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Abstract
Journal of Official Statistics, Vol.21, No.1, 2005. pp. 2138

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The Accuracy of Estimators of Number of Signatories to a Petition Based on a Sample

Abstract:
Petitions are a relatively widespread international phenomenon. In some countries, including New Zealand, and in several U.S. states, they have legal status and there is legislation which obligates the legislature to react to petitions which have widespread popular support. Normal practice at present is to check a sample of the signatures and from that estimate the number of eligible electors who have signed a petition, making allowance for signatories who are not eligible and multiple signatures from eligible electors.

The problem is related to a number of others, e.g., number of species in an ecosystem, but was found via a simulation study to be sufficiently different that a universally best estimator does not exist. The simulation drew samples from artificial petitions with known distributions of multiple signatures to assess the performance of several estimators described in the literature. The effect of sampling fraction on bias, distribution, variability and estimated variance of the estimators was also investigated. Bias adjustment factors previously proposed in the literature were investigated and found not to be particularly useful.

Ineligible and duplicate signatures often occur in the same petition. Extending the simulation to include ineligible signatures showed that estimating their number added to the variability of the overall estimate of number of eligible signatories. Although the estimated number of multiple signatures and the estimated number of ineligible signatures are correlated, the simulations suggest the correlation is small and can generally be ignored.

Keywords:
Biased estimators, number of classes, population size, referendum, duplicate signatures, multiple signatures

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