Overview

• Aggregating preferences

• The Social Welfare function

• The Pareto Criterion

• The Compensation Principle

Overview

• Whose preferences are going to prevail???• Should we judge others’ preferences?• the economist approach consists of trying to elicit

everyone’s preferences and aggregating them• Then policies are directed at the objective

calculated in that manner• this is easier to say than to do!

Aggregating preferences• finding a mechanism to aggregate the preferences

of different individuals• Economics of Social Choice handles that problem• We want the Social welfare function, starting

from the individual utility functions of each agent• Remember: we do not question those!

Aggregating preferences• individual utility functions might also include

altruism• That altruism might be concerned with future

generations too• …or with other non-human species• but we look at how these concerns are embodied

in the individual utility functions

The Social Welfare Function• social welfare function links certain allocation of

resources to the social utility (welfare) derived by society from it

• If we had one social welfare function, we would be able to compare two allocations and choose the best one!

• But how are we going to construct that social welfare function starting from individual preferences???

Social Choice Mechanisms• We need some mechanism to add up the different

preferences or utility functions• One way to aggregate preferences, to arrive at a

social decision is to use the Pareto criterion

The Pareto Criterion• If all individuals in a society prefer (or are

indifferent about) an allocation and at least one of them strictly prefers that allocation, society should prefer that allocation

The Pareto Criterion• If all individuals in a society prefer (or are

indifferent about) an allocation and at least one of them strictly prefers that allocation, society should prefer that allocation

• => for an allocation A to be considered socially preferable to another allocation B, everyone needs to be at least as well-off under A

The Pareto Criterion• This mechanism amounts to using a

unanimous voting rule

• If we all agree or are indifferent then we approve the motion!

The Pareto Criterion

Anna’s utility

Brewster’sutility

Consider this curve showing the possible utility combinations for two members of this society:

The Pareto Criterion

Anna’s utility

Brewster’sutility Consider some of these

utility combinations:

Z

Y

X S

RW

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The Pareto Criterion

A weakness of the Pareto criterion is that it is not complete:

•It is not useful for certain types of comparisons

•It is also biased towards the status quo, so it is not very operative

Potential Pareto Improvement Rule

Anna’s utility

Brewster’sutility Let us allow transfers (side-payments) between individuals now.

Compare X and Z again...

Z

Y

X S

RW

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The Compensation Principle

Anna’s utility

Brewster’sutility

The problem is that it is not always feasible or desirable to make those transfers

Z

X

Kaldor-Hicks compensation principle: as long as the compensation would result in unanimous agreement on a move, we should go ahead with the move, even if the compensation is not actually given!!

The Compensation Principle

• It is not always feasible or desirable to make

transfers

• But the problem with transfers is merely one of

equity in a sense, it can be separated from efficiency

• However, this idea has met with quite a lot of

controversy

The Compensation Principle

• Consider the issue of Scitovsky’s paradox

Voting

• But voting rules could not require unanimity• Majority can be enough• majority voting has its problems too• In fact it will only work fine if we restrict

ourselves to one type of preferences: single-peaked preferences about unidimensional issues

• Voting on those will make the median voter the winner of the election!

Voting

• Majority voting fails to allow for the expression of the intensity of preferences, so it can easily yield inefficient results!

Socially desirable decision-making system

• should satisfy– social preferences should be complete and transitive, as

are individual preferences– if everyone prefers Allocation a to Allocation b, then a

should be socially preferred to b – society's ranking of a and b should depend only on

individuals' ordering of these two allocations (not on how they rank other alternatives) independence of irrelevant alternatives

• dictatorship not allowed: social preferences must not reflect preferences of only a single individual

Arrow’s impossibility Theorem

• Arrow’s impossibility theorem, or Arrow’s paradox demonstrates the impossibility of designing a set of rules for social decision making that would obey every ‘reasonable’ criterion required by society

Arrow’s impossibility Theorem

• A society needs to agree on a preference order among several different options. Each individual in the society has a particular personal preference order.

• The problem is to find a social choice function, which transforms the set of preference orders, one for each individual, into a global societal preference order. It should have several desirable properties

Arrow’s impossibility Theorem• unrestricted domain or universality: the social

choice function should be complete (be able to rank every possible set of transitive individual preference orders)

• non-imposition or citizen sovereignty: every possible societal preference order should be achievable by some set of individual preference orders.

• non-dictatorship: the social choice function should not simply follow someone’s preferences while ignoring all others.

Arrow’s impossibility Theorem

• unanimity or Pareto efficiency: if every individual prefers a certain option to another, then so must the resulting societal preference order.

• independence of irrelevant alternatives: if we restrict attention to a subset of options, and apply the social choice function only to those, then the result should be compatible with the outcome for the whole set of options. (Changes in individuals’ rankings of “irrelevant” alternatives [i.e., ones outside the subset] should have no impact on the societal ranking of the “relevant” subset.)

Arrow’s impossibility Theorem

• Arrow’s theorem says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social choice function that satisfies all these conditions at once and respects transitivity too.

In Economics

• We use the notion of willingness to pay to aggregate individual preferences

• But in order to do that and guarantee transitivity, we need some restrictions

In Economics

• We use the notion of willingness to pay to aggregate indiviudal preferences

• We restrict the domain to preferences that can be represented by utility functions

• No big deal

In Economics

• We assume that the individual utility functions can be aggregated with the sum of individual incomes being one of the arguments in the aggregate utility function

everyone`s demand for each good must increase linearly with their income and at the same rate!

In Economics

• We assume that all individuals face the same set of prices

in competitive markets if the policy in question allocates goods

to individuals who cannot resell them in markets

Key terms

• Preferences• altruism• Social Choice• Social Welfare Function• Single-peaked preferences• Arrow’s Impossibility Theorem• unanimity