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Tags

#arrows-impossibility-theorem #computation #proof #social-choice

Question

Outline Proof: (Arrow, 1951). When there are three or more alternatives, then every SWF that is weakly Paretian and IIA must be a dictatorship. Hint: use two important lemmas.

Answer

Prove Contagion Lemma using weak Pareto and IIA. Prove Splitting Lemma using Contagion Lemma, transitivity, weak Pareto and IIA. Apply Splitting Lemma multiple times.

Tags

#arrows-impossibility-theorem #computation #proof #social-choice

Question

Outline Proof: (Arrow, 1951). When there are three or more alternatives, then every SWF that is weakly Paretian and IIA must be a dictatorship. Hint: use two important lemmas.

Answer

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Tags

#arrows-impossibility-theorem #computation #proof #social-choice

Question

Outline Proof: (Arrow, 1951). When there are three or more alternatives, then every SWF that is weakly Paretian and IIA must be a dictatorship. Hint: use two important lemmas.

Answer

Prove Contagion Lemma using weak Pareto and IIA. Prove Splitting Lemma using Contagion Lemma, transitivity, weak Pareto and IIA. Apply Splitting Lemma multiple times.

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status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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