Intergenerational Fairness Lecture 2 Fall 2024 PDF

Theories of intergenerational justice: a synopsis (Gosseries, 2008) Distributing resources Intergenerational Fairness Fall 2024, Lecture 2...

Theories of intergenerational justice: a synopsis (Gosseries, 2008) Distributing resources Intergenerational Fairness Fall 2024, Lecture 2 Paolo G. Piacquadio1 1FGN-HSG September 27, 2024........................................ Paolo G. Piacquadio Intergenerational Fairness Theories of intergenerational justice: a synopsis (Gosseries, 2008) Distributing resources Theories of intergenerational justice: a synopsis (Gosseries, 2008)........................................ Paolo G. Piacquadio Intergenerational Fairness  Theories of intergenerational justice: a synopsis (Gosseries, 2008) Distributing resources Comments....................................................... Paolo G. Piacquadio Intergenerational Fairness  Theories of intergenerational justice: a synopsis (Gosseries, 2008) Distributing resources Comments....................................................... Paolo G. Piacquadio Intergenerational Fairness  Theories of intergenerational justice: a synopsis (Gosseries, 2008) Distributing resources Comments....................................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Assumptions........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Simplifying assumptions Assumption 1 Each generation t lives only in one period of time. Assumption 2 Each generation t consists of a (single) representative agent. Assumption 3 Each generation lives for sure......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Simplifying assumptions Assumption 1 Each generation t lives only in one period of time. Assumption 2 Each generation t consists of a (single) representative agent. Assumption 3 Each generation lives for sure......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Simplifying assumptions Assumption 1 Each generation t lives only in one period of time. Assumption 2 Each generation t consists of a (single) representative agent. Assumption 3 Each generation lives for sure......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Simplifying assumptions Assumption 4 Time is descrete. Thus, t ∈ T ≡ [0, ∞) = N denotes both the generation and the period the generation lives. Assumption 5 There is a single consumption good. Thus, ct is the consumption of generation t, while c ≡ (c0 , c1 ,..., ct ,...) is a consumption stream. Assumption 6 Some consumption streams are feasible, others are not. Let Cf denote the set of all feasible consumption streams......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Simplifying assumptions Assumption 4 Time is descrete. Thus, t ∈ T ≡ [0, ∞) = N denotes both the generation and the period the generation lives. Assumption 5 There is a single consumption good. Thus, ct is the consumption of generation t, while c ≡ (c0 , c1 ,..., ct ,...) is a consumption stream. Assumption 6 Some consumption streams are feasible, others are not. Let Cf denote the set of all feasible consumption streams......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Simplifying assumptions Assumption 4 Time is descrete. Thus, t ∈ T ≡ [0, ∞) = N denotes both the generation and the period the generation lives. Assumption 5 There is a single consumption good. Thus, ct is the consumption of generation t, while c ≡ (c0 , c1 ,..., ct ,...) is a consumption stream. Assumption 6 Some consumption streams are feasible, others are not. Let Cf denote the set of all feasible consumption streams......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Desiderata........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Ethical compass How to formalize what we aim at? What is desirable?........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Value judgments Value judgments capture “simple” ethical views: these are the building blocks of theories of justice. Example of value judgments: “social welfare increases when all individuals are better off”; “it is morally wrong to transfer money from a poorer to a richer individual”; “equality is socially good.”........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Value judgments Value judgments capture “simple” ethical views: these are the building blocks of theories of justice. Example of value judgments: “social welfare increases when all individuals are better off”; “it is morally wrong to transfer money from a poorer to a richer individual”; “equality is socially good.”........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Axioms Axioms are mathematical formulations of value judgments. Example of axioms: For each pair of allocations a, a′ ∈ A, Ui (a) ≥ Ui (a′ ) implies a ! a′. For each allocation a ∈ A, the sets {a′ ∈ A |a ! a′ } and {a′ ∈ A |a′ ! a } are closed......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Axioms Axioms are mathematical formulations of value judgments. Example of axioms: For each pair of allocations a, a′ ∈ A, Ui (a) ≥ Ui (a′ ) implies a ! a′. For each allocation a ∈ A, the sets {a′ ∈ A |a ! a′ } and {a′ ∈ A |a′ ! a } are closed......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples The axiomatic approach The axiomatic approach consists of formulating axioms to interpret value judgments and study their (joint) implications. some axioms identify (large) families of “criteria”; other axioms characterize a single “criterion”; still others are jointly incompatible......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Approaches........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Two approaches Normative economics developed around two main approaches: Choosing identifies how society ought to choose for each situation in some domain; Ranking identifies how society ought to rank alternatives in some domain......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Choosing or ranking? There are similar concepts in consumer theory: choice-based and preference-based approach. From consumer theory, we learn that the two approaches are closely related: under some conditions, one can generate choices from preferences and preferences from choices. But these conditions are rarely met and, thus, there are key differences......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Choosing or ranking? There are similar concepts in consumer theory: choice-based and preference-based approach. From consumer theory, we learn that the two approaches are closely related: under some conditions, one can generate choices from preferences and preferences from choices. But these conditions are rarely met and, thus, there are key differences......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Choosing or ranking? There are similar concepts in consumer theory: choice-based and preference-based approach. From consumer theory, we learn that the two approaches are closely related: under some conditions, one can generate choices from preferences and preferences from choices. But these conditions are rarely met and, thus, there are key differences......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Choosing or ranking? Choosing is necessarily situation-specific: how should we share X? how to distribute foreign aid? how should I allocate tasks? how to create working groups for the presentation? In fact, the most common value judgments demand the choice to depend on the situation. In contrast, ranking tends to be universal: the ranking is unchanged, while the feasible set changes; we search for the optimum......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Choosing or ranking? Choosing is necessarily situation-specific: how should we share X? how to distribute foreign aid? how should I allocate tasks? how to create working groups for the presentation? In fact, the most common value judgments demand the choice to depend on the situation. In contrast, ranking tends to be universal: the ranking is unchanged, while the feasible set changes; we search for the optimum......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Choosing or ranking? Choosing is necessarily situation-specific: how should we share X? how to distribute foreign aid? how should I allocate tasks? how to create working groups for the presentation? In fact, the most common value judgments demand the choice to depend on the situation. In contrast, ranking tends to be universal: the ranking is unchanged, while the feasible set changes; we search for the optimum......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples A convergence? Recently, some attempts have been done to make the rankings situation specific. How? Reducing the application of axioms to simple settings or introducing setting-specific axioms. This approach combines the advantages of both criteria: easier to account for behavioral responses and look for second-best optima; possible to introduce a wide range of value judgments......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples A convergence? Recently, some attempts have been done to make the rankings situation specific. How? Reducing the application of axioms to simple settings or introducing setting-specific axioms. This approach combines the advantages of both criteria: easier to account for behavioral responses and look for second-best optima; possible to introduce a wide range of value judgments......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Social welfare functions........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Rankings: some formalism A ranking (or social preferences), denoted !, is a binary relation on C representing “betterness”. Said differently, for each pair c, c′ ∈ C, c ! c′ means that the consumption stream c is socially at least as desirable as c′......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Rankings: some formalism As for individuals’ preferences, we typically assume that the ranking is: transitive: c ! c′ and c′ ! c′′ implies c ! c′′ ; and complete: either c ! c′ or c′ ! c or both. We often also assume it is continuous: “small changes in the alternative do not change the ranking much.” When a ranking is transitive, complete, and continuous it can be represented by a social welfare function W: c ! c′ if and only if W (c) ≥ W (c′ )......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Rankings: some formalism As for individuals’ preferences, we typically assume that the ranking is: transitive: c ! c′ and c′ ! c′′ implies c ! c′′ ; and complete: either c ! c′ or c′ ! c or both. We often also assume it is continuous: “small changes in the alternative do not change the ranking much.” When a ranking is transitive, complete, and continuous it can be represented by a social welfare function W: c ! c′ if and only if W (c) ≥ W (c′ )......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Rankings: some formalism As for individuals’ preferences, we typically assume that the ranking is: transitive: c ! c′ and c′ ! c′′ implies c ! c′′ ; and complete: either c ! c′ or c′ ! c or both. We often also assume it is continuous: “small changes in the alternative do not change the ranking much.” When a ranking is transitive, complete, and continuous it can be represented by a social welfare function W: c ! c′ if and only if W (c) ≥ W (c′ )......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Puzzling examples........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 1 How to share a non-renewable resource? Let Rt ≥ 0 denote the stock or resource available at time t. Let R0 = R̄ > 0 be the initial stock. A consumption stream is feasible if, for each t ∈ T, Rt+1 = Rt − ct......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 1 How to share a non-renewable resource? Let Rt ≥ 0 denote the stock or resource available at time t. Let R0 = R̄ > 0 be the initial stock. A consumption stream is feasible if, for each t ∈ T, Rt+1 = Rt − ct......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 1 How to share a non-renewable resource? Let Rt ≥ 0 denote the stock or resource available at time t. Let R0 = R̄ > 0 be the initial stock. A consumption stream is feasible if, for each t ∈ T, Rt+1 = Rt − ct......................................... Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 1 An egalitarian planner would like to share the resource efficiently and equally across generations. Is it possible? No. Any positive consumption c̄ > 0 assigned equally to each generation is not feasible! ! c̄ = ∞ > R0 Giving c̄ = 0 to each is wasteful! Who gets R0 ?........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 1 An egalitarian planner would like to share the resource efficiently and equally across generations. Is it possible? No. Any positive consumption c̄ > 0 assigned equally to each generation is not feasible! ! c̄ = ∞ > R0 Giving c̄ = 0 to each is wasteful! Who gets R0 ?........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 1 An egalitarian planner would like to share the resource efficiently and equally across generations. Is it possible? No. Any positive consumption c̄ > 0 assigned equally to each generation is not feasible! ! c̄ = ∞ > R0 Giving c̄ = 0 to each is wasteful! Who gets R0 ?........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 2 Consider the axiom that the name of generations do not matter: Anonymity tells that any reshuffling of generations’ consumption is indifferent for the planner. Then, you should agree that the following consumption streams are equally desirable: c1 ≡ (1, 0, 1, 0, 1, 0,...) c2 ≡ (0, 1, 0, 1, 0, 1,...)........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 2 Consider the axiom that the name of generations do not matter: Anonymity tells that any reshuffling of generations’ consumption is indifferent for the planner. Then, you should agree that the following consumption streams are equally desirable: c1 ≡ (1, 0, 1, 0, 1, 0,...) c2 ≡ (0, 1, 0, 1, 0, 1,...)........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 2 By the same reasoning, the following consumption streams are also equally desirable: c2 ≡ (0, 1, 0, 1, 0, 1,...) c3 ≡ (0, 0, 1, 0, 1, 0,...) By transitivity of social preferences, c1 and c3 must be indifferent... c1 ≡ (1, 0, 1, 0, 1, 0,...) c3 ≡ (0, 0, 1, 0, 1, 0,...)...and the consumption of some generations (here the first one) is irrelevant. Efficiency fails again!........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 2 By the same reasoning, the following consumption streams are also equally desirable: c2 ≡ (0, 1, 0, 1, 0, 1,...) c3 ≡ (0, 0, 1, 0, 1, 0,...) By transitivity of social preferences, c1 and c3 must be indifferent... c1 ≡ (1, 0, 1, 0, 1, 0,...) c3 ≡ (0, 0, 1, 0, 1, 0,...)...and the consumption of some generations (here the first one) is irrelevant. Efficiency fails again!........................................ Paolo G. Piacquadio Intergenerational Fairness  Assumptions Desiderata Theories of intergenerational justice: a synopsis (Gosseries, 2008) Approaches Distributing resources Social welfare functions Puzzling examples Example 2 By the same reasoning, the following consumption streams are also equally desirable: c2 ≡ (0, 1, 0, 1, 0, 1,...) c3 ≡ (0, 0, 1, 0, 1, 0,...) By transitivity of social preferences, c1 and c3 must be indifferent... c1 ≡ (1, 0, 1, 0, 1, 0,...) c3 ≡ (0, 0, 1, 0, 1, 0,...)...and the consumption of some generations (here the first one) is irrelevant. Efficiency fails again!........................................ Paolo G. Piacquadio Intergenerational Fairness