Three brief proofs of Arrow’s Impossibility Theorem

@article{Geanakoplos2001ThreeBP,
  title={Three brief proofs of Arrow’s Impossibility Theorem},
  author={J. Geanakoplos},
  journal={Economic Theory},
  year={2001},
  volume={26},
  pages={211-215}
}
Summary.Arrow’s original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but complicating the second step. I give three brief proofs, all of which turn on replacing the decisive/pivotal voter with an extremely pivotal voter (a voter who by unilaterally changing his vote can… Expand
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Summary.Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classicalExpand
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