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Prerequisites Useful, but optional Consumption basics Frank Cowell: Microeconomics April 2010 Welfare: Basics MICROECONOMICS Principles and Analysis Frank Cowell Overview... Welfare: Basics Frank Cowell: Microeconomics Approaches to welfare Alternative ways of systematising social values The constitution Relaxing the assumptions Stocktaking… Frank Cowell: Microeconomics We now have a micro-model of the economy… We could treat it like a giant machine… …that is complete … and self contained. with many agents… many commodities… … that is as complex as we want to make it. But how should this “machine” be run? Introducing normative economics Frank Cowell: Microeconomics 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 What is meant by “Welfare?” Frank Cowell: Microeconomics 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…” Overview... Welfare: Basics Frank Cowell: Microeconomics Approaches to welfare A means for aggregating individual values The constitution Relaxing the assumptions Social objectives Frank Cowell: Microeconomics 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? Q Can it be related to individual preferences? objective 1 Idea of a constitution Frank Cowell: Microeconomics 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. Elements of a constitution Frank Cowell: Microeconomics Social states Q Individual (extended) preferences over Q. can incorporate all sorts of information: economic allocations, political rights, etc <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 Frank Cowell: Microeconomics The social ordering and the constitution Where does this ordering come from? Presumably from individuals' orderings over Q. 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 Assumes that social values are individualistic. Defined on a set of profiles. Yields an ordering <. So the social ordering is < = S(<a, <b, <c, ...) Some basic questions... Frank Cowell: Microeconomics Can we find reasonable axioms to impose on the aggregation rule S ? Will the results of aggregation be a transitive relation? who is to say what is “reasonable” here? usual way is to adopt a minimalist approach 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 begin with the assumption? axioms testing out our minimalist approach Axioms on the constitution Frank Cowell: Microeconomics Universality Pareto Unanimity if all consider that is better than ', then the social ordering should rank as better than '. Independence of Irrelevant Alternatives S should be defined for all profiles of preferences. 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 Focus on IIA Frank Cowell: Microeconomics The set of all social states A subset of Q Profile 1 ranking of states Q0 Q Profile 2 ranking of states 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 Arrow’s result Frank Cowell: Microeconomics Universality Pareto Unanimity Independence of Irrelevant Alternatives Non-Dictatorship Theorem: There is no constitution satisfying these axioms Arrow's result: restated Frank Cowell: Microeconomics 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? Overview... Welfare: Basics Frank Cowell: Microeconomics Approaches to welfare Ways out of the Arrow impasse? The constitution Relaxing the assumptions Is it worth modifying the axioms? Frank Cowell: Microeconomics Could we get an individualistic, transitive social order by relaxing one or other of these? Perhaps Universality No Pareto Unanimity Perhaps Independence of Irrelevant Alternatives ? Non-Dictatorship See what happens if we relax universality Relaxing universality Frank Cowell: Microeconomics 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 Alf, Bill, Charlie and the Bomb Scaling of axes is arbitrary preference Frank Cowell: Microeconomics 1-dimensional social states Three possible states Charlie Views about defence spending Each individual has dramatically different views. Alf ' " Bill defence spending But all three sets of preferences are “single peaked” The original views Frank Cowell: Microeconomics Consider the outcome of simple voting So social preferences are unambiguous: ' is better than which is better than " Alf ' better than ? Bill Charlie Verdict Yes " better than ' ? No better than " ? Yes Alf, Bill, Charlie and the Bomb (2) Same preferences as before preference Frank Cowell: Microeconomics Same states as before Bill Bill changes his mind Charlie Alf ' " Bill defence spending The modified views Frank Cowell: Microeconomics Again consider the outcome of simple voting So is better than " which is better than ' which is better than …? Alf ' better than ? Bill Charlie Verdict Yes " better than ' ? Yes better than " ? Yes Is it worth modifying the axioms? Frank Cowell: Microeconomics 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 Alternative voting systems... Frank Cowell: Microeconomics 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 But do these give sensible results...? None of these is intrinsically ideal Consider the results produced by third example The IOC Decision Process 1997 Frank Cowell: Microeconomics An elimination process Appears to give an orderly convergence. Athens is preferred to Rome irrespective of the presence of other alternatives. But... Round 1 Athens 32 Rome 23 Stockholm 20 Cape Town 16 Buenos Aires 16 2 3 4 38 28 19 22 - 52 35 20 - 66 41 - The IOC Decision Process 1993 Frank Cowell: Microeconomics Again an elimination process Ordering of Sydney and Peking depends on whether other alternatives are present. Violates IIA Round 1 2 3 4 Sydney Peking Manchester Berlin Istanbul 30 32 11 9 7 30 37 13 9 - 37 40 11 - 45 43 - The constitution: assessment Frank Cowell: Microeconomics 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.