Hi...today we will be discussing
Arrow's Impossibility Theorem
Arrow's Impossibility Theorem was introduced by
Kenneth Arrow, who is one of the famous American economist
who has won Nobel Prize in Economics in the year
1972 along with John Hicks
Arrow's Impssibiility Theorem is one of the
prominent contribution of Kenneth Arrow
So in this video we will be having a discussion on
Arrow's Impossibility Theorem
So before going to Arrow's Impossibility Theorem we should
have a little idea on Arrow's Theory of Social
Choice which he introduced in his famous book
“ Social Choice and Individual Values” published
in the year 1951
it is actually from this theory of Social Choice Arrow comes
to his impossibility theorem
As you know an economy may consist of millions of people
All these people will be having their own different charactaristics
so constructing a social welfare function which will be
reflecting the preferences of all these individuals
will be quite difficult. This is actually the
base of Arrow's theory of Social Choice
So when we put the preferences of all the individuals
each and every individuals in the economy
all together and when we
if you want to make a social decision
by comprising the decisions and preferences of
all the individuals
through a democratic procedure will be quiet difficult
as I told you because
the characteristics of each and every individual
will be entirely different from another one. So this
characteristics will make quiet difficult for making an
social choice which will be based upon the democratic principle
simply means that we can not make a
social decision which will be satisfying the preferences of
all the individuals in the economy
it is based upon the fact that individual ordering will be reflecting
only the individual's
or one's own taste and preferences not of the
society as whole
suppose if I'am preferring something out of something
it will be reflecting only my own preferences
not the society's preferences
so in order to construct a valid social welfare
function from individual preferences, Arrow
has introduced 5 conditions for social choice
first one is that Consistency and
Transitivity
so we have seen consistency and transitivity in various
microeconomics concepts
so consistency and transitivity simply means that
we should be consistent with your decision, for example if you are
given an option
for example, three baskets, A, B, C and you are choosing
from A, B,C you are choosing basket A
from a particular situation, OK, and
very next time if you are given chance for
choosing again from these A,B,C baskets
you are again choosing basket A, this actually meant by
consistency, you should be
consistent with your decisions
so this is the first condition of social choice
introduced by Arrow. Second condition is that
Responsiveness to individual preferences
it is simply means that
social choice should be in consistent with the
preferences of the individuals. That means
the social choice
should move in the same direction to the
individual preferences
The third condition is that non-imposition
it means that individual preferences should not be imposed by
some external forces. It should not be forced by
some one else who is living outside the community
the fourth condition is that the condition of
non-dictatorship. That means
if I'am making some decisions, if I'am making some preferences
it should not be dictated by or forced by
some one else in the economy. That is
my preferences should be based upon my own
taste and preferences, not by someone else's
preferences
fifth condition is that independence of
irrelevant alternatives. It means that if I'am making
some preferences for a particular choices
for example if I'am given
Basket A and Basket B
and making the choice only for that
OK, if I'am
in some another condition I have been a given a chance of
given a baskets of basket D
and E
My preference for that is actually not determined by the
first preferences. So according to Arrow
the construction of social preferences should be based upon
all these 5 conditions
so here we come to the Arrow's Impossibility Theorem. According to
Arrow, we can not make a social decision
from individual preferences which will be satisfying
all these conditions which is quiet impossible
The Arrow's Impossibility Theorem states that
you can not make social preferences
without violating at least one of these conditions
that means by fully satisfying
all these conditions you can not a social preferences
you must be violating at least one among them
so here in order to construct a social preferences from
individual preferences you will be depending the democratic
free voting system
and the final decision will be based upon the majority
voting rule. The preferences which has got
highest number of votes will be considered as a
social preference
Arrow states that even if you are making social choices
through democratic voting, still
your decision can go contradictory and inconsistent
that I will tell you with the help of the following table
The table shows there are three individuals
Joseph, George and John
who constitute the society who voted for three
alternative social states X, Y
and Z by writing 6 as
most preferred alternative, 4 as
next preferred and 2 as least preferred
in the table Joseph prefers X
to Y when X and Y are available
and Y to Z when Y and Z are availbe
and X to Z when X and Z are available
in the case of George he prefers
Y to  Z when Y and Z are available
he prefers Z to X when
Z and X are availbe
and he prefers Y to X
when Y and X are available
so in the case of last individual John
he prefers Z to X
when Z and X are available, he prefers
X to Y when X and Y are
available and finally he prefers Z
to Y when both Z and Y are available
so as I said there are only three individuals are
in the economy, and when any two of individual's
decisions are same, we can call it as majority
both Joseph and John prefer
X to Y when X and Y are available
and both Joseph and George prefer Y
to Z when Y and Z are available
George and John prefer Z to X
when Z and X are available
so this majority rule leads to
inconsistent social decision over here, because
on the one hand X has been preferred to Z
as per the majority rule and on the other hand Z is also been preferred to X based upon the majority rule
so this will result in a situation where
taking a social decision which is based upon the
democratic majority voting rule
will be quiet contradictory and inconsistent
so this is how Professor Arrow conclude his impossible
theorem that it is quiet impossible to
make social preferences based upon the
individual ordering without violating at least one
of the conditions of social choice
so that's all about Arrow's Impossible Theorem
hope you got at least some idea regarding the topic
thank  you for watching, have nice day
