Understanding Decision-Making: Ambiguity and Risk in Gambles
School
Northeastern University**We aren't endorsed by this school
Course
ANTH 330
Subject
Anthropology
Date
Dec 12, 2024
Pages
4
Uploaded by DoctorFly501
Brian FariasANTHROPOLOGYANTHROPOLOGY_292_TESTBy choosing Gamble D, the participant has a 1 in 3 chance of receiving nothing, and by choosing Gamble A, a 2 in 3 chance of receiving nothing.If Gamble A was less risky than Gamble B, it would follow that Gamble C was less risky than Gamble D (and vice versa), so the risk is not averted in this way.However, because the exact chances of winning are known for Gambles A and D and not known for Gambles B and C, this can be taken as evidence for some sort of ambiguity aversion, which cannot be accounted for in expected utility theory.It has been demonstrated that this phenomenon occurs only when the choice set permits the comparison of the ambiguous proposition with a less vague proposition (butnot when ambiguous propositions are evaluated in isolation).==== Possible explanations ====There have been various attempts to provide decision-theoretic explanations of Ellsberg's observation.Since the probabilistic information available to the decision-maker is incomplete, these attempts sometimes focus on quantifying the non-probabilistic ambiguity that the decision-maker faces – see Knightian uncertainty.That is, these alternative approaches sometimes suppose that the agent formulates a subjective (though not necessarily Bayesian) probability for possible outcomes.One such attempt is based on info-gap decision theory.The agent is told precise probabilities of some outcomes, though the practical meaning of the probability numbers is not entirely clear.For instance, in the gambles discussed above, the probability of a red ball is 30/90, which is a precise number.Nonetheless, the participant may not distinguish intuitively between this and
e.g.30/91.No probability information whatsoever is provided regarding other outcomes, so the participant has very unclear subjective impressions of these probabilities.In light of the ambiguity in the probabilities of the outcomes, the agent is unable to evaluate a precise expected utility.Consequently, a choice based on maximizing the expected utility is also impossible.The info-gap approach supposes that the agent implicitly formulates info-gap models for the subjectively uncertain probabilities.The agent then tries to satisfice the expected utility and maximize the robustness against uncertainty in the imprecise probabilities.This robust-satisficing approach can be developed explicitly to show that the choices of decision-makers should display precisely the preference reversal that Ellsberg observed.Another possible explanation is that this type of game triggers a deceit aversion mechanism.Many humans naturally assume in real-world situations that if they are not told the probability of a certain event, it is to deceive them.Participants make the same decisionsin the experiment as they would about related but not identical real-life problems where theexperimenter would be likely to be a deceiver acting against the subject's interests.When faced with the choice between a red ball and a black ball, the probability of 30/90 is compared to the lower part of the 0/90–60/90 range (the probability of getting a black ball).The average person expects there to be fewer black balls than yellow balls because, in most real-world situations, it would be to the advantage of the experimenter to put fewer black balls in the urn when offering such a gamble.On the other hand, when offered a choice between red and yellow balls and black and yellow balls, people assume that there must be fewer than 30 yellow balls as would be necessary to deceive them.When making the decision, it is quite possible that people simply neglect to consider that the experimenter does not have a chance to modify the contents of the urn in between the draws.In real-life situations, even if the urn is not to be modified, people would be afraid of being deceived on that front as well.== Decisions under uncertainty aversion ==
To describe how an individual would take decisions in a world where uncertainty aversion exists, modifications of the expected utility framework have been proposed.These include:Choquet expected utility: Created by French mathematician Gustave Choquet was a subadditive integral used as a way of measuring expected utility in situations with unknownparameters.The mathematical principle is seen as a way in which the contradiction betweenrational choice theory, Expected utility theory, and Ellsberg's seminal findings can be reconciled.Maxmin expected utility: Axiomatized by Gilboa and Schmeidler is a widely received alternative to utility maximization, taking into account ambiguity-averse preferences.This model reconciles the notion that intuitive decisions may violate the ambiguity neutrality, established within both the Ellsberg Paradox and Allais Paradox.== Alternative explanations ==Other alternative explanations include the competence hypothesis and the comparative ignorance hypothesis.Both theories attribute the source of the ambiguity aversion to the participant's pre-existing knowledge.== Daniel Ellsberg's 1962 paper, "Risk, Ambiguity, and Decision" ==Upon graduating in Economics from Harvard in 1952, Ellsberg left immediately to serve as aUS Marine before coming back to Harvard in 1957 to complete his post-graduate studies on decision-making under uncertainty.Ellsberg left his graduate studies to join the RAND Corporation as a strategic analyst but continued to do academic work on the side.He presented his breakthrough paper at the December 1960 meeting of the Econometric Society.Ellsberg's work built upon previous works by both J.M.Keynes and F.H Knight, challenging the dominant rational choice theory.The work was made public in 2001, some 40 years after being published, because of the Pentagon Papers scandal then encircling
Ellsberg's life.The book is considered a highly-influential paper and is still considered influential within economic academia about risk ambiguity and uncertainty.