Explain Arrow’s Impossibility Theorem.
The democratic procedure for reaching a social choice or group decision is the expression of their preferences by individuals through free voting. Social choice will be determined by the majority rule. But Arrow has demonstrated through his impossibility theorem that consistent social choices cannot be made without violating the consistency or transitivity condition. The social choice on the basis of majority rule may be inconsistent even if individual preferences are consistent. Arrow first considers a simple case of two alternative social states and proves that in this case group decision or social choice through a majority rule yields a social choice, which can satisfy all the five conditions. But when there are more than two alternatives, majority rule fails to yield a social choice without violating at least one of the five conditions. Thus, Arrow’s theorem says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social choice function that satisfies all these conditions at once.
Alternative Social States
| X | Y | Z | |
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