The theoretical Shapley–Shubik probability of an election inversion in a toy symmetric version of the US presidential electoral system

Olivier Mouzon, Thibault Laurent (), Michel Le Breton and Dominique Lepelley
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Olivier Mouzon: University of Toulouse Capitole
Thibault Laurent: University of Toulouse Capitole
Michel Le Breton: University of Toulouse Capitole

Social Choice and Welfare, 2020, vol. 54, issue 2, No 10, 363-395

Abstract: Abstract In this article, we evaluate asymptotically the probability $$\phi \left( n\right) $$ϕn of an election inversion in a toy symmetric version of the US presidential electoral system. The novelty of this paper, in contrast to all the existing theoretical literature, is to assume that votes are drawn from an IAC (Impartial Anonymous Culture)/Shapley–Shubik probability model. Through the use of numerical methods, it is conjectured, that $$\sqrt{n}$$n$$ \phi \left( n\right) $$ϕn converges to 0.1309 when n (the size of the electorate in one district) tends to infinity. It is also demonstrated that $$ \phi \left( n\right) =o\left( \sqrt{\frac{ln(n)^{3}}{n}}\right) $$ϕn=oln(n)3n and $$\phi \left( n\right) =\Omega \left( \frac{1}{\sqrt{n}}\right) $$ϕn=Ω1n.

Date: 2020
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Related works:
Working Paper: The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System (2020)
Working Paper: The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System (2018)
Working Paper: The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System (2018)
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DOI: 10.1007/s00355-018-1162-0

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