text: Commons-based peer production does seem to rest upon a paradox. Although users produce all contents, at the same time participation is commonly on a voluntary basis, and largely incentivized by achievement of project's goals. This means that users have to coordinate their actions and goals, in order to keep themselves from leaving. While this situation is easily explainable for small groups of highly committed, like-minded individuals, little is known about large-scale, heterogeneous projects, such as Wikipedia. In this contribution we present a model of peer production in a large online community. The model features a dynamic population of bounded confidence users, and an endogenous process of user departure. Using global sensitivity analysis, we identify the most important parameters affecting the lifespan of user participation. We find that the model presents two distinct regimes, and that the shift between them is governed by the bounded confidence parameter. For low values of this parameter, users depart almost immediately. For high values, however, the model produces a bimodal distribution of user lifespan. These results suggest that user participation to online communities could be explained in terms of group consensus, and provide a novel connection between models of opinion dynamics and commons-based peer production.
  @cite_18: Recently online communities have attracted great interest and have become an important medium of information exchange between users. The aim of this work is to introduce a simple model of the evolution of online communities. This model describes (a) the time evolution of users' activity in a web service, e.g., the time evolution of the number of online friends or written posts, (b) the time evolution of the degree distribution of a social network, and (c) the time evolution of the number of active users of a web service. In the second part of the paper we investigate the influence of the users' lifespan (i.e., the total time in which they are active in an online community) on the process of rumor propagation in evolving social networks. Viral marketing is an important application of such method of information propagation.
  @cite_7: Open collaborative projects, like FLOSS development projects and open content creation projects (e.g. Wikipedia), heavily depend on contributions from their respective communities to improve. In this context, an important question for both researchers and practitioners is: what is the expected lifetime of contributors in a community? Answering this question, we will be able to characterize these communities as an appropriate model can show whether or not users maintain their interest to contribute, for how long we could expect them to collaborate and, as a result, improve the organization and management of the project. In this paper, we demonstrate that survival analysis, a wellknown statistical methodology in other research areas such as epidemiology, biology or demographic studies, is a useful methodology to undertake a quantitative comparison of the lifetime of contributors in open collaborative initiatives, like the development of FLOSS projects and the Wikipedia, providing insightful answers to this challenging question.
  @cite_1: Online peer production systems have enabled people to coactively create, share, classify, and rate content on an unprecedented scale. This paper describes strong macroscopic regularities in how people contribute to peer production systems, and shows how these regularities arise from simple dynamical rules. First, it is demonstrated that the probability a person stops contributing varies inversely with the number of contributions he has made. This rule leads to a power law distribution for the number of contributions per person in which a small number of very active users make most of the contributions. The rule also implies that the power law exponent is proportional to the effort required to contribute, as justified by the data. Second, the level of activity per topic is shown to follow a lognormal distribution generated by a stochastic reinforcement mechanism. A small number of very popular topics thus accumulate the vast majority of contributions. These trends are demonstrated to hold across hundreds of millions of contributions to four disparate peer production systems of differing scope, interface style, and purpose.
  @cite_6: Retaining participation is crucial for information services, online knowledge sharing services among them. We present the first comprehensive analysis of users’ activity lifespan across three predominant online knowledge-sharing communities. Extending previous work focusing on initial interactions of new users, we use survival analysis to quantify participation patterns that can be used to predict individual lifespan over the long term. We discuss how cross-site differences in user participation and the underlying factors can be related to differences in system design and culture. We conduct a longitudinal comparison of the communities’ evolvement between two distinct stages, the initial days just after the site launch and one year later. We also observe that sub-communities corresponding to different topics differ in their ability to sustain users. All results reveal the complexity and diversity in users’ engagement to a site and design implications are discussed.
  @cite_15: We present a detailed study of network evolution by analyzing four large online social networks with full temporal information about node and edge arrivals. For the first time at such a large scale, we study individual node arrival and edge creation processes that collectively lead to macroscopic properties of networks. Using a methodology based on the maximum-likelihood principle, we investigate a wide variety of network formation strategies, and show that edge locality plays a critical role in evolution of networks. Our findings supplement earlier network models based on the inherently non-local preferential attachment. Based on our observations, we develop a complete model of network evolution, where nodes arrive at a prespecified rate and select their lifetimes. Each node then independently initiates edges according to a "gap" process, selecting a destination for each edge according to a simple triangle-closing model free of any parameters. We show analytically that the combination of the gap distribution with the node lifetime leads to a power law out-degree distribution that accurately reflects the true network in all four cases. Finally, we give model parameter settings that allow automatic evolution and generation of realistic synthetic networks of arbitrary scale.
  @cite_13: We study the distribution of the activity period of users in five of the largest localized versions of the free, on- line encyclopedia Wikipedia. We find it to be consis- tent with a mixture of two truncated log-normal distri- butions. Using this model, the temporal evolution of these systems can be analyzed, showing that the statis- tical description is consistent over time. contributions: 1. We find all datasets to be consistent with the hypothesis that the lifetime of an user account is described by the su- perposition of two truncated log-normal distributions. An interpretation for this phenomenon is that two different regimes govern the participation of individuals to these versions of the Wikipedia project: the occasional users, who fail to find interest in the project after the first few at- tempts to contribute, and the long-term users, whose with- drawal is probably more related to external factors like the loss of personal incentives in contributing and similar causes. 2. Using our model, we characterize how the participation of users over time evolves, as the system ages. We find that the statistical description of the one-timers is stable over time, while the properties of the group of long-term users change as a consequence of the aging of the system. 3. We find evidence that the inter-edit time distribution de- cays with an heavy tail. In view of this finding, we check that our analysis is not affected by the choice of the pa- rameter used for determining when an user is to be con- sidered "inactive"; we find that for the one-timers it has no quantitative effect. For the statistics of the long-lived users we find instead a very good qualitative agreement.
summary: The subject of user participation in mass collaboration systems has been already touched by several authors, for example on social networking sites @cite_15 , and knowledge sharing platforms @cite_6 . A momentum'' law has been proposed for the distribution of user life edits of inactive users @cite_1 . The distribution of user account lifespans has been shown to decay with a heavy tail, and a power-law model has been proposed after this observation @cite_18 . Empirical data from Wikipedia, however, seem to support a super-position of different regimes @cite_13 ; a feature of the model we present here is indeed a bimodal distribution of user lifespans. In the context of wikis and other free open source initiatives some authors have used survival analysis to outline the diffences between different communities, @cite_7 but this modeling technique is not suited to understand the connection between social influence, group coordination, and user retention. We advocate the need to explicitly model such processes explicitly.