Welfare: Basics

1. Prerequisites Useful, but optional Consumption basics Welfare: Basics MICROECONOMICS Principles and Analysis Frank Cowell April 2010

2. Overview... Welfare: Basics Approaches to welfare Alternative ways of systematising social values The constitution Relaxing the assumptions

3. Stocktaking… • We now have a micro-model of the economy… • …that is complete • … and self contained. • We could treat it like a giant machine… • with many agents… • many commodities… • … that is as complex as we want to make it. • But how should this “machine” be run?

4. Introducing normative economics • We are moving from a discussion of how the economy works… • …to a consideration of how it “ought to” work. • For this reason we need some sort of explicit story of what social objectives should be... • We need a story of social welfare. 3 approaches

5. What is meant by “Welfare?” • Three separate approaches: • A constitutional form of arriving at a consensus ordering of possible states of society, based on individual views. • something like individual preference orderings? • A set of general principles as to how well-ordered societies are run • efficiency, justice, fairness... • A “social” system of values. • “What this country wants…”

6. Overview... Welfare: Basics Approaches to welfare A means for aggregating individual values The constitution Relaxing the assumptions

7. objective 2 objective 1 Social objectives • Two dimensions of social objectives • Set of feasible social states • A social preference map? < • Assume we know the set of all social states • How can we draw a social preference map? • Can it be related to individual preferences? Q

8. Idea of a constitution • Is there such a thing as “society”? • Presumably the views of society should relate to the views of the citizens. • But can this relationship always be set up in a coherent fashion? • If so, then we can use the “constitution” as a device for aggregating individual views.

9. Elements of a constitution • Social states q Î Q • can incorporate all sorts of information: • economic allocations, • political rights, etc • Individual (extended) preferences over Q. • q<hq'means that person h thinks state q is at least as good as state q'. • An aggregation rule for the preferences so as to underpin the constitution. • A function defined on individual (extended) preferences

10. The social ordering and the constitution • Where does this ordering come from? • Presumably from individuals' orderings over Q. • Assumes that social values are individualistic. • Define a profile of preferences as • a list of orderings, one for each member of society • (<a,<b,<c, ...) • The constitution is an aggregation function S • Defined on a set of profiles. • Yields an ordering <. • So the social ordering is < = S (<a,<b,<c, ...)

11. Some basic questions... • Can we find reasonable axioms to impose on the aggregation rule S ? • who is to say what is “reasonable” here? • usual way is to adopt a minimalist approach • Will the results of aggregation be a transitive relation? • will it work like individual’s preference relations? • can we treat it as a true “social-welfare function”? • What is the effect of relaxing one or other assumption? • testing out our minimalist approach begin with the axioms

12. Axioms on the constitution • Universality • S should be defined for all profiles of preferences. • Pareto Unanimity • if all consider that q is better than q', then the social ordering should rank q as better than q'. • Independence of Irrelevant Alternatives • if two profiles are identical over a subset of Q then the derived social orderings should also be identical over this subset. • Non-Dictatorship • no one person alone can determine the social ordering More on IIA

13. Q Focus on IIA • The set of all social states • A subset of Q • Profile 1 ranking of states • Profile 2 ranking of states Q0 Q • The two profiles differ over Q \ Q0 • But they are the same over Q0. • So should they each lead to the same social ordering over Q0 ? • This is the IIA requirement on S

14. Arrow’s result • Universality • Pareto Unanimity • Independence of Irrelevant Alternatives • Non-Dictatorship • Theorem: There is no constitution satisfying these axioms

15. Arrow's result: restated • Don’t dismiss this result as trivial • If we restate it in an equivalent form, we can see its power: • “If you want the constitution to produce a coherent social ordering and to… • …work for all types of preferences • …satisfy Pareto Unanimity • …satisfy Independence of Irrelevant Alternatives • … then you must have one member of society act as a dictator.” • Is there a way of avoiding this depressing conclusion?

16. Overview... Welfare: Basics Approaches to welfare Ways out of the Arrow impasse? The constitution Relaxing the assumptions

17. Is it worth modifying the axioms? • Could we get an individualistic, transitive social order by relaxing one or other of these? • Universality • Pareto Unanimity • Independence of Irrelevant Alternatives • Non-Dictatorship Perhaps No Perhaps ? • See what happens if we relax universality

18. Relaxing universality • Could it be that the universal domain criterion is just too demanding? • Should we insist on coping with any and every set of preferences, no matter how bizarre? • Perhaps imposing restrictions on admissible preferences might avoid the Arrow impossibility result. • However, we run into trouble even with very simple versions of social states 1-dimensional example

19. Alf, Bill, Charlie and the Bomb • 1-dimensional social states • Scaling of axes is arbitrary • Three possible states preference Charlie • Views about defence spending   • Each individual has dramatically different views. • But all three sets of preferences are “single peaked”    Bill    Alf defence spending  q" q q'

20. The original views • Consider the outcome of simple voting • So social preferences are unambiguous: q' is better than q which is better than q" Alf Bill Charlie Verdict    Yes   No    Yes q' better than q ? q" better than q' ? q better than q" ?

21. Charlie      Bill    Alf  q" q q' Alf, Bill, Charlie and the Bomb (2) • Same states as before • Same preferences as before Bill • Bill changes his mind preference    defence spending

22. The modified views • Again consider the outcome of simple voting • So q is better than q" which is better than q' which is better than q …? Alf Bill Charlie Verdict    Yes    Yes    Yes q' better than q ? q" better than q' ? q better than q" ?

23. Is it worth modifying the axioms? • Could we get an individualistic, transitive social order by relaxing one or other of these? • Universality • Pareto Unanimity • Independence of Irrelevant Alternatives • Non-Dictatorship • See what happens if we relax IIA

24. Alternative voting systems... • Relaxing IIA involves an approach that modifies the type of “aggregation rule.” • Simple majority voting may (perhaps) make too little use of information about individual orderings or preferences. • Here are some alternatives: • de Borda (weighted voting) • Single transferable vote • Elimination voting • None of these is intrinsically ideal • Consider the results produced by third example But do these give sensible results...?

25. The IOC Decision Process 1997 • An elimination process • Appears to give an orderly convergence. • Athens is preferred to Rome irrespective of the presence of other alternatives. But... Round 1 2 3 4 Athens 32 38 52 66 Rome 23 28 35 41 Stockholm 20 19 20 - Cape Town 16 22 - - Buenos Aires 16 - - -

26. The IOC Decision Process 1993 • Again an elimination process • Ordering of Sydney and Peking depends on whether other alternatives are present. • Violates IIA Round 1 2 3 4 Sydney 30 30 37 45 Peking 32 37 40 43 Manchester 11 13 11 - Berlin 9 9 - - Istanbul 7 - - - 30 45 32 43

27. The constitution: assessment • The constitution is a general approach to the welfare-economics problem. • Focuses on a method of aggregating individual orderings (not utility levels) • At first sight Arrow result may appear amazing or depressingly realistic. • Clearly some progress is possible by relaxing one or other of the axioms – particularly IIA. • Its main contribution is to point up the limitations of a general approach to social decision making.