Stochastic Models of User-Contributory Web Sites

arXiv:0904.0016v1 [cs.CY] 31 Mar 2009 Stochastic Models of User-Contributory Web Sites Tad Hogg Hewlett-Packard Laboratories Kristina Lerman USC Information Sciences Institute November 7, 2021 Abstract We describe a general stochastic processes-based approach to modeling user-contributory web sites, where users create, rate and share content. These models describe aggregate measures of activity and how they arise from simple models of individual users. This approach provides a tractable method to understand user activity on the web site and how this activity depends on web site design choices, especially the choice of what information about other users’ behaviors is shown to each user. We illustrate this modeling approach in the context of user-created content on the news rating site Digg. 1 Introduction The Web is becoming more complex and dynamic as sites allow users to contribute and personalize content. Such sites include Digg, Flickr and YouTube where users share and rate news stories, photos and videos, respectively. Additional examples of such web sites include Wikipedia and Bugzilla, enabling anyone to contribute to encyclopedia articles or help develop open source software. These social web sites also often allow users to form explicit links with other users whose contributions they find interesting and highlight the activity of a user’s designated friends [13] to help users find relevant content. Web sites often provide users with aggregate summaries of recent activity. For example, both Digg and Flickr have a front page that features ‘hot’ (popular or interesting) content. News orga- nizations, such as The New York Times, allow users to subscribe to or embed RSS feeds of their most popular (e.g., emailed) stories in the users’ own pages. Feedback between individual and col- lective actions can lead to nonlinear amplification of even small signals. For example, the ‘Digg effect’ refers to the phenomenon where a ‘hot’ story on the social news aggregator Digg brings down servers hosting the story that are not equipped to deal with heavy traffic that a popular story on Digg generates. Aggregate activity of many users determines the structure and usefulness of user-participatory web sites. Understanding this emergent behavior will enable, for example, predicting which newly contributed content will likely become popular, identifying productive ways to change how infor- mation is displayed to users, or how to change user incentives so as to improve the content. The behavior of an individual user on a user-contributory web site is governed by a myriad of social, economic, emotional and cognitive factors, and often subject to unpredictable environmental 1 influences, such as the weather or the economy. Nevertheless, the combined activities of many users often produce remarkably robust aggregate behaviors [24, 25]. In this paper, we present a stochastic processes-based framework for relating aggregate behavior of web users to simple descriptions of their typical individual behavior. The models can be written directly from the individual behavior descriptions, and quantified with empirical observations of a representative sample of users. The methodology we describe applies to behaviors that can be modeled as Markov processes, i.e., where the relevant changes depend only on the current state of the system, not the detailed history of how it arrived at that state. In principle such models can always be applied by extending the complexity of the “state” describing the system. However, such complexity can lead to models requiring estimates for an impractically large number of parameters characterizing how the state changes. Instead, the Markov modeling assumption is useful primarily in connection with systems requiring only a few variables to define their current state. At first glance an assumption of Markov processes and simple states may appear overly restric- tive for describing human behavior. However, many online activities provide only a fairly limited set of actions for users and present information based on little or no historical context of particu- lar individuals. In these cases, a few state variables can capture the main context involved in user actions. Furthermore, we discuss simplifying approximations to the models that readily enable iden- tifying how key system behaviors relate to user actions. These simplifications come at a cost: while the resulting models correctly describe the typical aggregate behaviors, they say little about their extreme cases, e.g., where web site use is suddenly and briefly much larger than average. Even with this limitation, however, simplified models are often preferred over full models, which frequently require multiple simulation trials, which are computationally expensive and whose typical behaviors can be challenging to identify [14]. The paper is organized as follows. Section 2 reviews the stochastic modeling framework. In Section 3 we then illustrate the framework fo

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