JSM 2004 - Toronto

Abstract #301830

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Activity Number: 275
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
Sponsor: Business and Economics Statistics Section
Abstract - #301830
Title: A Better Estimate of the Number of Valid Signatures on a Petition
Author(s): Mary M. Whiteside*+ and Mark E. Eakin
Companies: University of Texas, Arlington and University of Texas, Arlington
Address: Box 19437, Arlington, TX, 76019,
Keywords: sampling ; signatures ; petition ; Goodman ; nonlinear ; replicates
Abstract:

The 2003 election of Governor Arnold Schwarznegger in California, the current attempt to recall Dallas Mayor Laura Miller, and the 2002 Austin City Council elections illustrate the need for a reliable sampling method for estimating the number of valid signatures on a petition. Signatures may be invalid for several reasons: not a registered voter, incorrect address, replicate, etc. The problem is interesting because replicated signatures must be estimated differently than signatures invalid for other reasons. Goodman's seminal work and subsequent Goodman-type estimators first estimate the total number of valid signatures on a petition, ignoring initially whether or not they are replicated. Then the problem reduces to estimating the number of classes in a finite population. We first estimate the number of unique, original signatures, and then the proportion that are valid. The result is a nonbiased nonlinear estimator with smaller variance than the Goodman-type statistics for the case where the proportion of duplicated signatures is the same for valid and invalid signatures.

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