Arrow’s Impossibility Theorem: The Limitations of Perfect Voting Systems in Decision-Making

Arrow’s Impossibility Theorem

A theorem that demonstrates that voting method that is guaranteed to always produce fair outcomes is a mathematical impossibility

Arrow’s Impossibility Theorem is a mathematical theorem that states that there is no perfect voting system that can meet certain desirable criteria. The theorem was introduced by economist Kenneth Arrow in 1951 and is also known as Arrow’s paradox or Arrow’s impossibility.

The theorem basically states that it is impossible for a voting system to have the following properties simultaneously:

1. Pareto efficiency, which means that if every voter prefers option A over option B, then the collective decision should also prefer A over B.

2. Individual independence, which means that the votes of each individual should only depend on their own preferences, and not influenced by the preferences or choices of others.

3. Non-dictatorship, which means that there should not be one individual whose vote dominates all others, and whose preference always determine the collective decision.

Arrow’s theorem demonstrates that achieving all three of these criteria is impossible in a voting system. In other words, any voting system must sacrifice one or more of these properties.

The practical implications of Arrow’s theorem are that some level of compromise is always required in any decision-making process in which multiple stakeholders are involved. No voting system can perfectly represent the preferences of all individuals, so it is important to seek consensus and make compromises to ensure that everyone’s voices are heard.

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