Latest News

About CAMQ

Information for Authors

Editorial Board

Browse CAMQ Online

Subscription and Pricing

CAMQ Contacts

CAMQ Home

 

Volume 15,     Number 2,     Summer 2007

 

CANONICAL INVARIANTS FOR
THREE-CANDIDATE PREFERENCE
RANKINGS
MARLOS VIANA

Abstract. It is shown that the data space for the three-candidate Condorcet Rule can be decomposed as the sum of two one-dimensional and one two-dimensional permutation invariant subspaces. The nontrivial one-dimensional invariant describes the variation in total number of votes between fully distinct preferences and preferences that agree on the ranking of exactly one candidate. The two-dimensional invariant describes the voting difference between the extreme (win vs. show) rankings for any two candidates. In contrast, the data space for the original voting data has one additional two-dimensional invariant subspace corresponding to win vs. place (or place vs. show) data for any two candidates. Canonical bases for these sub-spaces are constructed, interpreted, and graphically displayed as invariant plots. Permutation invariant distances among data points in the invariant subspaces are obtained. The presented data-analytic methodology equally applies to ranking data of an arbitrary number of choices. Related applications to race-track betting, short DNA words, and linear geometric optics are outlined.

Download PDF Files
 
(Subscribers Only)

© 2006, Canadian Applied Mathematics Quarterly (CAMQ)