1. Overview Aggregating preferences The Social Welfare function The Pareto Criterion The Compensation Principle

2. Overview Whose preferences are going to prevail??? Should we judge others’ preferences? the economist approach consists of trying to elicit everyone’s preferences and aggregating them Then policies are directed at the objective calculated in that manner this is easier to say than to do!

3. Aggregating preferences finding a mechanism to aggregate the preferences of different individuals Economics of Social Choice handles that problem We want the Social welfare function, starting from the individual utility functions of each agent Remember: we do not question those!

4. Aggregating preferences individual utility functions might also include altruism That altruism might be concerned with future generations too …or with other non-human species but we look at how these concerns are embodied in the individual utility functions

5. The Social Welfare Function social welfare function links certain allocation of resources to the social utility (welfare) derived by society from it If we had one social welfare function, we would be able to compare two allocations and choose the best one! But how are we going to construct that social welfare function starting from individual preferences???

6. Social Choice Mechanisms We need some mechanism to add up the different preferences or utility functions One way to aggregate preferences, to arrive at a social decision is to use the Pareto criterion

7. The Pareto Criterion If all individuals in a society prefer (or are indifferent about) an allocation and at least one of them strictly prefers that allocation, society should prefer that allocation

8. The Pareto Criterion If all individuals in a society prefer (or are indifferent about) an allocation and at least one of them strictly prefers that allocation, society should prefer that allocation => for an allocation A to be considered socially preferable to another allocation B, everyone needs to be at least as well-off under A

9. The Pareto Criterion This mechanism amounts to using a unanimous voting rule If we all agree or are indifferent then we approve the motion!

10. The Pareto Criterion Anna’s utility Brewster’s utility Consider this curve showing the possible utility combinations for two members of this society:

11. The Pareto Criterion Anna’s utility Brewster’s utility Consider some of these utility combinations: Z Y X S R W Go to hidden slide

12. The Pareto Criterion Anna’s utility Brewster’s utility Let us compare W and Z. Z is clearly Pareto preferred to W, right? Z Y X S R W Both Anna and Brewster will agree on a move from W to Z

13. The Pareto Criterion Anna’s utility Brewster’s utility Similarly, Y is clearly Pareto preferred to X Z Y X S R W

14. The Pareto Criterion Anna’s utility Brewster’s utility Let us compare now X and Z. What does the Pareto rule say? Z Y X S R W

15. The Pareto Criterion Anna’s utility Brewster’s utility Let us compare now X and Z. What does the Pareto rule say? Z Y X S R W The Pareto rule cannot compare X and Z, nor B and Z B

16. The Pareto Criterion Anna’s utility Brewster’s utility Let us compare now X and Z. What does the Pareto rule say? Z Y X S R W The Pareto rule cannot compare X and Z, nor B and Z B...because they involve movements whereby one agent gains and the other loses!

17. The Pareto Criterion A weakness of the Pareto criterion is that it is not complete: It is not useful for certain types of comparisons It is also biased towards the status quo, so it is not very operative

18. Potential Pareto Improvement Rule Anna’s utility Brewster’s utility Let us allow transfers (side-payments) between individuals now. Compare X and Z again... Z Y X S R W Go to hidden slide

19. Potential Pareto Improvement Rule Anna’s utility Brewster’s utility Now Z > X because, although Anna loses (red arrow) with Z to allow Brewster to gain, Brewster gains so much (blue arrow) that he could compensate Anna to leave her as well-off as with X and he would still be as better-off Z X

20. Potential Pareto Improvement Rule Anna’s utility Brewster’s utility Now Z >X because, although Anna loses (red arrow) with Z to allow Brewster to gain, Brewster gains so much (blue arrow) that he could compensate Anna to leave her as well-off as with X and he would still be as better-off Z X Scope for bargaining

21. The Compensation Principle Anna’s utility Brewster’s utility Now Z >X because, although Anna loses (red arrow) with Z to allow Brewster to gain, Brewster gains so much (blue arrow) that he could compensate Anna to leave her as well-off as with X and he would still be as better-off Z X There is scope for a mutually agreeable transfer of money that would help us achieve unanimity

22. The Compensation Principle Anna’s utility Brewster’s utility The problem is that it is not always feasible or desirable to make those transfers Z X Kaldor-Hicks compensation principle: as long as the compensation would result in unanimous agreement on a move, we should go ahead with the move, even if the compensation is not actually given!!

23. The Compensation Principle It is not always feasible or desirable to make transfers But the problem with transfers is merely one of equity in a sense, it can be separated from efficiency However, this idea has met with quite a lot of controversy

24. The Compensation Principle Consider the issue of Scitovsky’s paradox

25. Voting But voting rules could not require unanimity Majority can be enough majority voting has its problems too In fact it will only work fine if we restrict ourselves to one type of preferences: single- peaked preferences about unidimensional issues Voting on those will make the median voter the winner of the election!

26. Voting Majority voting fails to allow for the expression of the intensity of preferences, so it can easily yield inefficient results!

27. Socially desirable decision- making system should satisfy –social preferences should be complete and transitive, as are individual preferences –if everyone prefers Allocation a to Allocation b, then a should be socially preferred to b –society's ranking of a and b should depend only on individuals' ordering of these two allocations (not on how they rank other alternatives) independence of irrelevant alternatives dictatorship not allowed: social preferences must not reflect preferences of only a single individual

28. Arrow’s impossibility Theorem Arrow’s impossibility theorem, or Arrow’s paradox demonstrates the impossibility of designing a set of rules for social decision making that would obey every ‘reasonable’ criterion required by society

29. Arrow’s impossibility Theorem A society needs to agree on a preference order among several different options. Each individual in the society has a particular personal preference order. The problem is to find a social choice function, which transforms the set of preference orders, one for each individual, into a global societal preference order. It should have several desirable properties

30. Arrow’s impossibility Theorem unrestricted domain or universality: the social choice function should be complete (be able to rank every possible set of transitive individual preference orders) non-imposition or citizen sovereignty: every possible societal preference order should be achievable by some set of individual preference orders. non-dictatorship: the social choice function should not simply follow someone’s preferences while ignoring all others.

31. Arrow’s impossibility Theorem unanimity or Pareto efficiency: if every individual prefers a certain option to another, then so must the resulting societal preference order. independence of irrelevant alternatives: if we restrict attention to a subset of options, and apply the social choice function only to those, then the result should be compatible with the outcome for the whole set of options. (Changes in individuals’ rankings of “irrelevant” alternatives [i.e., ones outside the subset] should have no impact on the societal ranking of the “relevant” subset.)

32. Arrow’s impossibility Theorem Arrow’s theorem says that if the decision- making body has at least two members and at least three options to decide among, then it is impossible to design a social choice function that satisfies all these conditions at once and respects transitivity too.

33. In Economics We use the notion of willingness to pay to aggregate individual preferences But in order to do that and guarantee transitivity, we need some restrictions

34. In Economics We use the notion of willingness to pay to aggregate indiviudal preferences We restrict the domain to preferences that can be represented by utility functions No big deal

35. In Economics We assume that the individual utility functions can be aggregated with the sum of individual incomes being one of the arguments in the aggregate utility function  everyone`s demand for each good must increase linearly with their income and at the same rate!

36. In Economics We assume that all individuals face the same set of prices in competitive markets  if the policy in question allocates goods to individuals who cannot resell them in markets

37. Key terms Preferences altruism Social Choice Social Welfare Function Single-peaked preferences Arrow’s Impossibility Theorem unanimity