IJPAM: Volume 54, No. 3 (2009)

VOTING MATRICES AND TIE-BREAKING

Jeffrey L. Stuart$^1$, James R. Weaver$^2$
$^1$Department of Mathematics
Pacific Lutheran University
Tacoma, WA 98447, USA
e-mail: [email protected]
$^2$The University of West Florida
Pensacola, FL 32514, USA
e-mail: [email protected]


Abstract.Consider an election among $m$ candidates in which each of $n$ judges casts nonnegative, weighted votes with weights totaling $k>0$ subject to certain rules. The weight of the vote cast by judge $j$ for candidate $i$ is recorded in the $i,j$ entry of the $m\times n$ voting matrix $A.$ The row sums of the candidate matrix $C=AA^{T}$ are used to rank the candidates. Under simple restrictions on $A,$ the Perron vector for $C$ is used to help break ties that occur among the row sums. Ranking of the judges via the judge matrix $J=A^{T}A$ is also examined.

Received: June 30, 2009

AMS Subject Classification: 15A18

Key Words and Phrases: Perron vector, ranking, tie-breaking, voting

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3