Network Scale-up Methods on Aggregated Relational Data to Estimate the Outcome of Elections

Abstract

The Network Scale-Up Method (NSUM) is an estimation framework that aims to determine the size of hidden or hard-to-reach populations from questions such as ``How many people do you know who belong to the target population?'' The information collected from these questions is commonly referred to as aggregated relational data (ARD), and the estimation of hidden population sizes using NSUM in ARD has been widely applied to key problems in sociology and public health. Note that this approach has been widely used to estimate the size of populations subject to legal or social restrictions, such as sex workers and drug users, who are typically excluded from the formal census. Although voting intention is not a social stigma, this information has become a privacy-sensitive issue, particularly in polarized political contexts, and thus poses a challenge to determining the share of party support. In this work, we introduce a methodology for estimating vote-intention shares using NSUM techniques on ARD. The methodology involves the design of the indirect survey to collect ARD regarding the voting intention of the survey participant's contacts, jointly with other control questions, the processing of the data with appropriate filters to eliminate outliers, the study of sample stratification strategies, and finally, the support share estimation for each political group by using different NSUM techniques. The methodology is applied to estimate voting outcomes in the 2023 Spanish general elections, using the Madrid, Andalusia, and Valencia regions as experimental scenarios. Overall, the resulting estimates \cambios{are competitive with} those published by leading private and public survey institutes, despite using a significantly smaller number of participants.