Transcript An introduction to equality of opportunity

An introduction to
equality of opportunity
Marc Fleurbaey
Contents
1.
2.
3.
4.
Introduction
Theory: four solutions
Application 1: taxation
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
Theory: four solutions
• A simple model:
– U : outcome (utility)
– T : transfer
– C : circumstances (not
responsible)
– R : responsibility
characteristics (fixed)
• Three variants:
– Additive
– Multiplicative
– General
U i  Ti  Ci  Ri
Ui  Ti  Ci Ri
Ui  f (Ti , Ci , Ri )
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 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?
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
Ui (Ri )  Ti (Ci )  Ci Ri
•
No clash if separability of (T,C):
Ui  f (h(Ti , Ci ), Ri )
U i  Ti  Ci  Ri
Theory: four solutions
• Either give precedence to liberal reward:
Conditional Equality:
equalize ~
~
Ui  f (Ti , Ci , R)
• Or give precedence to compensation:
Egalitarian Equivalence:
~
equalize Ti in
~ ~
Ui  f (Ti , C, Ri )
Theory: four solutions
• Utilitarian reward:
– Equal C  maximize sum of U
• Problem: clash with compensation
R
• No clash if C classes dominate each other
for all R
Theory: four solutions
• Utilitarian reward:
– Equal C  maximize sum of U
• Problem: clash with compensation
R
• No clash if C classes dominate each other
for all 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:
U1(x) = x U2(x) = 2x (responsible)
• Liberal reward
 x1 = x2
• Utilitarian reward
 give everything to 2
Theory: four solutions
Liberal
Utilitarian
Compensation
Egalitarian
Equivalence
Mean of Mins
Reward
Conditional
Equality
Min of Means
Application 1: taxation
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
consumption
preferences
labor
full time
Application 1: taxation
consumption
consumption
preferen
ces
labor
full time
earnings
Application 1: taxation
consumption
consumption
preferen
ces
earnings
labor
full time
full wage
Application 1: taxation
consumption
consumption
labor
full time
full wage
earnings
Application 1: taxation
consumption
consumption
labor
full time
full wage
earnings
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
Maximin criterion on the
“equivalent budget”
consumption
Min wage rate
labor
full time
Application 1: taxation
Maximin criterion on the
“equivalent budget”
consumption
Justification:
• compensation (does not
depend on one’s wage)
Min wage rate
• respects interpersonal
comparisons for same
preferences
• liberal reward (equal
budget as the ideal
situation)
labor
full time
• participation (lowest
wage rate)
Application 1: taxation
consumption
consumption
preferences
earnings
labor
full time
full wage
Application 1: taxation
Application 1: taxation
• Optimal tax: zero marginal tax for low
incomes
consumption
earnings
full wage
Application 1: taxation
• Optimal tax: zero marginal tax for low
incomes
consumption
earnings
full wage
Application 2: inequality
measurement
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
~
~
Ui  f (Ti , Ci , R)
• Lorenz dominance on conditional outcomes
– Egalitarian equivalence:
• inequality index on equivalent transfers
~ ~
Ui  f (Ti , C, Ri )
• 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 / poor
Rich untalented/
poor talented
Conclusion
• 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:
U1 ( x)  x 
 due to aspirations
U 2 ( x)  2 x 
Equal opportunity for utility : make 2 x accessible
to 1 w henever x is to 2.
Both 1 and 2 agree that 1 has a better life!
The end