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What is arrow’s impossiblity theorem?

Arrow’s Impossibility Theorem, formulated by economist Kenneth Arrow in 1950, is a fundamental result in social choice theory. It highlights the inherent difficulties of constructing a fair and consistent voting system that satisfies certain desirable criteria.

The theorem asserts that no voting method or system can simultaneously meet three specific fairness criteria, known as Arrow’s fairness axioms, when there are three or more alternatives to choose from. These axioms are:

1. Universal Domain: The voting system should allow any possible preference orderings of the alternatives as input.

2. Non-Dictatorship: The voting system should not be controlled by a single voter who can unilaterally determine the outcome.

3. Pareto Efficiency: If every individual prefers alternative A to alternative B, then the collective preference should also rank A above B.

Arrow’s Impossibility Theorem mathematically proves that these three axioms cannot be simultaneously satisfied when there are at least three alternatives and more than two individuals with distinct preferences. The theorem implies that any voting system will unavoidably violate at least one of these fairness axioms.

Furthermore, Arrow’s theorem reveals that even seemingly reasonable and widely-used voting systems, such as majority voting or ranked preference voting, can lead to inconsistent or undesirable outcomes. It demonstrates that the process of aggregating individual preferences into a collective preference is inherently complex and subject to paradoxes.

The implications of Arrow’s Impossibility Theorem have had significant influence on political and social sciences. It has contributed to discussions on democratic decision-making, voting systems, and the challenges of achieving fairness and consensus in collective decision processes. While it highlights the limitations of certain voting systems, it also prompts researchers to explore alternative methods or consider additional criteria to address the issues raised by Arrow’s theorem.