Journal of Official Statistics, Vol.21, No.3, 2005. pp. 489–504
Estimating the Number of Distinct Valid Signatures in Initiative Petitions
Ruben A. Smith and David R. Thomas
Abstract:In some states in the U.S.A., if citizens are dissatisfied with certain laws or feel that new laws are needed, they can petition to place proposed legislation on the ballot. For the petition to be certified for the ballot, its sponsor must circulate the complete text of the proposal among voters and obtain signatures of those in favor. Petitions will contain both invalid and valid signatures. Valid signatures from registered voters can appear more than once. To qualify a petition as a ballot measure, the total number of distinct valid signatures collected must exceed a required number. We are considering the case when a simple random sample of signatures is drawn from the entire petition, and all signatures in the sample are verified. The problem is to estimate the total number of distinct valid signatures based on the sample information and the knowledge of the total number of signatures collected in the petition. We consider several linear estimators and one nonlinear estimator. Expressions for the variance of the linear estimators are provided. The performance of the estimators is evaluated using data from several Washington State petitions that have been completely verified.
Keywords:Estimation, sampling signatures, replicated signatures
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