an introduction to equality of opportunity marc fleurbaey
TRANSCRIPT
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An introduction to An introduction to equality of opportunityequality of opportunity
Marc FleurbaeyMarc Fleurbaey
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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
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IntroductionIntroduction
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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
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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
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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?
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Theory: four solutionsTheory: four solutions
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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
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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?
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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
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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
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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
~
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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
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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
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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
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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
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Theory: four solutions
Liberal Utilitarian
CompensationEgalitarian
EquivalenceMean of Mins
RewardConditional
EqualityMin of Means
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Application 1: taxationApplication 1: taxation
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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)
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Application 1: taxation
labor
consumption
full time
tax-free budget
(wage rate)
preferences
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Application 1: taxationconsumption
tax-free
budget
preferences
labor
consumption
earnings
tax-fre
e
budget
(45° l
ine)
after-tax
budget
full time
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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
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Application 1: taxationconsumption
labor
consumption
earningsfull wagefull time
45°
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Application 1: taxationconsumption
labor
consumption
earningsfull wagefull time
45°
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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
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Application 1: taxation
• Egalitarian Equivalence: several possibilities
• They all evaluate individual situations by choices in certain budget sets that would give the same satisfaction
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Application 1: taxationconsumption
laborfull time
Min wage rate
Maximin criterion on the “equivalent budget”
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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)
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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
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Application 1: taxation
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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
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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
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Application 2: inequality Application 2: inequality measurementmeasurement
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• 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
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• 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
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• 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
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Application 2: inequality measurement
• Agnostic approach:– Stochastic dominance per C-class
– Stochastic dominance per R-class
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Application 2: inequality measurement
• Two problems with stochastic dominance per C-class:
1. Clash with compensation:
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Application 2: inequality measurement
• Two problems with stochastic dominance per C-class:
2. Self-contradiction if partial C:
Rich / poor Rich untalented/ poor talented
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Conclusion
• Don’t forget– Compensation– Liberal reward
• Don’t forget– Compensation– Liberal reward
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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”
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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
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The endThe end