Social Choice Session 5 Carmen Pasca and Mattia de’ Grassi di Pianura

Social ChoiceSession 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

aUniversity of York, UKbLUISS Guido Carli, Italy

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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FleurbaeyEarnings No Work Work

Bad Luck £1 £3

Good Luck £3 £9

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Payments (Dividends) No Work Work

Bad Luck £10 (dividend £9) £10 (dividend £7)

Good Luck £10 (dividend £7) £10 (dividend £1)

Suppose we have £24 to distribute in dividends. One possibility is to be Egalitarian:

We might not like this. It looks a bit communistic. It compensates for luck but does not reward effort.

Fleurbaey’s Natural PolicyEarnings No Work Work

Bad Luck £1 £3

Good Luck £3 £9

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Again suppose we have £24 to distribute in dividends. Consider now what Fleurbaey calls a Natural Policy:

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.)

Fleurbaey’s Pro- and Anti- Work Policies

Earnings No Work Work

Bad Luck £1 £3

Good Luck £3 £9

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(Note that dividends are equal in the two Good Luck cells.)

Pro-Work

Anti-Work

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:

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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?”

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.

Implication 1If 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.

(and vice versa)

Implication 3

If J and K make the same decision then, whatever their respective luck, they have the same total payment.

(J and K are any two individuals)

Trouble? Mutually Inconsistent

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Bad Luck £4 £8

Good Luck £6 £12

Payments No Work Work

Bad Luck £4+£7=£11 £8+£7=£15

Good Luck £6+£5=£11 £12+£5=£17

Suppose we have £24 to distribute in dividends, can we achieve these goals?

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?

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.

Outline of experiment – part of instructions

sequence of events in Part 1 – part of instructions

you express a preference on the procedure by which the dividends are to be determined for your society

[1]

you are informed of the procedure decided at Stage [2] [3]

you are informed of the earnings values[4]

you choose whether to Leave or Stay for Part 2 [6]

the dividend values for your society are determined, according to the procedure decided at Stage [2]

[7]

you leave or stay for Part 2, as you chose at Stage [6] [8]

[2] the preferences of one member of your society are selected at random, to decide that procedure

you are informed whether your Luck is Bad or Good [5]

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.

Note that Staying for Part 2 is here abbreviated as In, while Leaving is abbreviated as Out.

Using these buttons you can simulate different positions for each of the four members of the society

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 re-position the four members and change the earnings values.

Depending on your currently chosen constraints …

In that case, pressing the ReRandomise button causes the computer to randomly produce another possible set of dividends.

… for any given set of positions and earnings values there may be many possible sets of dividends.

Depending on your currently chosen constraints …

In that case, you will be prompted with an error message and asked to either ReSelect …

… for any given set of positions and earnings values there may be no possible set of dividends.

… 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.

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.

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

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.

Thank you for your participation.

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.

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

Key to Sequence wxyz

w with Bad Luckx with Good Lucky Not Workz Work

0: no condition1: equal dividends2: equal payment

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Sequence Treatment 1 (% of time)

Treatment 2 (% of time)

0000 9.2 9.5

1111 7.9 12.6

2222 10.5 15.8

Interesting sets of conditions (because of departures from “Fleurbaey’s ideal”)

Key to Sequence wxyz

w with Bad Luckx with Good Lucky Not Workz Work

0: no condition1: equal dividends2: equal payment

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Sequence(c.f. with ‘my ideal’ 1122)

Treatment 1 (number out of

76 observations)

Treatment 2 (number out of

95 observations)

0122 1 2

1022 1 0

1102 1 5

1120 3 0

Summary of choices

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Choices Treatment 1 Treatment 2

Number % Number %0 in Bad luck (first position) 28 36 40 421 in Bad luck (first position) 25 33 28 292 in Bad luck (first position) 23 30 27 280 in Good luck (second position) 35 46 36 381 in Good luck (second position) 27 35 34 362 in Good luck (second position) 14 18 25 260 in Out (third position) 26 34 29 311 in Out (third position) 25 33 28 292 in Out (third position) 25 34 38 400 in In (fourth position) 33 43 26 271 in In (fourth position) 19 25 28 292 in In (fourth position) 24 32 41 43Totals 304 380

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”!35

Conditions triedTreatment 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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Documents

Social Choice Session 5 Carmen Pasca and Mattia de’ Grassi di Pianura