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English: This diagram accompanies part three of the proof of Arrow's Impossibility Theorem. It illustrates the two segments of voters and the possible positions of certain pivotal voters. It illustrates the two segments of voters and the possible positions of certain pivotal voters.
Because of this example, some authors credit Condorcet with having given an intuitive argument that presents the core of Arrow's theorem. [20] However, Arrow's theorem is substantially more general; it applies to methods of making decisions other than one-man-one-vote elections, such as markets or weighted voting, based on ranked ballots.
English: This diagram accompanies part two of the proof of Arrow's Impossibility Theorem. It illustrates how the pivotal voter for B over A is a dictator for B over C It illustrates how the pivotal voter for B over A is a dictator for B over C
English: This diagram accompanies part one of the proof Arrow's Impossibility Theorem. It illustrates the process of successively moving one candidate from the bottom to the top of ballots. It illustrates the process of successively moving one candidate from the bottom to the top of ballots.
Arrow's Theorem [2]: The constitution is impossible, that is, the 4 conditions of a constitution imply a contradiction. Each voter has an ordering (by attribution). Yet a set of orderings used as an argument of the voting rule does not carry over to a social ordering, with a corresponding loss of social adaptivity and constitutional generality ...
Arrow's impossibility theorem is a key result on social welfare functions, showing an important difference between social and consumer choice: whereas it is possible to construct a rational (non-self-contradictory) decision procedure for consumers based only on ordinal preferences, it is impossible to do the same in the social choice setting ...
Unrestricted domain is one of the conditions for Arrow's impossibility theorem. Under that theorem, it is impossible to have a social choice function that satisfies unrestricted domain, Pareto efficiency, independence of irrelevant alternatives, and non-dictatorship. However, the conditions of the theorem can be satisfied if unrestricted domain ...
Impossibility theorems. Arrow's theorem; Majority impossibility; Moulin's impossibility theorem; ... [29] A notable example of this can be seen in Alaska's 2024 race, ...