## 1 Introduction  
Public administrations (PAs) play an important role in modern societies, processing huge amounts of personal data related to governance, public services, and citizen interactions. The growing reliance on digital technologies has dramatically increased the volume and complexity of data created and managed by public authorities [1]. These data sets encapsulate essential information for policy formulation, resource allocation, and overall decision-making processes, shaping the direction of public policies and services and highlighting the critical role of data in effective governance [2]. Furthermore, as digital technologies advance, PAs are increasingly relying on collaborative initiatives to harness collective intelligence while protecting individual privacy [3, 4]. The integration of modern technologies into PA practices reflects and highlights data-driven governance solutions, as well as the need to find a balance between innovation and privacy [5]. In this context of PA requirements, federated learning (FL) is a potential solution to collaborative model training that does not share raw data, allowing organizations to secure sensitive information while benefiting from collective intelligence. FL presents a viable solution to address privacy concerns in the context of data sharing between organizations [6]. While ensuring privacy in FL for PA is critical, especially when working with real-world sensitive data sets such as public opinions and financial records, differential privacy (DP) emerges as an essential and advanced privacy-preserving mechanism to achieve this goal. DP purposefully injects controlled noise into model updates, creating a layer of ambiguity that discourages attempts to identify individual contributors. This proactive technique greatly improves the entire privacy protection process in FL systems [7; 8]. The combination of FL and DP, called differential private federated learning (DPFL), is an effective way to train machine learning (ML) models that use geographically distributed data (such as PA data) while maintaining data privacy. DPFL is a promising approach, but accurately determining the amount of privacy achieved remains a challenge. This shortcoming prevents businesses from successfully evaluating and ensuring the efficacy of privacy-preserving measures in FL implementations. This study investigates and quantifies privacy in the context of FL, using data provided by collaborating entities to assess the level of privacy protection obtained in FL systems. An effort is made to provide valuable information on the DPFL process for organizations to support decision making. The insight is also obtained in light of membership inference attacks (MIAs), which assess the effectiveness of DPFL from various points of view for PA. The main contributions of our work are as follows. * Insights for PA process modeling: This study investigates the possibilities of DPFL as a procedure for PA that protects citizens' privacy while enabling data-driven governance. DPFL enables PA to use collaborative data analysis to improve service delivery, make informed decisions, and increase efficiency. * Reduced MIA vulnerability: This study investigates how the use of DPFL with noise injection considerably reduces the sensitivity of participant data to MIA in PA contexts. The constant decrease in MIA success rates with increasing noise levels demonstrates the potential of DPFL to improve data privacy. * Real-world evaluation and competitive performance: The proposed DPFL technique undergoes evaluations in two real-world PA scenarios that use data from two public sectors. The results show that the strategy outperforms traditional ML techniques in both settings while maintaining the anonymity of the participants through DP. The rest of this paper is structured as follows. Section 2 provides a background of the work, including an overview of DPFL in the PA context.