an introduction to equality of opportunity marc fleurbaey

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An introduction to An introduction to equality of equality of opportunity opportunity Marc Fleurbaey Marc Fleurbaey

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Page 1: An introduction to equality of opportunity Marc Fleurbaey

An introduction to An introduction to equality of opportunityequality of opportunity

Marc FleurbaeyMarc Fleurbaey

Page 2: An introduction to equality of opportunity Marc Fleurbaey

ContentsContents

1.1. IntroductionIntroduction

2.2. Theory: four solutionsTheory: four solutions

3.3. Application 1: taxationApplication 1: taxation

4.4. Application 2: inequality Application 2: inequality measurementmeasurement

Page 3: An introduction to equality of opportunity Marc Fleurbaey

IntroductionIntroduction

Page 4: An introduction to equality of opportunity Marc Fleurbaey

Introduction

• Equal opportunity? A special case of responsibility:1. Equalize opportunity sets2. Individuals are held responsible for their choice in their set

• Better to broaden the perspective: responsibility in general

Page 5: An introduction to equality of opportunity Marc Fleurbaey

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

Page 6: An introduction to equality of opportunity Marc Fleurbaey

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?

Page 7: An introduction to equality of opportunity Marc Fleurbaey

Theory: four solutionsTheory: four solutions

Page 8: An introduction to equality of opportunity Marc Fleurbaey

Theory: four solutions

• A simple model:– U : outcome (utility)– T : transfer– C : circumstances (not

responsible)– R : responsibility

characteristics (fixed)

• Three variants:– Additive– Multiplicative– General

iiii RCTU

iiii RCTU

),,( iiii RCTfU

Page 9: An introduction to equality of opportunity Marc Fleurbaey

Theory: four solutions

• Compensation principle: neutralize C by T1. Equal R equal U

2. Solidarity wrt C : all win or lose in U if the profile of C change

• 21: let Ri = Rj. Permute Ci and Cj. By anonymity, permute Ui and Uj. By solidarity, both win or lose: Ui = Uj .

• Equal U not always possible maximin?

Page 10: An introduction to equality of opportunity Marc Fleurbaey

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

Page 11: An introduction to equality of opportunity Marc Fleurbaey

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):iiiiii RCCTRU )()(

)),,(( iiii RCThfU iiii RCTU

Page 12: An introduction to equality of opportunity Marc Fleurbaey

Theory: four solutions

• Either give precedence to liberal reward:Conditional Equality:equalize

• Or give precedence to compensation:Egalitarian Equivalence:equalize in

)~

,,(~

RCTfU iii

),~

,~

( iii RCTfU iT

~

Page 13: An introduction to equality of opportunity Marc Fleurbaey

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

Page 14: An introduction to equality of opportunity Marc Fleurbaey

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

Page 15: An introduction to equality of opportunity Marc Fleurbaey

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

Page 16: An introduction to equality of opportunity Marc Fleurbaey

Theory: four solutions

A problem with utilitarian reward:U1(x) = x U2(x) = 2x (responsible)

• Liberal reward x1 = x2

• Utilitarian reward give everything to 2

Page 17: An introduction to equality of opportunity Marc Fleurbaey

Theory: four solutions

Liberal Utilitarian

CompensationEgalitarian

EquivalenceMean of Mins

RewardConditional

EqualityMin of Means

Page 18: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxationApplication 1: taxation

Page 19: An introduction to equality of opportunity Marc Fleurbaey

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)

Page 20: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxation

labor

consumption

full time

tax-free budget

(wage rate)

preferences

Page 21: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxationconsumption

tax-free

budget

preferences

labor

consumption

earnings

tax-fre

e

budget

(45° l

ine)

after-tax

budget

full time

Page 22: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxationconsumption

tax-free

budget

preferences

labor

consumption

earnings

tax-fre

e

budget

(45° l

ine)

after-tax

budget

full wagefull time

after-tax

budget

Page 23: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxationconsumption

labor

consumption

earningsfull wagefull time

45°

Page 24: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxationconsumption

labor

consumption

earningsfull wagefull time

45°

Page 25: An introduction to equality of opportunity Marc Fleurbaey

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

Page 26: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxation

• Egalitarian Equivalence: several possibilities

• They all evaluate individual situations by choices in certain budget sets that would give the same satisfaction

Page 27: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxationconsumption

laborfull time

Min wage rate

Maximin criterion on the “equivalent budget”

Page 28: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxationconsumption

laborfull 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)

Page 29: An introduction to equality of opportunity Marc Fleurbaey

consumption

tax-free

budget

preferences

labor

consumption

earnings

tax-fre

e

budget

(45° l

ine)

after-tax

budget

full wagefull time

after-tax

budget

Application 1: taxation

Page 30: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxation

Page 31: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxation

• Optimal tax: zero marginal tax for low incomes consumption

earnings

tax-fre

e

budget

(45° l

ine)

after-tax

budget

full wage

Page 32: An introduction to equality of opportunity Marc Fleurbaey

Application 1: taxation

• Optimal tax: zero marginal tax for low incomes consumption

earnings

tax-fre

e

budget

(45° l

ine)

after-tax

budget

full wage

Page 33: An introduction to equality of opportunity Marc Fleurbaey

Application 2: inequality Application 2: inequality measurementmeasurement

Page 34: An introduction to equality of opportunity Marc Fleurbaey

• 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

Page 35: An introduction to equality of opportunity Marc Fleurbaey

• 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

)~

,,(~

RCTfU iii

),~

,~

( iii RCTfU

Page 36: An introduction to equality of opportunity Marc Fleurbaey

• 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

Page 37: An introduction to equality of opportunity Marc Fleurbaey

Application 2: inequality measurement

• Agnostic approach:– Stochastic dominance per C-class

– Stochastic dominance per R-class

Page 38: An introduction to equality of opportunity Marc Fleurbaey

Application 2: inequality measurement

• Two problems with stochastic dominance per C-class:

1. Clash with compensation:

Page 39: An introduction to equality of opportunity Marc Fleurbaey

Application 2: inequality measurement

• Two problems with stochastic dominance per C-class:

2. Self-contradiction if partial C:

Rich / poor Rich untalented/ poor talented

Page 40: An introduction to equality of opportunity Marc Fleurbaey

Conclusion

• Don’t forget– Compensation– Liberal reward

• Don’t forget– Compensation– Liberal reward

Page 41: An introduction to equality of opportunity Marc Fleurbaey

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”

Page 42: An introduction to equality of opportunity Marc Fleurbaey

What should individuals be held responsible for?

• This excludes:– Equal opportunity for dire straits

– Compensation for aspiration levels:

life! better a has 1 that agree 2 and 1 Both

2. to is whenever1 to

accessible make :utility fory opportunit Equal

saspiration to due

x

x

xxU

xxU

2

2)(

)(

2

1

Page 43: An introduction to equality of opportunity Marc Fleurbaey

The endThe end