ELITISM AND STOCHASTIC DOMINANCE

Stephen BAZEN (GREQAM, Université d’Aix-Marseille II)

Patrick MOYES (GREThA, Université de Bordeaux IV)

Presentation at the Tenth SSCW International Meeting, Moscow, 21-24 July 2010

Comparison of distributions

Risk : distribution of returns

Inequality: distribution of income (earnings, wealth,…)

In general, emphasis on progressive transfers

Elitism

8,5,4,1x

7,5,4,2z

x is obtained from z by a regressive transfer

8,5,4,1x

8,5,3,2 y

Progressive transfer

- Academic performance

- Affluence

Welfare function for distribution h(.): dxxhxuW

0

GF WW

Comparison of two distributions in terms of social welfare

dxxfxuWF

0

dxxgxuWG

0

00

dxxgxfxuWW GF

Stochastic dominance

00

dxxgxfxuWW GF

0

'0

0

dxxGxFxuxGxFxu

Stochastic dominance – standard application

xxGxFdxxGxFxuxu

0if0'0'0

First order stochastic dominance

GF

x

WWxdttFtG 00

0",0' xuxu

Second order stochastic dominance

)(xG)(xF

x

dttGx

)(0

x

dttFx

)(0

First order stochastic dominance(F dominates G)

Second order stochastic dominance(F dominates G)

1

Elitism and stochastic dominance

dxxhxvW

0

Performance :

xh density of individuals’ publication scores

xv value function

Assumption 1 :

An additional publication increases performance 0' xv

)(1 xF

1

x

)(1 xG

xxGxFdxxgxfxvxvb

011if00'0

xxFxG 0)(or

Assumption 2 :

A regressive transfer of publication scores increases performance 0" xv

Convexity of the value function rather than concavity in the standard case

Criterion for ranking departments by performance :

xdttGdttF

dxxgxfxvxv

xv

b

x

b

x

b

11if

00"

0'

0

x

dttFb

x 1

dttGb

x 1

b

F

G

x~0

)max()max()( GxFxi

xExEii GF )(

If distribution F stochastically dominates G in terms of the survival function then

Assumption 3 :

A regressive transfer of publication scores of given size increases perfomance more at the higher end of the scale than at the lower end

0"' xv

Criterion for ranking departments by performance :

xdudttGdudttF

dxxgxfxvxv

xvxv

b

x

b

t

b

x

b

t

b

11(b) and

(a) if

00'"

0"0'

GF

0

Tilburg

EssexToulouse dominates all departments except

Louvain

dominate: LSEStockholm U. Nottingham

Second order stochastic dominance

UCLNo dominance over :Essex, Cantab, Erasmus

dominates: LSEStockholm U. Amsterdam

Stockholm School of Economics

dominates:

WarwickYorkMaastrichtAutonoma BarcelonaBonnLondon Business School

Amsterdam

dominates:

OxonStockholm School of Economics

dominates:

Free University of Amsterdam

Amsterdam

Nottingham

Tilburg and UCL

dominate:Nottingham

Louvain

dominates:

Free University of Amsterdam

Amsterdam

Does more affluence mean less poverty ?

Ranked by both criteria - an example

3,2,1y 5.3,5.1,5.1x

(i) Generalised Lorenz dominance :

5.0,5.0,5.0 yx

progressive transfer increment

(ii) Reverse Generalised Lorenz dominance :

5.0,5.0,5.0 yx

regressive transferincrement