A note on the voting problem

Abstract

Let $v(n)$ be the minimum number of voters with transitive preferences which are needed to generate any strong preference pattern (ties not allowed) on $n$ candidates. Let $k=\lfloor {\log }_{2}n\rfloor$. We show that $v(n)\le n-k$ if $n$ and $k$ have different parity, and $v(n)\le n-k+1$ otherwise.

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