

Ambiguity can be found as variable in situations in which information is unreliable or conflicting, where expectations differ from expected behavior, and where confidence in such expectations or predictions is low.

Uncertainty

Because knowledge is limited, and the processes and characteristics may not have the ability to be completely known, without specific and narrowed knowledge on a subject, everyday decisions are made off of crude estimates. Confidence of such estimates rests in perceived probabilities and judgements, even though there is usually not enough information or ability to calculate probabilities to exactly support such confidence.

Risk vs Uncertainty

Frank Knight, an American economist suggested a key difference between risk and uncertainty. Risk, as Knight proposed is a type of uncertainty (which soon becomes an effective certainty) in which probability of the outcomes can be applied. Uncertainty in turn involves a class of situations in which the probability behind outcomes seems ambiguous, or is not known. Ellsberg, who outlines the Ellsberg paradox as a class of situations in which it is observed that in certain circumstances there are decision rules which are based in an uncertainty that lack the use of probability to describe such circumstances.

Conservative Decision Rule

Faced with a situation that involves a set of decisions which contain pay offs and weights involving different actions which can be pursued which have ambiguous values. In Ellsberg's analysis of such a simulation conservative decision towards dealing with known risks rather than uncertainty in ambiguity. Ellsberg makes this assertion that as ambiguity in a situation decreases, because of conservative though which suggests that individuals act as though the worst case scenario are more likely than their personal best estimate in order to ambiguity, and instead navigate towards known risk.

Connections to Neuroscience

Risk and Ambiguity

• Risk

Aversion to risk and ambiguity have large and obvious ties to connections in neuroscience, in which the human mind reacts to situations involving the two uncertainties. In the case of risk, it is seem that aversion to risk coincides with fear responses. Such responses are known to be found in the amygdala area of the brain, which is responsible for immediate reaction to situations which potentially involve fear, as well as input associations involving fear, and thus risk aversion.With the ability for strong emotional responses, it is observed that there is a strong ability to aversion to situations with greater risk.

• Ambiguity

Aversion to ambiguity also can be actively observed by neurocognitive processes, specifically to emotional activity within the brain. Facing a situation of ambiguity versus a situation of certainty it has been observed that the insula cortex of the brain, which relays and processes information about bodily states such as pain, hunger, discomfort activated differently suggesting a difference in the neuroactivity in certain and ambiguous situations.