In economics, Arrow’s impossibility theorem is a statement about the inefficiency of certain voting systems. The theorem is named after economist Kenneth Arrow, who first proposed it in a 1951 paper.
The theorem states that, under certain reasonable conditions, it is impossible to design a voting system that is both fair and efficient. That is, there is no voting system that can consistently produce outcomes that everyone agrees are fair, and at the same time, are also efficient in the sense of reflecting the preferences of the voters.
The conditions required for Arrow’s impossibility theorem to apply are:
– There are at least three different alternatives (candidates, policies, etc.) that can be voted on.
– Each voter has a preference ordering over the alternatives. That is, each voter ranks the alternatives from most preferred to least preferred.
– The preferences of different voters are not necessarily the same. In other words, there is at least some degree of voter heterogeneity.
If these conditions are met, then it is impossible to design a voting system that satisfies all of the following criteria:
– Non-dictatorship: The outcome of the vote should not be predetermined by any single voter or group of voters.
– Pareto efficiency: The outcome of the vote should reflect the preferences of the majority of voters.
– Independence of irrelevant alternatives: The outcome of the vote should not be affected by alternatives that are not on the ballot.
– No cycles: There should be no circumstances in which switching the order of two alternatives on the ballot would change the outcome of the vote.
Arrow’s impossibility theorem has important implications for economics. In particular, it suggests that it is impossible to design an economic system that is both fair and efficient. This means that there is always a trade-off between fairness and efficiency in economics, and that it is not possible to have both.
The theorem also has implications for voting systems in general. It suggests that no voting system can be both fair and efficient, and that any voting system will have to make a trade-off between the two. This has led to a great deal of debate about the best way to design voting systems, with no clear consensus emerging.