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The Limit of the Non-dictatorship Index

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Pure Mathematics and Applications
Special issue dedicated to 70th anniversary of prof. Peter Tallos
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In this paper we determine the asymptotic behavior of the Non-dictatorship Index (NDI) introduced in Bednay, Moskalenko and Tasnádi (2019). We show that if m denotes the number of alternatives, then as the number of voters tends to infinity the NDI of any anonymous voting rule tends to (m − 1)/m, which equals the NDI of the constant rule.