Question

Briefly discuss the impossibility theorem as well as the ethical conditions that it advocates are the short-comings of the majority voting rule.

Answer 1

The general impossibility theorem or Arrow's impossibility theorem states that we cannot formulate a clear order of preferences while sticking to mandatory rules of fair voting procedures. It is a social-choice paradox that shows the faults of ranked voting systems.

In cases where there is ranking of preferences , it is not possible to determine a social ordering without violating one of the following conditions listed below:

• Nondictatorship: The choices of multiple voters should be taken into account and should not be neglected
• Pareto Efficiency: Unanimous individual preferences must be respected: that means if every voter is prefering candidate B over candidate C, then the winner should be candidate B and not C.
• Independence of Irrelevant Alternatives: If a choice is removed from the choices that are ranked, then the order will still remain the same. For example , suppose candidate B ranks ahead of candidate C, candidate B should still be ahead of candidate C, even if the third candidate that is, candidate D is removed from from the choices.
• Unrestricted Domain: Voting must be considered for all individual preferences.
• Social Ordering: Each voter should be able to order their preferences and point if there ia any tie.

For example consider there are 3 voters say A,B,C.Lets assume,

• 25 people prefer A over B and B over C (A>B>C)
• 20 people prefer B over C and C over A (B>C>A)
• 10 people prefer C over A and A over B( C>A>B)

Candidate A has the maximum votes so he/she would be the winner. However, if B was removed then the winner would be C since more people prefer C over A. that is, A would get 25 votes and C would get 30 votes. This illustrates the general impossibility theorem or Arrow's theorem.