Social Choice
Session 5
Carmen Pasca and Mattia de’ Grassi di Pianura
Chance vs Choice
eliciting preferences over fairness trade-offs
John Bonea, John Heya and Carmen Pascab
University of York, UK
bLUISS Guido Carli, Italy
a
We thank the Super Pump Priming fund of DERS for funds to
finance this research.
The general context of our
research
• This research was inspired by the current
social and political context.
• The return of social issues: social and
fiscal reforms.
• The new approach of responsibility:
social and individual aspects.
• The treatment of inequalities.
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The Research Objective
• The research objective is to try to discover
social choice preferences by direct
questioning.
• The usual method is indirect (through, for
example, income distributions).
• The tricky thing is to provide appropriate
incentives.
• We think that we do.
• Let us start with Fleurbaey’s book.
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Fleurbaey
Earnings
No Work
Work
Bad Luck
£1
£3
Good Luck
£3
£9
Suppose we have £24 to distribute in dividends. One possibility is to be
Egalitarian:
Payments (Dividends)
No Work
Work
Bad Luck
£10 (dividend £9)
£10 (dividend £7)
Good Luck
£10 (dividend £7)
£10 (dividend £1)
We might not like this. It looks a bit communistic. It compensates for luck but
does not reward effort.
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Fleurbaey’s Natural Policy
Earnings
No Work
Work
Bad Luck
£1
£3
Good Luck
£3
£9
Again suppose we have £24 to distribute in dividends. Consider now what
Fleurbaey calls a Natural Policy:
Payments (Dividends)
No Work
Work
Bad Luck
£9 (dividend £8)
£11 (dividend £8)
Good Luck
£9 (dividend £6)
£11 (dividend £2)
This equalises the payments across luck states and gives more to those that
work. But this is not the only way to do this.
(Note by the way that dividends are equal in the two Bad Luck cells.)
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Fleurbaey’s Pro- and Anti- Work Policies
Earnings
No Work
Work
Bad Luck
£1
£3
Good Luck
£3
£9
Payments (Dividends)
No Work
Work
Bad Luck
£7 (dividend £6)
£13 (dividend £10)
Good Luck
£7 (dividend £4)
£13 (dividend £4)
Pro-Work
(Note that dividends are equal in the two Good Luck cells.)
Anti-Work
Payments (Dividends)
No Work
Work
Bad Luck
£11 (dividend £10)
£9 (dividend £6)
Good Luck
£11 (dividend £8)
£9 (dividend £0)
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Compensation and Reward
“Compensation for unequal circumstances
cannot be the only goal of social policy; it
must be supplemented by a reward principle
telling us whether and how redistribution
should be sensitive to responsibility
characteristics as well, and, eventually, how
final well-being should relate to responsibility
characteristics.” (Fleurbaey, Fairness,
Responsibility and Welfare, pp 21-22)
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Notation
(note: payments = earnings plus dividends/transfers)
Suppose we start with a set of earnings x:
Earnings
No Work
Work
Bad Luck
x1
x2
Good Luck
x3
x4
And we can choose dividends yi: s.t. y1 + y2 + y3 + y4 = Y.
Then we get (final) payments as below.
Payments
No Work
Work
Bad Luck
x1+y1
x2+y2
Good Luck
x3+y3
x4+y4
The question is: “how are dividends chosen?”
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We can impose various conditions
• In each case (Bad Luck, Good Luck, Not
Work, Work) we could think of imposing
one of the following:
• 1) No condition
• 2) Equality of Dividends
• 3) Equality of Payments
• (There are obviously other possibilities – these are the ones
Fleurbaey suggests.)
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My Preferences
• In the case of Bad Luck I prefer Equality of Dividends.
• In the case of Good Luck I prefer Equality of
Dividends.
• In the case of Not Work I prefer Equality of
Payments.
• In the case of Work I prefer Equality of Payments.
• Where do I get these from?
• Because I believe in No Envy – explained next….
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I arrive at these conditions by considering Fairness in Dividends,
defined as envy-freeness – or No Envy.
Given her (No Work/Work) decision, J would have no higher a payment
with K’s luck and dividend than she is with her own.
(and vice versa)
(J and K are any two individuals)
Implication 1
If J and K are in the same position, i.e. same decision and same luck, then
they have the same dividend.
Implication 2
If J and K have the same luck then, whatever their respective decisions,
they have the same dividend.
Implication 3
If J and K make the same decision then, whatever their respective luck,
they have the same total payment.
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Trouble? Mutually Inconsistent
Earnings
No Work
Work
Bad Luck
£4
£8
Good Luck
£6
£12
Suppose we have £24 to distribute in dividends, can we achieve these goals?
Payments
No Work
Work
Bad Luck
£4+£7=£11
£8+£7=£15
Good Luck
£6+£5=£11
£12+£5=£17
The answer is NO: we can achieve three of the four, but not all four. One has to
be dropped or some other compromise made. This is what the experiment
was designed to discover: what compromises do people make?
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Outline of experiment – part of instructions
The experiment is in two Parts.
Part 1 will last around 35 minutes (including these onscreen
instructions).
Further details of Part 1 will appear shortly.
[Part 1 asked them their conditions.]
Part 2 is a questionnaire which will take around 20 minutes to
complete. [Part 2 was a work task. Their decision on that and their
luck determined what cell they were in.]
Part 2 is optional. Towards the end of Part 1 you will be asked to decide
whether or not to stay for Part 2.
sequence of events in Part 1 – part of instructions
[1]
you express a preference on the procedure by which the dividends
are to be determined for your society
[2]
the preferences of one member of your society are selected at
random, to decide that procedure
[3]
you are informed of the procedure decided at Stage [2]
[4]
you are informed of the earnings values
[5]
you are informed whether your Luck is Bad or Good
[6]
you choose whether to Leave or Stay for Part 2
[7]
the dividend values for your society are determined, according to the
procedure decided at Stage [2]
[8]
you leave or stay for Part 2, as you chose at Stage [6]
Further Detail
• The earnings in Bad/Out and In/Good were £4
and £12. The earnings in the other two cells
were between these two amounts and were
decided and announced at the end.
• Total dividends were fixed at £40.
• Subjects did not know ex ante how many
people there would be in each cell.
• Rules must be applicable for any configuration
(since not known ex ante).
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The screen for exploring and selecting constraints looks like this.
The screen has three main areas.
The screen for exploring and selecting constraints looks like this.
The screen has three main areas.
This is the Instructions area.
Various messages will appear in it, at various times.
So keep an eye on it.
This is the Preferences area.
It shows the various possible
constraints on the dividends, and
allows you to select them.
Notice that you must make a
selection in each of the four
categories, even if only to select No
constraint.
Once you have made your
choices,
the Show implications button
becomes active.
Pressing this button gives you
access to …
the Implications area
Here you can explore the
implications of any set of
constraints, before confirming
your preferred constraints.
You can do this by simulating
the effect of those
constraints.
Using these buttons you can simulate different
positions for each of the four members of the
society
Note that Staying for Part 2 is here
abbreviated as In, while Leaving is
abbreviated as Out.
Using these sliders you can simulate different
earnings values for the two positions Bad/In
and Good/Out.
For example like this.
If instead you press the
Reselect button then the
computer will randomly reposition the four members and
change the earnings values.
Depending on your currently
chosen constraints …
… for any given set of positions
and earnings values there may be
many possible sets of dividends.
In that case, pressing the
ReRandomise button causes the
computer to randomly produce
another possible set of dividends.
Depending on your currently
chosen constraints …
… for any given set of positions
and earnings values there may be
no possible set of dividends.
In that case, you will be prompted
with an error message and asked
to either ReSelect …
… or to Revise your choices
of constraints
Indeed at any time you can revise
your current choice of constraints,
and so explore the implications of
different combinations of
constraints, before confirming your
preference.
You will have 20 minutes to do this, as indicated by Time
left clock at the bottom of the screen.
Please make full use of this time. It is in your interest, and
ours, that you have as full an understanding as possible of the
implications of these constraints, under various different
scenarios regarding earnings values and members’ positions
At the end of that time the button OK. All Done will become
active.
Then press this button to register your current choices as
your preferred constraints.
You will then see a screen like this.
It will take you quickly through the remaining stages of Part 1
At that point, Part 1 ends.
If you have chosen to stay for Part 2 you will then start Part 2, after
which you will be paid according to the screen that you saw towards
the end of Part 1.
If you have chosen not to stay for Part 2 you will be paid according to the
screen that you saw towards the end of Part 1, and then you will be free to
leave.
When we pay you, we will ask you to sign a receipt.
Thank you for your participation.
Results
•
•
•
•
•
Most frequent sets of conditions.
Interesting sets of conditions.
Summary of choices.
Choice between Equal Dividend and Equal Payment.
We also have detailed information on what the
subjects did during the 20 minute ‘exploration’ – we
have much still to still to analyse but we have made a
start by looking at the combinations of conditions
which the subjects tried/explored, and hence
whether there was interest in Fleurbaey’s conditions.
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Most frequent sets of conditions
Sequence
Treatment 1
(% of time)
Treatment 2
(% of time)
0000
9.2
9.5
1111
7.9
12.6
2222
10.5
15.8
Key to Sequence
wxyz
w with Bad Luck
x with Good Luck
y Not Work
z Work
0: no condition
1: equal dividends
2: equal payment
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Interesting sets of conditions
(because of departures from “Fleurbaey’s ideal”)
Sequence
(c.f. with ‘my
ideal’ 1122)
Treatment 1
Treatment 2
(number out of (number out of
76
95
observations)
observations)
0122
1
2
1022
1
0
1102
1
5
1120
3
0
Key to Sequence
wxyz
w with Bad Luck
x with Good Luck
y Not Work
z Work
0: no condition
1: equal dividends
2: equal payment
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Summary of choices
Choices
Treatment 1
Treatment 2
Number
%
Number
%
0 in Bad luck (first position)
28
36
40
42
1 in Bad luck (first position)
25
33
28
29
2 in Bad luck (first position)
23
30
27
28
0 in Good luck (second position)
35
46
36
38
1 in Good luck (second position)
27
35
34
36
2 in Good luck (second position)
14
18
25
26
26
25
25
33
19
24
304
34
33
34
43
25
32
29
28
38
26
28
41
380
31
29
40
27
29
43
0 in Out (third position)
1 in Out (third position)
2 in Out (third position)
0 in In (fourth position)
1 in In (fourth position)
2 in In (fourth position)
Totals
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Choice between Equal Dividend and Equal Payment
• In Bad Luck: Equal Dividend higher (31% (ED) and
29% (EP))
• In Good Luck: Equal Dividend higher (35% (ED)
and 22% (EP))
• In Not Work: Equal Payment higher (31% (ED) and
37% (EP))
• In Work: Equal Payment higher (27% (ED) and
38% (EP))
• Close to “Fleurbaey’s ideal”!
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Conditions tried
Treatment 1
Treatment 2
No
condition
Equal
Dividends
Equal
Payments
No
condition
Equal
Dividends
Equal
Payments
Bad Luck
627
464
470
1044
562
531
Good
Luck
642
530
389
1068
553
516
No Work
567
473
521
913
549
675
Work
548
493
520
898
579
660
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Conclusions
• There is some evidence of No Envy.
• John Bone thinks that the design could and should be
simplified:
• …subjects should be asked to indicate a 1 or a 2 for
just 3 of the categories.
• … and we are also planning to introduce a third
dimension – skill…
• … and analyse them first in pairs.
• Your comments are invited!
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