Open Access
March, 1964 The Enumeration of Election Returns by Number of Lead Positions
John Riordan
Ann. Math. Statist. 35(1): 369-379 (March, 1964). DOI: 10.1214/aoms/1177703760


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.


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John Riordan. "The Enumeration of Election Returns by Number of Lead Positions." Ann. Math. Statist. 35 (1) 369 - 379, March, 1964.


Published: March, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0123.36402
MathSciNet: MR161804
Digital Object Identifier: 10.1214/aoms/1177703760

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 1 • March, 1964
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