The Annals of Mathematical Statistics

The Enumeration of Election Returns by Number of Lead Positions

John Riordan

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Abstract

In an election return with two candidates $A$ and $B$, if $\alpha_r$ is the number of votes for $A$ in the first $r$ counted, $\beta_r$ the similar number for $B$, then $r$ is a $c$-lead position for $A$ if $\alpha_r > \beta_r + c - 1$. With final vote $(n, m) (n$ for $A, m$ for $B$), what is the number $l_j(n, m; c)$ of returns with $j c$-lead positions? Or, what is the enumerator $l_{n m}(x; c) = \sum l_j(n, m; c)x^j$ of election returns by number of lead positions? For $c = 0, \pm 1, \pm 2, \cdots$ it is shown that all enumerators may be expressed in terms of $l_{n m}(x; 0)$ and $l_{n m}(x; 1)$, which are given explicit expression.

Article information

Source
Ann. Math. Statist., Volume 35, Number 1 (1964), 369-379.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177703760

Digital Object Identifier
doi:10.1214/aoms/1177703760

Mathematical Reviews number (MathSciNet)
MR161804

Zentralblatt MATH identifier
0123.36402

JSTOR
links.jstor.org

Citation

Riordan, John. The Enumeration of Election Returns by Number of Lead Positions. Ann. Math. Statist. 35 (1964), no. 1, 369--379. doi:10.1214/aoms/1177703760. https://projecteuclid.org/euclid.aoms/1177703760


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