1. Frank Cowell: Welfare Basics WELFARE: BASICS MICROECONOMICS Principles and Analysis Frank Cowell Useful, but optional Consumption basics Useful, but optional Consumption basics Prerequisites March 2012 1

2. Frank Cowell: Welfare Basics Overview… Approaches to welfare The constitution Relaxing the assumptions Welfare: Basics Alternative ways of systematising social values March 2012 2

3. Frank Cowell: Welfare Basics 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? March 2012 3

4. Frank Cowell: Welfare Basics 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 March 2012 4

5. Frank Cowell: Welfare Basics What is meant by “Welfare?”  Three separate approaches: 1. A constitutional form of arriving at a consensus ordering of possible states of society, based on individual views something like individual preference orderings? 2. A set of general principles as to how well-ordered societies are run efficiency, justice, fairness… 3. A “social” system of values “What this country wants…” March 2012 5

6. Frank Cowell: Welfare Basics Overview… Approaches to welfare The constitution Relaxing the assumptions Welfare: Basics A means for aggregating individual values March 2012 6

7. Frank Cowell: Welfare Basics Social objectives  Two dimensions of social objectives  objective 2 objective 1 < <  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? March 2012 7

8. Frank Cowell: Welfare Basics 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 March 2012 8

9. Frank Cowell: Welfare Basics Elements of a constitution  Social states  can incorporate all sorts of information: economic allocations, political rights, etc  Individual (extended) preferences over   < h  ' means that person h thinks state  is at least as good as state  '  An aggregation rule for the preferences so as to underpin the constitution A function defined on individual (extended) preferences March 2012 9

10. Frank Cowell: Welfare Basics The social ordering and the constitution  Where does this ordering come from?  Presumably from individuals' orderings over  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  Defined on a set of profiles Yields an ordering <  So the social ordering is < =  ( < a, < b, < c, …) March 2012 10

11. Frank Cowell: Welfare Basics Some basic questions…  Can we find reasonable axioms to impose on the aggregation rule  ? 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 March 2012 11

12. Frank Cowell: Welfare Basics Axioms on the constitution  Universality  should be defined for all profiles of preferences  Pareto Unanimity if all consider that  is better than  ', then the social ordering should rank  as better than  '  Independence of Irrelevant Alternatives if two profiles are identical over a subset of  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 March 2012 12

13. Frank Cowell: Welfare Basics Focus on IIA  The set of all social states  A subset of    Profile 1 ranking of states  Profile 2 ranking of states   The two profiles differ over  \    But they are the same over    So should they each lead to the same social ordering over   ?  This is the IIA requirement on    March 2012 13

14. Frank Cowell: Welfare Basics Arrow’s result  Universality  Pareto Unanimity  Independence of Irrelevant Alternatives  Non-Dictatorship  Theorem: There is no constitution satisfying these axioms March 2012 14

15. Frank Cowell: Welfare Basics 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? March 2012 15

16. Frank Cowell: Welfare Basics Overview… Approaches to welfare The constitution Relaxing the assumptions Welfare: Basics Ways out of the Arrow impasse? March 2012 16

17. Frank Cowell: Welfare Basics 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 ? ?  See what happens if we relax universality March 2012 17

18. Frank Cowell: Welfare Basics 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 March 2012 18

19. Frank Cowell: Welfare Basics Alf, Bill, Charlie and the Bomb '' "" preference defence spending Alf Bill Charlie            1-dimensional social states  Scaling of axes is arbitrary  Three possible states  Views about defence spending  Each individual has dramatically different views  But all three sets of preferences are “single peaked” March 2012 19

20. Frank Cowell: Welfare Basics The original views   Yes    No  Yes  ' better than  ?  " better than  ' ?  better than  " ? Alf Bill Charlie Verdict  Consider the outcome of simple voting  So social preferences are unambiguous:  ' is better than  which is better than  " March 2012 20

21. Frank Cowell: Welfare Basics  Bill   Alf, Bill, Charlie and the Bomb (2) preference defence spending Bill '' ""     Alf Charlie        Same states as before  Same preferences as before  But Bill changes his mind March 2012 21

22. Frank Cowell: Welfare Basics The modified views   Yes     ' better than  ?  " better than  ' ?  better than  " ? Alf Bill Charlie Verdict  Again consider the outcome of simple voting  So  is better than  " which is better than  ' which is better than  …? March 2012 22

23. Frank Cowell: Welfare Basics 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 March 2012 23

24. Frank Cowell: Welfare Basics 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…? March 2012 24

25. Frank Cowell: Welfare Basics 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… Round1234 Athens32385266 Rome23283541 Stockholm201920- Cape Town 1622-- Buenos Aires 16--- March 2012 25

26. Frank Cowell: Welfare Basics 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 3030 3745 Peking 32 374043 Manchester 11 1311- Berlin 9 9-- Istanbul 7 -- - 30 45 32 43 March 2012 26

27. Frank Cowell: Welfare Basics 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 March 2012 27