1. Social Choice Session 4 Carmen Pasca and John Hey

2. Preamble In sessions 2 and 3 we asked the question: is there some way we can aggregate individual preferences into social preferences. The answer was a resounding ‘NO’. So getting the State to work by aggregating preferences is not going to work. Let us try something else: can we specify general principles that the state should use for deciding things? Rather than talk about ‘things’ over which people might have preferences......we talk here about distributions of income over which the state must decide.

3. Plan for this session 1 In session 2 we started with preferences and asked if we could aggregate them into social preferences. Answer? NO. This session we are going to ask a different question: can we start with principles for choosing? We start with a very simple one-dimensional context: choosing income distributions, where each individual’s income is a random drawing from the distribution. We report on an experiment to see if there is agreement on principles determining distribution and redistribution. Then we make the problem two-dimensional – income is partly chosen and partly random. Which (re-)distributions should society chose... using which principles?

4. Plan for this session 2 We start with Amiel and Cowell’s book, Thinking about Inequality, Cambridge University Press, 1999. And report on an experiment seeing if there is agreement about principles of choosing between distributions (and redistributions) in one dimension. (45 minutes) We then take a break. (15 minutes) We then return and look at Fleurbaey’s book, Fairness, Responsibility and Welfare – where there are two dimensions. We propose some reasonable principles and show that they work in one context. (45 minutes) In a second break we ask you to apply them in another context. We then return and discuss what we find for the last 30 minutes.

5. The first part of this session is actually a published paper “On Choosing a Constitution (at least the part relating to the distribution of income)” by John Hey and Carmen Pasca Applied Economics Letters 2011. The paper can be found here.here

6. Outline This is a part of the published paper. For the purpose of the course of Social Choice it is an exercise in seeing which of various axioms used in the literature for choosing between distributions of income are acceptable. Each axiom has an implication also for re-distribution – taxation if you like. This is one of the main concerns of social choice. We will not look at all the paper but just the bits relevant to the course.

7. Introduction and Motivation Here we ask directly which principles people prefer for choosing between income distributions. Previous experiments have asked about preferences over distributions. Well-summarised in Amiel and Cowell, Thinking about Inequality, Cambridge University Press, 1999. In this experiment we ask subjects with which principles/axioms they are in agreement, and their responses are appropriately incentivated.

8. The Axioms 5 fundamental axioms and their “opposites”: Rawls. Dispersion. Transfer. Transfer in groups. Lorenz. In the following slides we are not going to detail the ‘opposites’ of the principles. Full details can be found in the published paper. Moreover we are not going to detail all the axioms.

9. Rawls “If the poorest in distribution 1 has a higher income than the poorest in distribution 2, then I prefer distribution 1.” This axiom is implementated lexicographically.

10. Dispersion “I prefer the distribution in which the dispersion of income is the smallest.” We measure dispersion with standard deviation.

11. The Transfer Principle. “I think that the distribution improves if we take away 1 euro from one individual and we give it to someone poorer.” The subjects were advised that this axiom could be invoked several times.

12. The Lorenz principle. “If the n poorest individuals in distribution 1 have a larger proportion of the total income than the n poorest in distribution 2, for all values of n between 1 and N then I prefer distribution 1.” (In the experiment N was 10.)

13. The Experiment (1) Two treatments (5 sessions of each): (1) 10 subjects, one of them chosen at random to be the Social Planner (who will be part of the society) and then the position of the 10 in society randomised. (2) 11 subjects, one of them chosen at random to be the Social Planner (who will NOT be part of the society) and then the position of the remaining 10 in society randomised. Three repetitions. Forced to spend at least 60 (30,20) seconds on each reply on Repetition 1 (2,3).

14. The Experiment (2) At the end of the experiment, one subject chosen at random to be the Social Planner and then the order of the subjects in society randomly chosen. The preferred distribution of the Social Planner, using his or her preferences to chose one from a randomly generated set of 100 distributions (all with the same mean), distributed to the 10 members of society.

15. Partecipante12345678910 Distribuzione 1 2568914172930 Distribuzione 2 03814 1720212330 Distribuzione 3 01711131921232728 Distribuzione 4 031214171820212223 Distribuzione 5 33910 2021 2429 Distribuzione 6 22571516 282930 Distribuzione 7 341114151617192526 Distribuzione 8 0681216 17212628 Distribuzione 9 227914 19262730 Distribuzione 10 0241318 192426 Distribuzione 11 051112151718202527 Distribuzione 12 048101118212427 Distribuzione 13 045912172426 27 Distribuzione 14 122111620 212730 Distribuzione 15 0291114 22242628 Distribuzione 16 25911121518222630 Distribuzione 17 11811 1821232630 Distribuzione 18 2377151619252630 Distribuzione 19 49101214 19212225 Distribuzione 20 7910 111314192829 Distribuzione 21 051112131719202627 Distribuzione 22 344141718 212229 Distribuzione 23 131115161819212224 Distribuzione 24 2444182123 2427 Distribuzione 25 0466131523252830 Esempi delle distribuzioni possibili

16. The Experiment (3) On each repetition, subjects were first asked to state which axioms they agreed with...... and then in which order they wanted them implemented. Conflicts were pointed out. If a unique distribution was not implied by the axioms they wanted implemented, they were asked to implement more. Subjects were told that if they had no axioms left to implement, the distribution would be chosen at random.

21. Results There was not a big difference between the two treatments. We note that there were subjects who agreed with several principles but did not try to implement them simultaneously. Many subjects agreed with a principle and its opposite (which is OK if implemented sequentially but not if implemented simultaneously). Perhaps subjects were confused about the implications of the principles? Or they deliberately wanted to implement them sequentially?

22. Agreement and Implementation (in percentage terms) AxiomTreatment 1Treatment 2 Agreed-toImplementedAgreed-toImplemented R 14.6 18.3 15.8 20.2 RR 11.8 9.6 11.2 7.9 D 9.5 19.1 12.1 26.4 RD 9.2 15.7 7.0 10.3 T 11.1 5.7 11.4 6.6 RT 2.4 0.9 3.1 1.7 GT 11.4 10.0 12.5 9.9 RGT 3.0 2.5 2.1 L 14.6 8.7 14.7 7.9 RL 12.4 9.1 9.7 7.0

23. Conclusion and questions for the break We have reported on an experiment designed to see which principles relating to the distribution and redistribution of income are agreed with. It is the axioms that are important for this course. Suppose society could choose any possible redistribution of a given total income, which would it choose? Obviously the answer depends on the principles it agrees with. Answer this question supposing that society agrees with (1) Rawls (2) Transfer (3) Reverse Rawls (4) Reverse Transfer (at home you might like to think about the other axioms and their reverses).

24. Fairness, Responsibility and Welfare Marc Fleurbaey, Oxford UP, 2008. We focus on social issues concerned with distribution and redistribution of income. We continue with the theme of whether we can agree on general principles determining distribution and redistribution. We will focus on two key dimensions – those of effort and luck. So income is determined by luck and effort. Following Fleurbaey’s initial treatment we will assume that these two are independent of each other.

25. Responsibility and Fairness So a person’s income is determined partly by his work but partly by his luck. This is a generalisation of what we did before. We assume that the first is determined solely by the individual and the latter solely by fate. To keep our discussion simple we assume that each of these takes just two values: the individual either works or does not; the individual has bad or good luck. We consider what the state ‘should’ do in terms of redistribution to ‘appropriately’ take into account these two features. We might agree that the state ‘should’ compensate for bad luck but should it do so equally for those who work and those who do not?

26. Income We suppose that individuals get income which depends on whether they work or not and also whether they have bad or good luck. Here is an example: In this context, Social Choice is about redistribution of the earnings. Should society redistribute and if so how? No WorkWork Bad luck14 Good luck36

27. Transfers We suppose that Social Choice here is about deciding some transfers (you can think of these as being taxes and subsidies). Further we suppose that people’s happiness depends upon their income after transfers. Let us suppose for convenience that the total transfers must be zero – so it is simple redistribution. What principles should be used in deciding on these transfers? One obvious principle in this context is no envy. In the next slide we define it and explore its implications.

28. No Envy We have assumed that people decide whether to work or not but then fate decides their income. NO ENVY here means that no-one envies anyone else given their decision whether to work or not. This implies the following: After-tax income is the same for all people who work. After-tax income is the same for all people who don’t work. Fleurbaey calls this Equal Well-Being for Equal Responsibility. The tax/subsidy is the same for all people with bad luck. The tax/subsidy is the same for all people with good luck. Fleurbaey calls this Equal Treatment for Equal Circumstances.

29. No envy here? Before-tax incomesNo WorkWork Bad luck14 Good luck36 TransfersNo WorkWork Bad luck+1 Good luck After-tax incomesNo WorkWork Bad luck25 Good luck25

30. Yippee! We seem to be able to have no envy here. Two questions: Is this the only way to do it with these before-tax incomes? Is it always possible? Consider the following: Why is this different? These are questions for the break. Before-tax incomesNo WorkWork Bad luck14 Good luck38

31. No envy in this second case? Before-tax incomesNo WorkWork Bad luck14 Good luck38 TransfersNo WorkWork Bad luck+1 Good luck After-tax incomesNo WorkWork Bad luck25 Good luck27

32. That does not work – does this? Before-tax incomesNo WorkWork Bad luck14 Good luck38 TransfersNo WorkWork Bad luck+2 Good luck-2 After-tax incomesNo WorkWork Bad luck36 Good luck16

33. What does? Before-tax incomesNo WorkWork Bad luck14 Good luck38 TransfersNo WorkWork Bad luck Good luck After-tax incomesNo WorkWork Bad luck Good luck

34. No Envy does not always work The reason is simply that luck has a different effect on income in the work and no-work states. The implication is that we have to weaken one of the two implications of No Envy, either Equal Well-Being for Equal Responsibility or Equal Treatment for Equal Circumstances. Which? This is a real pity as it seems we might have a principle to which everybody might agree. It gives more work to Social Choice theorists...... their work is never (can never be?) done.

35. Conclusions Once again we seem to have an impossibility result. Even if we agree on the general principle of No Envy, it is impossible to implement it everywhere......there is bound to be envy somewhere. Is this surprising? What do we do about it?