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An introduction to equality of opportunity

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maximize mean of lowest U of R-classes (tranches) = the same if domination of C-classes ... (tranche) Equals zero only if equality in each R-class (tranche) ... – PowerPoint PPT presentation

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Title: An introduction to equality of opportunity


1
An introduction to equality of opportunity
  • Marc Fleurbaey

2
Contents
  • Introduction
  • Theory four solutions
  • Application 1 taxation
  • Application 2 inequality measurement

3
Introduction
4
Introduction
  • Equal opportunity? A special case of
    responsibility1. Equalize opportunity sets2.
    Individuals are held responsible for their choice
    in their set
  • Better to broaden the perspective responsibility
    in general

5
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
  • Dont want a pill? But disadvantages may stick

6
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?

7
Theory four solutions
8
Theory four solutions
  • A simple model
  • U outcome (utility)
  • T transfer
  • C circumstances (not responsible)
  • R responsibility characteristics (fixed)
  • Three variants
  • Additive
  • Multiplicative
  • General

9
Theory four solutions
  • Compensation principle neutralize C by T
  • Equal R ? equal U
  • Solidarity wrt C all win or lose in U if the
    profile of C change
  • 2?1 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?

10
Theory four solutions
  • The reward problem Equal R ? equal U is
    compatible with many different functions U g(R)
  • Three proposals
  • Liberal laisser-faire, no redistribution for R
  • Utilitarian zero inequality aversion
  • Desert (Arneson) reward the saints

11
Theory four solutions
  • Liberal reward
  • Equal C ? equal T
  • 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)

12
Theory four solutions
  • Either give precedence to liberal
    rewardConditional Equalityequalize
  • Or give precedence to compensationEgalitarian
    Equivalenceequalize in

13
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
14
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
15
Theory four solutions
  • Either give precedence to utilitarian rewardMin
    of Meansmaximize lowest mean of C-classes
    (types)
  • Or give precedence to compensationMean 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

16
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

17
Theory four solutions
18
Application 1 taxation
19
Application 1 taxation
  • Modelconsumption 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)

20
Application 1 taxation
consumption
preferences
tax-free budget (wage rate)
labor
full time
21
Application 1 taxation
consumption
consumption
preferences
after-tax budget
tax-free budget (45 line)
tax-free budget
earnings
labor
full time
22
Application 1 taxation
consumption
consumption
preferences
after-tax budget
after-tax budget
tax-free budget (45 line)
tax-free budget
earnings
labor
full wage
full time
23
Application 1 taxation
consumption
consumption
45
labor
earnings
full wage
full time
24
Application 1 taxation
consumption
consumption
45
labor
earnings
full wage
full time
25
Application 1 taxation
  • Utilitarian solutionsassuming no correlation
    between wage and utility functions, there is
    domination of wage classes? only one
    solutionmaximize average utility of lowest
    skilled individuals? ??? for non-linear income
    tax

26
Application 1 taxation
  • Egalitarian Equivalence several possibilities
  • They all evaluate individual situations by
    choices in certain budget sets that would give
    the same satisfaction

27
Application 1 taxation
Maximin criterion on the equivalent budget
consumption
Min wage rate
labor
full time
28
Application 1 taxation
Maximin criterion on the equivalent budget
consumption
  • Justification
  • compensation (does not depend on ones wage)
  • respects interpersonal comparisons for same
    preferences
  • liberal reward (equal budget as the ideal
    situation)
  • participation (?lowest wage rate)

Min wage rate
labor
full time
29
Application 1 taxation
consumption
consumption
preferences
after-tax budget
after-tax budget
tax-free budget (45 line)
tax-free budget
earnings
labor
full wage
full time
30
Application 1 taxation
31
Application 1 taxation
  • Optimal tax zero marginal tax for low incomes

consumption
after-tax budget
tax-free budget (45 line)
earnings
full wage
32
Application 1 taxation
  • Optimal tax zero marginal tax for low incomes

consumption
after-tax budget
tax-free budget (45 line)
earnings
full wage
33
Application 2 inequality measurement
34
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

35
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

36
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

37
Application 2 inequality measurement
  • Agnostic approach
  • Stochastic dominance per C-class
  • Stochastic dominance per R-class

38
Application 2 inequality measurement
  • Two problems with stochastic dominance per
    C-class
  • Clash with compensation

39
Application 2 inequality measurement
  • Two problems with stochastic dominance per
    C-class
  • Self-contradiction if partial C

40
Conclusion
  • Dont forget
  • Compensation
  • Liberal reward

41
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

42
What should individuals be held responsible for?
  • This excludes
  • Equal opportunity for dire straits
  • Compensation for aspiration levels

43
The end
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