An introduction to equality of opportunity Marc Fleurbaey

Contents 1. Introduction 2. Theory: four solutions 3. Application 1: taxation 4. Application 2: inequality measurement

Introduction

Introduction Equal opportunity? A special case of responsibility: 1. Equalize opportunity sets 2. Individuals are held responsible for their choice in their set Better to broaden the perspective: responsibility in general

Introduction What should individuals be held responsible for? The philosophers’ answer –Choice? (Arneson, Cohen, Roemer) Free will??? Not consensual Economic models are deterministic Unforgiving, self-righteous, Thatcherite –Preferences? (Rawls, Dworkin) Preferences are determined Don’t want a pill? But disadvantages may stick

Introduction The economists’ answer (Roemer, Maniquet, etc.) Max U ( x ) subject to x in X (circumstances,policy) –responsible for X ? –responsible for x ? –  responsible for U (a fixed characteristic!) More at the end?

Theory: four solutions

A simple model: – U : outcome (utility) – T : transfer – C : circumstances (not responsible) – R : responsibility characteristics (fixed) Three variants: –Additive –Multiplicative –General

Theory: four solutions Compensation principle: neutralize C by T 1.Equal R  equal U 2.Solidarity wrt C : all win or lose in U if the profile of C change 2  1: let R i = R j. Permute C i and C j. By anonymity, permute U i and U j. By solidarity, both win or lose:  U i = U j. Equal U not always possible  maximin?

Theory: four solutions The reward problem: “Equal R  equal U ” is compatible with many different functions U = g(R) Three proposals: 1.Liberal: laisser-faire, no redistribution for R 2.Utilitarian: zero inequality aversion 3.Desert (Arneson): reward the saints

Theory: four solutions Liberal reward: 1.Equal C  equal T 2.No redistribution if change in the profile of R Exercise: (under anonymity) 2  1 Problem: clash with compensation No clash if separability of ( T, C ):

Theory: four solutions Either give precedence to liberal reward: Conditional Equality: equalize Or give precedence to compensation: Egalitarian Equivalence: equalize in

Theory: four solutions Utilitarian reward: –Equal C  maximize sum of U Problem: clash with compensation No clash if C classes dominate each other for all R R

Theory: four solutions Utilitarian reward: –Equal C  maximize sum of U Problem: clash with compensation No clash if C classes dominate each other for all R R

Theory: four solutions Either give precedence to utilitarian reward: Min of Means: maximize lowest mean of C -classes (types) Or give precedence to compensation: Mean of Mins: (Roemer) maximize mean of lowest U of R -classes (tranches) = the same if domination of C -classes (no clash) Note: there are leximin variants

Theory: four solutions A problem with utilitarian reward: U 1 (x) = x U 2 (x) = 2x (responsible) Liberal reward  x 1 = x 2 Utilitarian reward  give everything to 2

Theory: four solutions LiberalUtilitarian Compensation Egalitarian Equivalence Mean of Mins Reward Conditional Equality Min of Means

Application 1: taxation

Model: consumption = transfer + (wage rate x labor) Assumption: Individuals not responsible for wage rate, only for utility function u(consumption,labor) Note: only partly responsible for their labor (this is a theory of partial responsibility)

Application 1: taxation labor consumption full time tax-free budget (wage rate) preferences

Application 1: taxation consumption tax-free budget preferen ces labor consumption earnings tax-free budget (45° line) after-tax budget full time

Application 1: taxation consumption tax-free budget preferen ces labor consumption earnings tax-free budget (45° line) after-tax budget full wagefull time after-tax budget

Application 1: taxation consumption labor consumption earningsfull wagefull time 45°

Application 1: taxation consumption labor consumption earningsfull wagefull time 45°

Application 1: taxation Utilitarian solutions: assuming no correlation between wage and utility functions, there is domination of wage classes  only one solution: maximize average utility of lowest skilled individuals  ??? for non-linear income tax

Application 1: taxation Egalitarian Equivalence: several possibilities They all evaluate individual situations by choices in certain budget sets that would give the same satisfaction

Application 1: taxation consumption labor full time Min wage rate Maximin criterion on the “equivalent budget”

Application 1: taxation consumption labor full time Min wage rate Maximin criterion on the “equivalent budget” Justification: compensation (does not depend on one’s wage) respects interpersonal comparisons for same preferences liberal reward (equal budget as the ideal situation) participation (  lowest wage rate)

consumption tax-free budget preferences labor consumption earnings tax-free budget (45° line) after-tax budget full wagefull time after-tax budget Application 1: taxation

Optimal tax: zero marginal tax for low incomes consumption earnings tax-free budget (45° line) after-tax budget full wage

Application 1: taxation Optimal tax: zero marginal tax for low incomes consumption earnings tax-free budget (45° line) after-tax budget full wage

Application 2: inequality measurement

Utilitarian approach: –Preliminary question: what is the outcome? –Min of means: inequality index on means per C-class (type) Lorenz dominance on means –Mean of mins: Compute equal-equivalent per R-class (tranche) Equals zero only if equality in each R-class (tranche): compensation Application 2: inequality measurement

Liberal approach: –Conditional equality: inequality index on conditional outcomes Lorenz dominance on conditional outcomes –Egalitarian equivalence: inequality index on equivalent transfers Lorenz dominance on equivalent transfers Application 2: inequality measurement

Similar to standardization: U = g(C,R) compute inequalities due to C –Direct standardization: inequality in U* = g(C,R*) advantage: independent of R –Indirect standardization: inequality in U – g(C*,R) advantage: equals zero only if zero inequality due to C Application 2: inequality measurement

Agnostic approach: –Stochastic dominance per C-class –Stochastic dominance per R-class

Application 2: inequality measurement Two problems with stochastic dominance per C-class: 1.Clash with compensation:

Application 2: inequality measurement Two problems with stochastic dominance per C-class: 2.Self-contradiction if partial C: Rich / poorRich untalented/ poor talented

Conclusion Don’t forget –Compensation –Liberal reward Don’t forget –Compensation –Liberal reward

What should individuals be held responsible for? A proposal: responsibility derived from freedom and respect of preferences: –Choice has value but does not trump outcomes  Offer menus with good options only –Give people what they want (i.e., good lives) ≠ “make them satisfied” Utility = f(life, aspirations) Equally good lives implies unequal utilities  responsibility for satisfaction “level”

What should individuals be held responsible for? This excludes: –Equal opportunity for dire straits –Compensation for aspiration levels:

The end