Question

8a. Research and define Arrow’s “impossibility theorem”.
8b. Using three sets of voting preferences, illustrate Arrow’s impossibility theorem.
8c. In less than 50 words, argue the implication of Arrow’s impossibility theorem on the provision of public goods.

Answer 1

8a. According to Arrow's "impossibility theorem," there cannot exist any fair method of voting in the election while maintaining the principles of the fair voting procedure.

8b. Let's consider the following example, where voters are asked to rank their preference of candidates M, N, and O:

Now,

55 votes M > N > O

This means 55 people prefered M over N and prefer N over O

50 votes N > O > M

This means 50 people prefer N over O and prefer O over M

40 votes O > M > N

This means 30 people prefer O over M and prefer M over N

So, M is the winner here since it gets the majority of votes. But if we don't consider N as operating, O would clearly be the winner as more people prefered O over M. This is the “paradox of voting”.

8c. According to Arrow, there is no possibility to come to a conclusion which includes everyone's preferences. Someone has to compromise. Meanwhile, this theorem was applied to the provision of public goods which says that all products are individualized and there are no collective social goods different.