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

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

Frank Cowell: Microeconomics Stocktaking… We now have a micro-model of the economy… We now have a micro-model of the economy…  …that is complete  … and self contained. We could treat it like a giant machine… 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? But how should this “machine” be run?

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

Frank Cowell: Microeconomics What is meant by “Welfare?” Three separate approaches: 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 A “social” system of values.  “What this country wants…”

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

Frank Cowell: Microeconomics 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?

Frank Cowell: Microeconomics Idea of a constitution Is there such a thing as “society”? Is there such a thing as “society”? Presumably the views of society should relate to the views of the citizens. 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? 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. If so, then we can use the “constitution” as a device for aggregating individual views.

Frank Cowell: Microeconomics Elements of a constitution Social states  Social states   can incorporate all sorts of information:  economic allocations,  political rights, etc Individual (extended) preferences over . Individual (extended) preferences over .   < h  'means that person h thinks state  is at least as good as state  '.   < 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. 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? Where does this ordering come from? Presumably from individuals' orderings over . Presumably from individuals' orderings over .  Assumes that social values are individualistic. Define a profile of preferences as 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  The constitution is an aggregation function   Defined on a set of profiles.  Yields an ordering.  Yields an ordering <. So the social ordering is =  (,,,...) So the social ordering is < =  ( < a, < b, < c,...)

Frank Cowell: Microeconomics Some basic questions... Can we find reasonable axioms to impose on the aggregation rule  ? 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 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? What is the effect of relaxing one or other assumption?  testing out our minimalist approach begin with the axioms

Frank Cowell: Microeconomics Axioms on the constitution Universality Universality   should be defined for all profiles of preferences. Pareto Unanimity Pareto Unanimity  if all consider that  is better than  ', then the social ordering should rank  as better than  '. Independence of Irrelevant Alternatives 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 Non-Dictatorship  no one person alone can determine the social ordering More on IIA

Frank Cowell: Microeconomics 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   

Frank Cowell: Microeconomics Arrow’s result Universality Universality Pareto Unanimity Pareto Unanimity Independence of Irrelevant Alternatives Independence of Irrelevant Alternatives Non-Dictatorship Non-Dictatorship Theorem: Theorem: There is no constitution satisfying these axioms

Frank Cowell: Microeconomics Arrow's result: restated Don’t dismiss this result as trivial Don’t dismiss this result as trivial If we restate it in an equivalent form, we can see its power: 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… “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.” … then you must have one member of society act as a dictator.” Is there a way of avoiding this depressing conclusion? Is there a way of avoiding this depressing conclusion?

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

Frank Cowell: Microeconomics Is it worth modifying the axioms? Could we get an individualistic, transitive social order by relaxing one or other of these? 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 See what happens if we relax universality

Frank Cowell: Microeconomics Relaxing universality Could it be that the universal domain criterion is just too demanding? 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? 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. 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 However, we run into trouble even with very simple versions of social states 1-dimensional example

Frank Cowell: Microeconomics 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”

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

Frank Cowell: Microeconomics Alf, Bill, Charlie and the Bomb (2) preference defence spending Bill '' ""     Alf Charlie         Same states as before   Same preferences as before Bill      Bill changes his mind

Frank Cowell: Microeconomics The modified views   Yes     ' better than  ?  " better than  ' ?  better than  " ? Alf Bill Charlie Verdict Again consider the outcome of simple voting Again consider the outcome of simple voting So is better than " which is better than ' which is better than …? So  is better than  " which is better than  ' which is better than  …?

Frank Cowell: Microeconomics Is it worth modifying the axioms? Could we get an individualistic, transitive social order by relaxing one or other of these? 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 See what happens if we relax IIA

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

Frank Cowell: Microeconomics The IOC Decision Process 1997 An elimination process An elimination process Appears to give an orderly convergence. Appears to give an orderly convergence. Athens is preferred to Rome irrespective of the presence of other alternatives. But... Athens is preferred to Rome irrespective of the presence of other alternatives. But... Round1234 Athens Rome Stockholm Cape Town Buenos Aires 16---

Frank Cowell: Microeconomics The IOC Decision Process 1993 Again an elimination process Again an elimination process Ordering of Sydney and Peking depends on whether other alternatives are present. Ordering of Sydney and Peking depends on whether other alternatives are present. Violates IIA Violates IIA Round Sydney Peking Manchester Berlin Istanbul

Frank Cowell: Microeconomics The constitution: assessment The constitution is a general approach to the welfare-economics problem. The constitution is a general approach to the welfare-economics problem. Focuses on a method of aggregating individual orderings (not utility levels) Focuses on a method of aggregating individual orderings (not utility levels) At first sight Arrow result may appear amazing or depressingly realistic. 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. 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. Its main contribution is to point up the limitations of a general approach to social decision making.