IF lecture 5

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 π_s ∈ [0, 1] and such that Σ_sπ_s = 1
• A risky income distribution is:
• y = [y₁¹ ... y₁^S]
• ...
• [y_I¹ ... y_I^S]

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:
• U_i(y_i) = Σ_s π_su_i(y_i^s)
• Assumption 2 (Social rationality): Social preferences admit an expected utility representation:
• W(y) = Σ_s π_sw(y^s)
• Assumption 3: Pareto efficiency: If individuals are better off, social welfare is larger

Expected Utilitarianism: Result

• Theorem: Assumptions 1-3 imply that
• W(y) = Σ_iU_i(y_i) = Σ_s π_sΣ_iu_i(y_i^s)
• 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 = Σ_s π_su(y_i) = Σ_sπ_s (y_i^s)^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: W_ea(y) = Σ_if(u_i(y_i))
• Ex-post utilitarianism: W_ep(y) = Σ_sπ_sΣ_ig(u_i(y_i^s))
• 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[Σ_t π_tv(x_t/r_t)]

• 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.

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.