###### Abstract  
Citizen sensing applications need to have a number of users defined that ensures their effectiveness. This is not a straightforward task because neither the relationship between the size of the userbase or its effectiveness is easily quantified, nor is it clear which threshold for the number of users would make the application 'effective'. This paper presents an approach for estimating the number of users needed for location-based crowdsourcing applications to work successfully, depending on the use case, the circumstances, and the criteria of success. It circumvents various issues, ethical or practical, in performing real-world controlled experiments and tackles this challenge by developing an agent-based modelling and simulation framework. This framework is tested on a specific scenario, that of missing children and the search for them. The search is performed with the contribution of citizens being made aware of the disappearance through a mobile application. The result produces an easily reconfigurable testbed for the effectiveness of citizen sensing mobile applications, allowing the study of the marginal utility of new users of the application. The resulting framework aims to be the digital twin of a real urban scenario, and it has been designed to be easily adapted and support decisions on the feasibility, evaluation, and targeting of the deployment of spatial crowdsourcing applications. agent-based modelling; human mobility; simulation; urban mobility; citizen sensing; spatial crowdsourcing +
Footnote †: journal: Applied Sciences  
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be used for various purposes, such as modelling interactions, recording local conditions, measuring community statistics, stimulating collective awareness, and identifying hidden connections among social and physical phenomena [11]. Therefore, social sensing applications have played a critical role in very diverse application domains, such as environmental protection, urban environment and transportation monitoring, public health surveillance, crisis awareness, disaster recovery, and behavioural epidemiology [9; 12; 13; 14; 15]. In general, citizen sensing apps are horizontal, real-time, open, accessible to anyone, geo-aware--since local information is more probable to be accurate--and they allow information sharing [15]. In this context, several research challenges regarding citizen sensing applications emerge, such as trust, privacy and data accuracy. Some of the most predominant issues encountered are 'noise' in the data, information overload, bias (propagation of the most famous idea), and misinformation. In that sense, several researchers have been working on those challenges [9]. For instance, in [16], users' contributions are validated by dividing them spatially, temporally, and contextually since an actual event will probably be documented more. Apart from these critical and widely identified challenges, every discussion on citizen sensing applications should start with the crucial challenge of recruitment. This is especially true for urban sensing or spatial crowdsourcing. In these cases, the coverage of an area, both in time and space, by human sensors for their involvement in data collection and decision making is a key metric [7]. Having human sensors provide high-quality data at scattered locations does not necessarily lead to success. Therefore, the question is whether there exists a minimum number of users, also known as 'critical mass', ensuring the promised experience and objectives. The quantification of this number is neither a straightforward task nor one that produces a concrete number. This paper aims to present a novel approach for estimating the critical mass of users in a citizen sensing application for most cases where it is difficult, unrealistic, or even unethical to run observational studies or controlled experiments on identical settings by only changing the number of users participating.