IF lecture 5
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Questions and Answers

What does the term 'endogenous discounting' refer to in the context of risk?

  • Discount rates fluctuate based on perceived risks of extinction. (correct)
  • Discounting is solely determined by historical data.
  • Discount rates are fixed regardless of circumstances.
  • Discount rates remain constant over time regardless of future uncertainties.

    • Which function represents aversion to inequities in reference-dependent utilitarianism?

  • W
  • v (correct)
  • r
  • E

    • In reference-dependent utilitarianism, how does increased risk of extinction affect discounting?

  • It leads to higher discounting. (correct)
  • It leads to lower discounting.
  • It has no effect on discounting.
  • It requires exponential discounting.

    • What is implied by the equitable reference 'r' in the formula provided?

    <p>It defines the baseline of fairness in utility distribution.</p> Signup and view all the answers

    What is the primary focus of the expected utilitarianism framework?

    <p>Balancing risks and benefits in utility calculations.</p> Signup and view all the answers

    What does expected utilitarianism primarily focus on?

    <p>Maximizing expected utility</p> Signup and view all the answers

    What is a critique of inequality aversion in the context of risk?

    <p>It ignores the time aspect of resolving risk.</p> Signup and view all the answers

    In the context of utility, what does constant relative risk aversion imply?

    <p>Individuals have a consistent level of risk aversion regardless of wealth.</p> Signup and view all the answers

    What aspect of risk does ex-ante utilitarianism consider?

    <p>The anticipated outcomes before the event occurs</p> Signup and view all the answers

    What does indifference to the distribution of utilities imply?

    <p>Proposed actions do not consider how benefits are spread.</p> Signup and view all the answers

    What consequence does the timing of risk resolution carry in ethical considerations?

    <p>It can influence individual risk assessments significantly.</p> Signup and view all the answers

    How does risk aversion relate to inequality aversion?

    <p>Individuals who are risk-averse may also show inequality aversion.</p> Signup and view all the answers

    Which of the following is a flaw of ex-post utilitarianism?

    <p>It evaluates outcomes only after risks have been realized.</p> Signup and view all the answers

    What is the relationship between equitable consumption and efficiency according to the discussion?

    <p>Small deviations from equitable consumption may lead to efficiency gains.</p> Signup and view all the answers

    What does the term 'ex-ante equity' refer to in this context?

    <p>Equity that considers expected outcomes before any risks are taken.</p> Signup and view all the answers

    Which of the following best describes the concept of utilitarianism as mentioned?

    <p>An ethical framework that seeks the greatest happiness for the greatest number.</p> Signup and view all the answers

    In the context of Piacquadio's axioms, which aspect is primarily examined?

    <p>The ethical implications of resource allocation across generations.</p> Signup and view all the answers

    How does the lecture suggest managing the tradeoff between equity and efficiency?

    <p>By accepting some deviations from equity for greater efficiency.</p> Signup and view all the answers

    What does 'ex-post utilitarianism' likely focus on?

    <p>Evaluation of outcomes after decisions have been made.</p> Signup and view all the answers

    Which of the following is a potential criticism of equitable consumption?

    <p>It may overlook individual needs in favor of group equity.</p> Signup and view all the answers

    What does the function 'f' represent in the context of ex-ante utilitarianism?

    <p>A concave function expressing aversion for inequality</p> Signup and view all the answers

    What does the term 'risk and justice' imply in relation to equitable consumption?

    <p>The distribution of risks should be equitable among individuals.</p> Signup and view all the answers

    In ex-post utilitarianism, what does the function 'g' signify?

    <p>A concave function expressing aversion for inequality of utilities</p> Signup and view all the answers

    Which of the following best describes 'ex-ante utilitarianism'?

    <p>It focuses on expected utility before outcomes are known</p> Signup and view all the answers

    What is the primary concern of utilitarianism in the context of risk?

    <p>Maximizing utility while addressing inequality concerns</p> Signup and view all the answers

    In the formula for expected utility in ex-post utilitarianism, what does 'W' represent?

    <p>The expected utility derived from choices made</p> Signup and view all the answers

    Which of the following components is essential in both ex-ante and ex-post utilitarianism?

    <p>A function that reflects aversion to inequality</p> Signup and view all the answers

    What differentiates ex-ante utilitarianism from ex-post utilitarianism?

    <p>The timing of when utilities are considered</p> Signup and view all the answers

    Why is a concave function preferred in frameworks assessing inequality?

    <p>It diminishes the impact of very high utilities</p> Signup and view all the answers

    What is the definition of social welfare according to the provided content?

    <p>The sum of individuals’ expected utilities or the expectation of the social welfare in each state</p> Signup and view all the answers

    Which type of utilitarianism is mentioned in the context of risk and justice?

    <p>Expected utilitarianism</p> Signup and view all the answers

    In the equation provided, what does W(y) represent?

    <p>The social welfare based on expected utilities</p> Signup and view all the answers

    What key concept involves both risk and time in the context of intergenerational fairness?

    <p>Expected utilitarianism</p> Signup and view all the answers

    Which of the following best describes the framework of risk discussed?

    <p>It combines risk assessment with social welfare considerations</p> Signup and view all the answers

    What does the utility representation for individual preferences indicate?

    <p>It allows for expected utility representation.</p> Signup and view all the answers

    What does the term 'social rationality' refer to in the context of expected utility?

    <p>The representation of social preferences in utility terms.</p> Signup and view all the answers

    Which aspect of utilitarianism considers preferences before an event occurs?

    <p>Ex-ante utilitarianism</p> Signup and view all the answers

    In the framework mentioned, what role does 'W(y)' play?

    <p>It denotes social welfare representation.</p> Signup and view all the answers

    How are individual preferences represented mathematically in the framework?

    <p>Using a summation of weighted utilities.</p> Signup and view all the answers

    What does intergenerational fairness primarily address?

    <p>How different generations affect social welfare.</p> Signup and view all the answers

    What is a significant factor in choosing among various utility representations?

    <p>The alignment with ethical considerations of risk.</p> Signup and view all the answers

    What does 'risk and time' refer to in the context of this framework?

    <p>The timing of decisions and their risk assessments.</p> Signup and view all the answers

    Study Notes

    Lecture 5: Intergenerational Fairness

    • Topic: Intergenerational fairness
    • Speaker: Paolo G. Piacquadio
    • Date: 18th October, 2024
    • Location: St. Gallen

    Discussion of the Ethics of Risk

    • Risk and justice
    • Framework
    • Expected utilitarianism
    • Ex-ante and ex-post utilitarianism
    • Risk and time

    Comments

    • Risk vs uncertainty
    • Precautionary approach
    • Time and generations
    • Minimizing risk?
    • Minimizing harm?

    Notation

    • There are I individuals and S states of the world
    • Each state s has probability πs ∈ [0, 1] and such that Σsπs = 1
    • A risky income distribution is:
    • y = [y11 ... y1S]
    • ...
    • [yI1 ... yIS]

    How to Assess Risky Income Distributions?

    • Difficulties: Matrix of incomes + vector of probabilities = a lot of information to summarize!
    • Individuals might have preferences over income lotteries
    • Should social preferences agree with individuals?
    • Time is an essential aspect of risk:
    • Before (risk is resolved) -> After (risk is resolved)
    • Information is also fundamental
    • Are individuals aware of the risk?

    Standard Approach

    • Assumption 1 (Individual rationality): Individuals' preferences admit an expected utility representation:
    • Ui(yi) = Σs πsui(yis)
    • Assumption 2 (Social rationality): Social preferences admit an expected utility representation:
    • W(y) = Σs πsw(ys)
    • Assumption 3: Pareto efficiency: If individuals are better off, social welfare is larger

    Expected Utilitarianism: Result

    • Theorem: Assumptions 1-3 imply that
    • W(y) = ΣiUi(yi) = Σs πsΣiui(yis)
    • Social welfare is:
    • The sum of individuals' expected utilities, or
    • The expectation of the social welfare in each state (i.e., the sum of the utilities of individuals in that state)
    • This result is Harsanyi's (1955) aggregation theorem.

    Expected Utilitarianism: Pros and Cons

    • Pros: Simple, intuitive, powerful
    • Cons: Inequality aversion is given by individuals' risk aversion; indifference to the distribution of utilities across states and individuals; no role for the timing of resolution of risk.

    Inequality Aversion and Risk Aversion

    • Suppose individuals' utility is (constant relative risk aversion)
    • U = Σs πsu(yi) = Σsπs (yis)1-γ/(1 - γ)
    • with risk aversion γ
    • Expected utilitarianism requires inequality aversion to be exactly γ!

    Inequality Aversion and Risk Aversion

    • This is an implication of the theorem.
    • To avoid it, there are three options:
    • Drop individual rationality
    • Drop social rationality
    • Drop Pareto efficiency

    Expected Utilitarianism

    • Expected utilitarianism is insensitive to the distribution of utilities across individuals and equally-likely states

    Beyond Expected Utilitarianism

    • Society might be concerned with e.g.
    • Ex-ante egalitarianism
    • Ex-post fairness

    Expected, ex-ante, and ex-post

    • Ex-ante and ex-post concerns can be captured, but not jointly!
    • Ex-ante utilitarianism satisfies Pareto efficiency and violates "social rationality"
    • Ex-post utilitarianism satisfies social rationality and violates Pareto efficiency

    Ex-ante vs ex-post utilitarianism

    • Ex-ante utilitarianism: Wea(y) = Σif(ui(yi))
    • Ex-post utilitarianism: Wep(y) = ΣsπsΣig(ui(yis))
    • Expected utilitarianism is the special case when f and g are the identity function.

    Introduction

    • The standard approach is to add the expectation to the standard exponentially discounted utilitarian criterion
    • Yet, it is not clear this is an appropriate choice.
    • Issues:
    • Timing of risk resolution is disregarded
    • No "risk preferences" to aggregate
    • How to consider extinction

    Equality with Risk and Time?

    • A strong underlying assumption is that one should eliminate inequalities

    • But what are inequalities in this context?

    • Equality without risk is trivial…

    • ...but what is equality with risk when later generations have different risk?

    • Earlier generations are different than later ones!

    • If equality is impossible, what is equitable?

    • When future technology is risky, some precautionary saving might be in order.

    • How much is an ethical choice.

    • An allocation of consumption is equitable if at any point in time, the consumption is socially as desirable as the risky consumption of a later generation

    Equitable Consumption: An Optimum?

    • Consider the equitable consumption that allocates all resources. Is it the best distribution?
    • Generally no.
    • It is equitable, but one might believe that small deviations could be acceptable if these bring about enough efficiency gains.
    • How to manage the tradeoff between "deviations from equitable consumption" and "efficiency"?

    Ex-ante equity

    • In Piacquadio (2020), I introduce two axioms.
    • Ex-ante equity tells that the equitable (r0, r1) is socially at least as desirable as (x0, x1):
    • There is less inequity between the two generations at (r0, r1) than at (x0, x1).

    Ex-post equity

    • Ex-post equity tells that the equitable (r0, r1) is socially at least as desirable as (x0, x1):
    • Inequity is less likely for generation 1 at (r0, r1) than at (x0, x1).

    Main Result

    • Reference-dependent utilitarianism:

    • W2(y) = E[Σt πtv(xt/rt)]

    • where v is a concave function expressing aversion to inequities and r is the equitable reference

    • Discounting is endogenous:

    • Higher risk of extinction → more discounting

    • More future risk → less discounting

    • Expected utilitarianism is the special case when r is constant.

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    Lecture 5 Intergenerational Fairness PDF

    Description

    Explore the critical discussion around intergenerational fairness and its ethical implications in the context of risk and justice. This quiz will delve into concepts like expected utilitarianism and the differences between risk and uncertainty, focusing on how these ideas relate to future generations.

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