Prerequisites
Useful, but optional
Consumption basics
WELFARE: BASICS
MICROECONOMICS
Principles and Analysis
Frank Cowell
July 2015
Frank Cowell: Welfare Basics
1
Overview
Welfare: Basics
Approaches to
welfare
Alternative ways of
systematising social
values
The
constitution
Relaxing the
assumptions
July 2015
Frank Cowell: Welfare Basics
2
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?
July 2015
Frank Cowell: Welfare Basics
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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
July 2015
Frank Cowell: Welfare Basics
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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…”
July 2015
Frank Cowell: Welfare Basics
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Overview
Welfare: Basics
Approaches to
welfare
A means for
aggregating
individual values
The
constitution
Relaxing the
assumptions
July 2015
Frank Cowell: Welfare Basics
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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?
Q
Can it be related to
individual preferences?
objective 1
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Frank Cowell: Welfare Basics
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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
July 2015
Frank Cowell: Welfare Basics
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Elements of a constitution
 Social states Q
• can incorporate all sorts of information:
• economic allocations,
• political rights, etc
 Individual (extended) preferences over Q
•  ≽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
July 2015
Frank Cowell: Welfare Basics
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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 ,…)
July 2015
Frank Cowell: Welfare Basics
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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
July 2015
Frank Cowell: Welfare Basics
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Axioms on the constitution
 Universality
• S 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 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
July 2015
Frank Cowell: Welfare Basics
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Focus on IIA
 The set of all social states
 A subset of Q
 Profile 1 ranking of states
Q0
 Profile 2 ranking of states
 The two profiles differ over Q \ Q0
Q
Q
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
July 2015
Frank Cowell: Welfare Basics
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Arrow’s result
 Universality
 Pareto Unanimity
 Independence of Irrelevant Alternatives
 Non-Dictatorship
 Theorem:
There is no constitution satisfying these axioms
July 2015
Frank Cowell: Welfare Basics
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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?
July 2015
Frank Cowell: Welfare Basics
15
Overview
Welfare: Basics
Approaches to
welfare
Ways out of the
Arrow impasse?
The
constitution
Relaxing the
assumptions
July 2015
Frank Cowell: Welfare Basics
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Is it worth modifying the axioms?
 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
July 2015
Frank Cowell: Welfare Basics
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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
July 2015
Frank Cowell: Welfare Basics
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Alf, Bill, Charlie and the Bomb
1-dimensional social states
preference
Scaling of axes is arbitrary
Three possible states
Views about defence spending
Charlie


 Each individual has
dramatically different views





Alf
 But all three sets of
preferences are “single peaked”



July 2015
'
Bill
defence
spending
"
Frank Cowell: Welfare Basics
19
The original views
 Consider the outcome of simple voting
 So social preferences are unambiguous: ' is
better than  which is better than "
Bill Charlie



Yes
" better than ' ? 


No
 better than " ? 


Yes
' better than ?
July 2015
Verdict
Alf
Frank Cowell: Welfare Basics
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Alf, Bill, Charlie and the Bomb (2)
 Same states as before
preference
 Same preferences as before
 But Bill changes his mind
Charlie




Alf



July 2015
Bill




'
Bill
defence
spending
"
Frank Cowell: Welfare Basics
21
The modified views
 Again consider the outcome of simple voting
 So  is better than " which is better than '
which is better than …?
Alf
' better than ?
July 2015
Bill Charlie
Verdict



Yes
" better than ' ? 


Yes
 better than " ?


Yes

Frank Cowell: Welfare Basics
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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
July 2015
Frank Cowell: Welfare Basics
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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
July 2015
Frank Cowell: Welfare Basics
But do these
give sensible
results…?
24
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
Athens
32
Rome
23
Stockholm 20
Cape Town 16
Buenos Aires 16
July 2015
2
3
4
38
28
19
22
-
52
35
20
-
66
41
-
Frank Cowell: Welfare Basics
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The IOC Decision Process 1993
 Again an elimination process
 Ordering of Sydney and Peking depends on whether
other alternatives are present
 Violates IIA
July 2015
Round
1
2
3
4
Sydney
Peking
Manchester
Berlin
Istanbul
30
32
11
9
7
30
37
13
9
-
37
40
11
-
45
43
-
Frank Cowell: Welfare Basics
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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
July 2015
Frank Cowell: Welfare Basics
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