This document discusses social choice and collective decision making. It begins by defining social choices as those made by governments that influence many people, such as economic and social policy decisions. It then discusses two approaches to understanding social choices - the public interest approach views individuals as subordinate to social organizations, while the self-interest approach sees individuals as acting to maximize their own utility. The document goes on to examine criteria for acceptable social choice rules, including rationality, independence, Pareto principles, unrestricted domain, and non-dictatorship. It analyzes majority voting rules and concludes they can produce intransitive outcomes, violating Arrow's criteria for social choice. Relaxing some assumptions, like restricting preferences to a single-peak pattern,

1. Social Choice

2. INTRODUCTION
� Government make decision that influence the lives of most people of the state economic decisions are
taken on particular policy variables.
� Social policy decisions are taken on who and who will not receive benefits of specific welfare
program.
� Decisions in the field of international relations establish the basis for future exchanges such as
economic and non-economic between the citizen of different nation states.
� Social choices (collective choices) are concern with relationship between individual member of the
state or society and the collective choices made by government.

3. � For example, in liberal democracy people elect representatives through voting to represent their views.
The group of representatives then make decision on behalf of wider group who has elected them.
� In dictatorship, the preferences of dictator are supreme and will overrule or dominate all other
competing preferences.
� This chapter discusses the problem of liberal democracy on two behalf, first, the prevalence of liberal
democracy in one form or other in one or many countries and second, its implicitly such as a theory
that underlies most of our analysis of social choices
� The approach for debate to tends to the problem between economists and political scientists is
complex methodological debate. Second, we consider number of normative questions in social choice
theory. Third, recent development in positive of collective choice will be discussed.

4. The problem of social choice defined
� From the previous chapter, Pareto-efficient allocation of resources to public goods (i.e. ∑MRS=MRT)
each individual was assumed to pay price or tax for public good which was directly proportional to
benefits received by consuming public good.
� Samuelson has pointed out that what the model demonstrate is the amount of information a perfectly
discriminating monopolist would require in order to establish Pareto-efficiency as seen in market
failure situation.
� The problem of deciding upon optimal distribution of welfare over the individuals in the society was
solved by Samuelson public good model by using Bergson social welfare function. Such social
welfare function assume that non-economic influences on individuals are exogenous it consider the
role of distribution function in economics. Samuelson model highlighted two problems in social
choice theory.

5. � (1) Collective decision: Each member of the society has his own preferences over the set of
alternatives, how would the society collectively decide or how to aggregate diverse individuals
preferences into a group decision.
� (2) The social welfare judgment: where does the society objective function or social welfare function
originates.
� Once the economists know the aggregate rule, and once he knows what function is to be maximized
then he can apply his standard tools for the optimization od social choices.
� A constitution establish the rules of political game by defining the right and obligations of individuals
operating in a verity of role, e.g. voter, citizen, property owner and bureaucrat.
� Or a contract among citizens they must follow when they make collective decision.

6. � This discussion is summarized in figure 4.1when choosing between alternative social choice rule,
three questions are generally discussed.
� (1) Is the rule ethnically acceptable ?
� (2) Is the rule technically feasible to operate ?
� (3) Is the rule costly to use in practice ?
� Answer to these question will be discussed in the reminder of this chapter.
� Thus we consider set of possible social/collective choice rule and evaluate them.

7. Figure 4.1

8. The public interest vs. The self-interest approaches
� Generally speaking political scientists use public interest approach while Economists apply self-
interest approach.
� (1) The public interest approach: This is set out in the works of Wildaysky, Lindblom and Lindblom,
and Dahl. In the public interest approach the individual, in the analysis of collective choice, plays a
subservient role to the set of social organizations that makes social choices.
� Question that arises, Where does the public interest originate? Within this approach there is no single
answer to the question. First, there is a group who might be called the 'rationalists', who take the
existence of the public interest, or as they prefer to call it 'the common good', as given. The common
good is assumed to be expressed through the popular or common will of the people, and it is the
function of political and social organizations to interpret this common will. Second, there are 'the
idealists', who regard the public interest to reside within the natural law.

9. � (2) The self-interest approach: This work is usually associated with the work of Downs, Buchanan and
Tullock, and McKean. Individuals have a set of preferences and are assumed to behave in such a way
as to maximize their objective (i.e. utility), subject to a number of constraints, which will include a
resource constraint, legal and organizational constraints, imperfect knowledge and imperfect foresight.
� The self-interest approach can be used to explain a good deal of political behavior. By postulating that
the individual behaves 'as if' he maximizes utility.
� A set of testable hypotheses can be generated , the self-interest approach is more scientific in the
Popperian sense since its hypotheses are at least cast capable of falsification by recourse to empirical
investigation.
� Unlike the public interest approach, it does not depend upon the notion of some external set of
circumstances generating the public interest.

10. Criteria for social choice rules
� This section address the following problem: What are the minimum conditions we would require a
social choice rule (i.e. a constitution) to conform to for it to be ethically acceptable? This is the
problem that Kenneth Arrow considered and his results have provided a much deeper understanding
of the foundations of social choice. Arrow's analysis proceeds by making the following
assumptions.
� (1) Rationality assumptions: For any given set of individual preferences the social choice rule must
produce a social ordering that is complete and transitive where: (i) completeness is defined as: for
each pair of alternative social states either one is preferred to the other or the relationship between the
two is indifference. (ii) transitivity: if social state x is preferred to social state y and social state y is
preferred to social state z then x is preferred to z.
� (2) Independence of irrelevant alternatives: Social choice over a set of alternative social states only
depends upon the orderings of individuals over these alternatives and not on anything else Thus if the
choice is between x and y and if the relationship between x and w changes then this change is
irrelevant to the ordering of x and y. Likewise, if the relationship between alternatives w and z
changes then this does not affect the ordering of x and y).

11. �
� (3) Pareto principle: If every individual in society strictly prefers x to y then the social ordering must
show that x is preferred to y. If at least one person in society prefers x to y and if everyone else is
indifferent between x and y then the social ordering must show that x is preferred to y.
� (4) Unrestricted domain: The social ordering must be produced in such a way that the domain from
which it is derived includes all logically possible individual orderings. That is, we do not wish to
generate a social ordering by restricting the domain of individual orderings.
� (5) Non-dictatorship: There does not exist an individual “i” such that, for all alternatives x and y, if “i”
strictly prefers x to y then society will strictly prefer x to y regardless of other individuals' preferences.
� This approach was criticized by many writers for being too tough in not allowing interpersonal
comparison.

12. Majority voting
� In a democracy one of the most prevalent social/collective choice rules is that of majority voting. The
majority voting requires that the least the first whole integer above n/2 support an issue before it can
be adopted (where n = number of votes).
� two distinct forms of majority first, decision-making direct democracy, whereby social choices are
determined directly by citizens on a major voting rule. Second, representative democracy which
individuals elected (via a majority voting procedure) to represent interests of those who elected them
to office.
� Does the majority decision rule conform to Arrow's conditions as outlined in the previous section; i.e.
is majority decision rule a good rule? Consider the following example.

13. � There are three voters labeled 1, 2 and 3, and there are three alternatives labeled A, B and C. The three
alternatives could be thought of as three different policies or could be thought of different budget; a
high budget, a medium budget and a low budget. Each individual's preference ordering is revealed in
his ranking of the three alternatives as shown below.
Figure 4.2
� (1) Compare alternatives A and B, since individuals 1 and 3 prefer A to B, A will wins over B, two
votes for and one against.
� (2) Now compare A with C, individuals 2 and 3 prefer C to A, therefore, C wins over A.

14. � (3) The overall winner is C. But if C is compared with B individuals 1 and 2 Prefer B to C, hence B
wins over C
� In other words, the outcome of this voting process is intransitive. The majority decision rule does not,
therefore, conform to all of Arrow's conditions.,
� Arrow's analysis goes much further than the observation that the majority decision rule produces an
intransitive social ordering. After all, this voting paradox was well known following the work of
Condorcet in the eighteenth century

15. Single-peaked preferences
� Lets relax some assumptions of Arrow's results. It has been suggested by Duncan Black's that by
suitably restricting individual preferences to conform to a specific pattern, a transitive outcome to
majority decision-making can be produced. The particular pattern imposed on individual preferences
by Black was that they be single-peaked.
� in this example, given the particular configuration of individual preferences, the outcome of the
majority decision rule is transitive.
� in Figure 4.3 The top panel shows that configuration of individual preferences which will produce an
intransitive social ordering whereas the bottom panel results in a transitive ordering. The difference is
that in the second case all individual preferences are “single peaked”

16. Figure 4.3
Figure 4.3 shows that the idea of single peakedness can be seen by looking at the configuration of
individual 3's preferences in Figure 4.3(a). It is seen that this individual's preference ordering has two
peaks; i.e. the line goes down and then up.

17. Intensity of preferences (point voting system)
� In simple majority decision models it is not possible for the individual to express his intensity of
preference for one alternative compared with another. The individual has a single vote, which is cast
in favor of one of the alternatives.
� There are a number of ways round this problem of majority decision-making This is done in the 'point
voting system' shown below.
Figure 4.4

18. � The above figure shows that, each voter is assigned 100 points and allocates them to each alternative
policy (A, B or C) depending on the extent to which he prefers one alternative relative to another.
Thus, in this example individual 1 is indifferent between policies B and C but feels strongly about
policy A. The number of points assigned to each policy are added up and the policy with the greatest
number of points wins. Another advantage of the point voting system is that its outcomes will be
transitive; however, the probability of ties increases The point voting system does not, however,
conform to the requirements of Arrow's system since individual preferences are now regarded as
being cardinal rather than ordinal. Furthermore, the point voting system is more complex and costly to
administer than the simple majority voting system.

19. “Naseebullah” is discussant of this
topic. He will further discuss this
topic in class.

20. Thank You