Question

Explain Arrow's impossibility theorem. What is Arrow's main conclusion? What is his main contribution ?

Answer 1

Arrow’s impossibility theorem is a choice paradox. It illustrates that the ranked voting system is flawed. It states that it is impossible to know the preference order while adhering to the principals of fair voting.

Its usage can be explain in the voting system for electing a government. When a it is the time for new government to be formed, elections are bound to occur and people run to the polling booths to vote but Arrow’s impossibility theorem states that it is impossible to formulate a social ordering and also to adhere to the general principlals of fair voting and if done, there will be atleast one condition that is violated. The conditions are given below:

1. The economy should be a non-dictatorship i.e. voters’ wishes should be considered.

2. Outcome should be Pareto Efficient i.e. if all the voters opts for candidiate A over B then A should win.

3. Alternatives should be independently of each other i.e. if a voter chooses candidate A over B, he should again prefer A over B even if a third alternative is given to them.

4. Preferences of all the voters should be taken into consideration.

5. It should be possible that all the available choice to voters can be ordered and if not the voters can specefy who of them ties.

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