Question

7 a. Describe Arrow’s Impossibility Theorem and explain the assumptions (there are five of

them) from which the theorem is derived.

. b. Describe the Median Voter Theorem and the assumptions from which it is derived. (10 points)

Answer 1

a) Arrows Impossibility theorm was discover by the Kenneth Arrows, the thoem was also known as general possibility theorem.Arrows impossibility theorem states that the a clear order of preferences cannot be determined while adhering to mandatory principles of fair voting procedures.There are some people whose preferences will inform this choice and the question is which procedures are there for deriving from what is known or can be found out about their preferences.Arrow's theorem said that,its satisfy certain assumptions that are concerning the autonomy of the people and rationality of their preferences.The assumptions are

• Unrestricted Domain(U) :- when the domain f is required for individual preferences and when f produces ordering of alternatives gives the f includes list of 〈R1,…,Rn〉〈R1,…,Rn〉 of n weak orderings of X.
• Social Ordering(SO) :- f〈Ri〉 is a weak ordering of X for any profile 〈Ri〉.
• Weak Pareto (WP) :- if in a profile of 〈Ri〉 which contains a domain of f and alternatives as x and y,then for all values of i, xPiy, then xPy.
• Nondictatorship (D) :- in this assumption we assumed that the f has no dictator.
• Independence of Irrelevant Alternatives (I) :- In a domain which have an alternatives of x and y in the X and which has a profiles of 〈Ri〉 and 〈Ri*〉.It gives the result of f〈Ri〉|{x,y} = f〈Ri*〉|{x,y}.

b).Median Voter Theorem

• it was developed by the Anthony Downs on his book of "an economic theory of democracy".
• The theory explains about the the two ends of spectrum of the politicians.Its explain why the politicians ends of the both spectrum tend.
• It explains about the how the voters can think about the the political policies of the ploiticians in between the two extreems.

the theorem was derived some of the assumptions,There are

1.Voter preferences are single peaked : On the basis of policy positions preference curve,the voters have a single point on its curve according to the curve policy position.They think about from which point they got the highest ulitility from the politicians.

2.Voter preferences are one dimensional : The voter preferences are measured in one dimensional .They preferences about the a single dimensional policies about they got the favour.

3. Assumption of candidates or parties competing for votes : The voter will think about the different perspective about the two politicians,and think about which is the best in the policy.Which makes a competition in between the politicians and the do their best policy.This will make competing among the politicians and the voter will do choose their best option from that.