Advanced Primer in Decision Theory
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Questions and Answers

What is a key feature that allows prospect theory to address the Allais paradoxes?

  • Simplicity of decision-making
  • The certainty effect (correct)
  • Framing of choices
  • Overweighting of large probabilities

    • Which phenomenon does prospect theory explain through loss aversion?

  • Framing effects in marketing
  • Small stake risk aversion (correct)
  • Insurance take-up without lottery play
  • Preference reversals observed in gambling

    • How does prospect theory address the Ellsberg paradox?

  • Through underweighting of moderate probabilities (correct)
  • Through preference consistency across scenarios
  • By simplifying decisions to two outcomes
  • By emphasizing the overweighting of large probabilities

    • What aspect does the reflection effect in prospect theory illustrate?

    <p>Risk aversion for losses and risk seeking for gains (D)</p> Signup and view all the answers

    Which statement about prospect theory is most accurate?

    <p>It accounts for real-world phenomena beyond expected utility violations. (D)</p> Signup and view all the answers

    What does probabilistic insensitivity refer to in prospect theory?

    <p>Overweighting of very high and very low probabilities (C)</p> Signup and view all the answers

    Which theory asserts that individuals make decisions based primarily on perceived gains and losses?

    <p>Prospect Theory (B)</p> Signup and view all the answers

    What is the implication of state-dependent reference points in prospect theory?

    <p>Choices are influenced by prior outcomes. (B)</p> Signup and view all the answers

    What does EUT stand for in the context of decision-making theories?

    <p>Expected Utility Theory (A)</p> Signup and view all the answers

    What significant choice pattern did Allais observe in his experiments?

    <p>Preference reversal between two different choice problems (D)</p> Signup and view all the answers

    In Ellsberg's paradox, which situation demonstrates the violation of expected utility theory?

    <p>Choosing from urns with unknown ball proportions (C)</p> Signup and view all the answers

    Why can expected utility theory be considered violated according to the Allais and Ellsberg paradoxes?

    <p>Choices are influenced by irrelevant information or mixed probabilities (A)</p> Signup and view all the answers

    What is a key characteristic of the urns described in Ellsberg's example?

    <p>The proportions of red and green balls in one urn are unknown. (D)</p> Signup and view all the answers

    What psychological factor was suggested to influence the choices observed in the Allais paradox?

    <p>Dislike of uncertain probabilities (D)</p> Signup and view all the answers

    What was the central focus of Ellsberg's 1961 paper regarding expected utility theory?

    <p>Use of subjective probabilities with unknown chance distributions (B)</p> Signup and view all the answers

    What outcome would a participant achieve in Ellsberg's experiment if they chose the correct color from the urn?

    <p>They would receive e100. (D)</p> Signup and view all the answers

    What is the term used to describe a preference for known probabilities over unknown probabilities?

    <p>Ambiguity aversion (A)</p> Signup and view all the answers

    What paradox arises when probabilities in the unknown urn sum to less than one?

    <p>Preference reversal (A)</p> Signup and view all the answers

    Which axiom of Expected Utility Theory (EUT) is primarily violated by ambiguity aversion?

    <p>Independence axiom (A)</p> Signup and view all the answers

    If the known-proportion urn yields a higher perceived probability of drawing a specific color, what does that imply about the unknown-proportion urn?

    <p>The probabilities in the unknown urn are underestimated. (C)</p> Signup and view all the answers

    What does the expression $p_{ru} + p_{gu} < p_{rk} + p_{gk}$ signify?

    <p>Unknown urn probabilities sum to less than one. (B)</p> Signup and view all the answers

    Which of the following describes the violation of the transitivity axiom in decision making?

    <p>Choosing A over B, B over C, but not choosing A over C. (A)</p> Signup and view all the answers

    When decision makers display preference for the known-proportion urn, which of the following can be inferred?

    <p>They perceive its winning probability to be higher. (A)</p> Signup and view all the answers

    Which outcome is more likely due to preference reversals?

    <p>Fluctuating preferences in similar contexts. (D)</p> Signup and view all the answers

    Flashcards

    Probability Overweighting

    The tendency to overweight small probabilities in decision-making, particularly when it comes to potential gains (like lotteries) or losses (like insurance).

    Loss Aversion

    The phenomenon where individuals are more sensitive to losses than gains of the same magnitude. This asymmetry impacts risk preferences.

    Prospect Theory

    A theory that describes how people make decisions under risk and uncertainty, emphasizing the role of subjective value and probability weighting.

    Small Stake Risk Aversion

    Describes the observation that risk aversion for small stakes (e.g., small bets) can be explained by the overweighting of potential losses in prospect theory.

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    Certainty Effect

    States that people generally prefer certainty over uncertainty, even if the expected value of the certain option is slightly lower.

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    Reflection of Risk Preferences

    The phenomenon where people's risk preferences are reversed depending on whether they are presented with potential gains or losses.

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    Framing Effects

    Situations where individuals exhibit inconsistent choices depending on how the choices are framed, highlighting the influence of cognitive framing on decision-making.

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    Gain-Loss Framing

    A type of framing effect where people make different choices depending on whether they are prompted to think about a decision in terms of gains or losses.

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    Allais Paradox

    A choice situation where an individual makes different decisions when presented with the same choice in slightly different formats, specifically when a certain outcome becomes uncertain.

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    Expected Utility Theory (EUT)

    A theory that states that individuals make decisions based on the expected utility of each option, calculated by weighing the potential outcomes against their respective probabilities.

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    Dislike of Unknown Probabilities

    A pattern of decision-making where individuals prefer choices with known probabilities over choices with unknown probabilities, even if the potential outcomes are similar.

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    Ellsberg Paradox

    A choice situation involving two urns with different, but unknown, proportions of red and green balls. The paradox arises when individuals demonstrate inconsistent preferences between choosing a specific color and selecting an urn.

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    Subjective Expected Utility Theory

    A version of Expected Utility Theory that applies when the true probabilities of outcomes are unknown and individuals must rely on their subjective estimations.

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    Ambiguity Aversion

    The phenomenon where individuals tend to favor choices with known probabilities over choices with ambiguous probabilities, even if the expected value of the choices is identical.

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    Irrelevant Alternatives

    When the probability of a particular outcome is substituted by a different probability in a choice problem, but this should not influence the decision according to Expected Utility Theory.

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    Choice Problem

    A scenario where a choice is presented between two options with different payoffs and probabilities, where the individual's preference may not align with the predictions of standard economic theory.

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    Ambiguity Aversion Paradox

    A paradox that arises within Expected Utility Theory (EUT) when individuals demonstrate ambiguity aversion. This paradox occurs because under EUT, if someone prefers the urn with a known proportion of red balls, it implies their perceived probability for getting a red ball is higher in the known urn. But if this is true, the probability perceived for a green ball must similarly be higher in the known urn, leading to a contradiction: the probabilities cannot sum to one, as they should.

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    Preference Reversals

    A violation of EUT where a decision maker's preferences are not consistent across decision contexts, violating the property of transitivity. These preferences involve a switch in the ranking of two options based on the introduction of another option.

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    Probability Weighting

    A situation where a person's choices are not consistent with their preferences, suggesting an inconsistency in how they weigh probabilities. This is a common violation of EUT, particularly when dealing with small probabilities.

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    Study Notes

    Advanced Primer in Decision Theory

    • Decision theory studies individual decision-making processes, and applies to various fields, including economics and psychology
    • Expected utility theory (EUT) is a core concept: It's essential for modeling decision-making under risk.
    • EUT has shortcomings as a descriptive theory: it doesn't accurately reflect observed human behavior under risk
    • Alternative models like rank-dependent models and prospect theory attempt to improve upon EUT's shortcoming

    Risk Preferences

    • Decision theory uses prospects over uncertain outcomes, often monetary, to study decision-making
    • Risk, in the context of decision theory, signifies situations where probabilities are known or knowable, like state lotteries
    • Descriptive theories aim to represent actual decision-making patterns, while normative theories prescribe ideal behaviors, such as maximizing utility
    • Expected Value Theory (EVD) is a simple theory based on mathematical expectation to predict a choice, but doesn't account for risk aversion, where people often prefer a guaranteed smaller prize rather than a potentially larger prize

    Expected Utility Theory

    • A normative model where an individual's decisions are driven by maximizing the expected utility of a prospect
    • Introduces subjective utility function U(ξ) that transform prospects or outcomes based on their utility. The utility of a certainty equivalent equals the expected utility of a prospect
    • Utility functions are unique up to a positive linear transformation. These theories are good for certain applications but don't account for all aspects of human decision-making.

    EUT as a Descriptive Theory of Choice

    • EUT presents a good normative theory of decision-making. However, it doesn't adequately describe observed decision patterns
    • It has shortcomings: Notably, people display risk aversion, especially with smaller amounts of money, contradicting the predictions of EUT and the use of concave utility function.
    • Preference reversals, where people exhibit different preferences when choosing versus stating a price, add to EUT's weaknesses

    Empirical Violations of EUT

    • The Allais paradox highlights that individuals' preferences can violate EUT assumptions, particularly concerning the ratio of outcomes in choices
    • The Ellsberg paradox demonstrates ambiguity aversion: individuals exhibit preference reversals even when they don't know the probabilities involved.

    Prospect Theory

    • It's a model used in decision-making theory that suggests that people make decisions based on perceived gains and losses rather than final outcomes
    • It introduces a value function v(x) and weighting function w(p) that are nonlinear for both losses and gains that reflect loss aversion
    • Framing effects, where identical outcomes from the same decision presented in different ways can affect choices

    Uncertainty and Ambiguity

    • Uncertainty refers to situations where probabilities aren't known, unlike risk where probabilities are known.
    • Ambiguity refers to situations where the probabilities of events are unknown and cannot be meaningfully estimated.

    Time Preferences

    • Time preference is a concept in decision theory where individuals consider the value of rewards obtained at different points in time, often reflecting that earlier rewards have a higher value than later ones
    • The literature on time preferences is similar to models of risk, exhibiting similar violations

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    Description

    Explore the intricate concepts of decision theory, focusing on expected utility theory and its critiques. Learn about alternative models like prospect theory that aim to better explain human behavior under risk. This quiz covers essential frameworks and theories applicable in various fields such as economics and psychology.

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