Petition estimators and their variance (Stats NZ WP 10-04)

Petition estimators and their variance reviews the statistical and mathematical aspects of determining how many registered electors have signed a petition authorised under the New Zealand Citizens Initiated Referenda Act (1993). If 10 percent or more of registered electors have signed such a petition, the government is required to hold a (non-binding) referendum on the petition question. Establishing whether this threshold has been met involves complex statistical and mathematical determinations. To assist those involved in this work, this paper brings together details scattered throughout the technical literature and compares approaches in a convenient technical reference. The paper also makes new technical contributions in the form of unbiased variance estimators and an efficient simulation program.