A New Interpretation of Dictatorship with Applications in Social Choice Theory

Posted: 20 Jan 2016 Last revised: 12 Jun 2016

See all articles by Mohammad Akbarpour

Mohammad Akbarpour

Stanford University

Sam Nariman

affiliation not provided to SSRN

Date Written: January 11, 2016

Abstract

We say that a social choice function is sensitive to collective change if whenever all inputs change, the outcome necessarily changes. Then, we prove that a social choice function is sensitive to collective change if and only if it is dictatorial. This provides a new interpretation of the essential meaning of dictatorship. We provide an intuitive, geometric proof for a special case of the theorem, which reveals the geometric meaning of dictatorship. In addition, the theorem provides a unified framework to prove other dictatorship results in theoretical social choice; to illustrate this, we show how the Arrow and Gibbard-Satterthwaite theorems can be deduced from this theorem.

Keywords: Social Choice, Dictatorship, Arrow's Impossibility Theorem

JEL Classification: D70, D71

Suggested Citation

Akbarpour, Mohammad and Nariman, Sam, A New Interpretation of Dictatorship with Applications in Social Choice Theory (January 11, 2016). Available at SSRN: https://ssrn.com/abstract=2713921 or http://dx.doi.org/10.2139/ssrn.2713921

Mohammad Akbarpour (Contact Author)

Stanford University ( email )

Sam Nariman

affiliation not provided to SSRN

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