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

2. Chance vs Choice eliciting preferences over fairness trade-offs John Bone a, John Hey a and Carmen Pasca b a University of York, UK b LUISS Guido Carli, Italy We thank the Super Pump Priming fund of DERS for funds to finance this research.

3. 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. 3

4. 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. 4

5. Fleurbaey EarningsNo WorkWork Bad Luck£1£3 Good Luck£3£9 5 Payments (Dividends)No WorkWork 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.

6. Fleurbaey’s Natural Policy EarningsNo WorkWork Bad Luck£1£3 Good Luck£3£9 6 Payments (Dividends)No WorkWork Bad Luck£9 (dividend £8)£11 (dividend £8) Good Luck£9 (dividend £6)£11 (dividend £2) 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.)

7. Fleurbaey’s Pro- and Anti- Work Policies EarningsNo WorkWork Bad Luck£1£3 Good Luck£3£9 7 Payments (Dividends)No WorkWork Bad Luck£7 (dividend £6)£13 (dividend £10) Good Luck£7 (dividend £4)£13 (dividend £4) Payments (Dividends)No WorkWork Bad Luck£11 (dividend £10) £9 (dividend £6) Good Luck£11 (dividend £8) £9 (dividend £0) (Note that dividends are equal in the two Good Luck cells.) Pro-Work Anti-Work

8. 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) 8

9. Notation (note: payments = earnings plus dividends/transfers) Suppose we start with a set of earnings x: 9 EarningsNo WorkWork Bad Luckx1x1 x2x2 Good Luckx3x3 x4x4 And we can choose dividends y i : s.t. y 1 + y 2 + y 3 + y 4 = Y. Then we get (final) payments as below. PaymentsNo WorkWork Bad Luckx 1 +y 1 x 2 +y 2 Good Luckx 3 +y 3 x 4 +y 4 The question is: “how are dividends chosen?”

10. 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.) 10

11. 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…. 11

12. 12 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 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. (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)

13. Trouble? Mutually Inconsistent 13 EarningsNo WorkWork Bad Luck£4£8 Good Luck£6£12 PaymentsNo WorkWork 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?

14. 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

15. 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]

16. 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). 16

17. The screen for exploring and selecting constraints looks like this. The screen has three main areas.

18. 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.

19. 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.

20. Once you have made your choices, the Show implications button becomes active. Pressing this button gives you access to …

21. 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.

22. 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

23. Using these sliders you can simulate different earnings values for the two positions Bad/In and Good/Out.

24. 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.

25. 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.

26. 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

27. 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.

28. 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

29. You will then see a screen like this. It will take you quickly through the remaining stages of Part 1

30. 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.

31. 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. 31

32. Most frequent sets of conditions 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 32 SequenceTreatment 1 (% of time) Treatment 2 (% of time) 00009.29.5 11117.912.6 222210.515.8

33. Interesting sets of conditions (because of departures from “Fleurbaey’s ideal”) 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 33 Sequence (c.f. with ‘my ideal’ 1122) Treatment 1 (number out of 76 observations) Treatment 2 (number out of 95 observations) 012212 102210 110215 112030

34. Summary of choices 34 ChoicesTreatment 1Treatment 2 Number% % 0 in Bad luck (first position) 28364042 1 in Bad luck (first position) 25332829 2 in Bad luck (first position) 23302728 0 in Good luck (second position) 35463638 1 in Good luck (second position) 27353436 2 in Good luck (second position) 14182526 0 in Out (third position) 26342931 1 in Out (third position) 25332829 2 in Out (third position) 25343840 0 in In (fourth position) 33432627 1 in In (fourth position) 19252829 2 in In (fourth position) 24324143 Totals 304380

35. 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

36. Conditions tried Treatment 1Treatment 2 No condition Equal Dividends Equal Payments No condition Equal Dividends Equal Payments Bad Luck6274644701044562531 Good Luck 6425303891068 553516 No Work567473521913549675 Work548493520898 579660 36

37. 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! 37