An introduction to equality of opportunity

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An introduction to equality of opportunity

• Marc Fleurbaey

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Contents

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

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Introduction
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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

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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
• Dont 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 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

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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?

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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
• Liberal laisser-faire, no redistribution for R
• Utilitarian zero inequality aversion
• Desert (Arneson) reward the saints

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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)

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Theory four solutions

• Either give precedence to liberal
  rewardConditional Equalityequalize
• Or give precedence to compensationEgalitarian
  Equivalenceequalize in

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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 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

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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
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Application 1 taxation
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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)

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Application 1 taxation
consumption
preferences
tax-free budget (wage rate)
labor
full time
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Application 1 taxation
consumption
consumption
preferences
after-tax budget
tax-free budget (45 line)
tax-free budget
earnings
labor
full time
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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
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Application 1 taxation
consumption
consumption
45
labor
earnings
full wage
full time
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Application 1 taxation
consumption
consumption
45
labor
earnings
full wage
full time
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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

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

• Optimal tax zero marginal tax for low incomes

consumption
after-tax budget
tax-free budget (45 line)
earnings
full wage
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Application 1 taxation

• Optimal tax zero marginal tax for low incomes

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

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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

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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

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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
• Clash with compensation

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Application 2 inequality measurement

• Two problems with stochastic dominance per
  C-class
• Self-contradiction if partial C

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Conclusion

• Dont 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

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The end