Title: An introduction to equality of opportunity
1An introduction to equality of opportunity
2Contents
- Introduction
- Theory four solutions
- Application 1 taxation
- Application 2 inequality measurement
3Introduction
4Introduction
- 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
5Introduction
- 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
6Introduction
- 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?
7Theory four solutions
8Theory four solutions
- A simple model
- U outcome (utility)
- T transfer
- C circumstances (not responsible)
- R responsibility characteristics (fixed)
- Three variants
- Additive
- Multiplicative
- General
9Theory 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?
10Theory 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
11Theory 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)
12Theory four solutions
- Either give precedence to liberal
rewardConditional Equalityequalize - Or give precedence to compensationEgalitarian
Equivalenceequalize in
13Theory 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
14Theory 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
15Theory 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
16Theory four solutions
- A problem with utilitarian reward
- U1(x) x U2(x) 2x (responsible)
- Liberal reward? x1 x2
- Utilitarian reward? give everything to 2
17Theory four solutions
18Application 1 taxation
19Application 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)
20Application 1 taxation
consumption
preferences
tax-free budget (wage rate)
labor
full time
21Application 1 taxation
consumption
consumption
preferences
after-tax budget
tax-free budget (45 line)
tax-free budget
earnings
labor
full time
22Application 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
23Application 1 taxation
consumption
consumption
45
labor
earnings
full wage
full time
24Application 1 taxation
consumption
consumption
45
labor
earnings
full wage
full time
25Application 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
26Application 1 taxation
- Egalitarian Equivalence several possibilities
- They all evaluate individual situations by
choices in certain budget sets that would give
the same satisfaction
27Application 1 taxation
Maximin criterion on the equivalent budget
consumption
Min wage rate
labor
full time
28Application 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
29Application 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
30Application 1 taxation
31Application 1 taxation
- Optimal tax zero marginal tax for low incomes
consumption
after-tax budget
tax-free budget (45 line)
earnings
full wage
32Application 1 taxation
- Optimal tax zero marginal tax for low incomes
consumption
after-tax budget
tax-free budget (45 line)
earnings
full wage
33Application 2 inequality measurement
34Application 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
35Application 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
36Application 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
37Application 2 inequality measurement
- Agnostic approach
- Stochastic dominance per C-class
- Stochastic dominance per R-class
38Application 2 inequality measurement
- Two problems with stochastic dominance per
C-class - Clash with compensation
39Application 2 inequality measurement
- Two problems with stochastic dominance per
C-class - Self-contradiction if partial C
40Conclusion
- Dont forget
- Compensation
- Liberal reward
41What 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
42What should individuals be held responsible for?
- This excludes
- Equal opportunity for dire straits
- Compensation for aspiration levels
43The end