2016 ISCEE International Conference on the Science of Electrical Engineering 978-1-5090-2152-9/16/$31.00 ©2016 IEEE Alon Sela Tel Aviv University alonsela@post.tau.ac.il Erez Shmueli Tel Aviv University erez.shmueli@gmail.com Dima Goldenberg Tel Aviv University dimgold@gmail.com Irad Ben-Gal Tel Aviv University bengal@tauex.tau.ac.il Abstract – Many studies in the field of information spread through social networks focus on the detection of influencers. The spread dynamics assumes these influencers are first selected to be infected with a message, and then this message spreads through the networks through a viral process. The following work presents some difficulties with this separation between the infection stage and the viral stage, and provides a case where the more nodes are initially seeded, the fewer is the number of nodes which eventually adopt the message. Such cases, where an increased effort spent on the spread of an idea results in lower final rates of spread, can be prevented by the Scheduling Seeding approach. This approach gradually plans the timing of infection for each particular node as the viral process progresses. It outperforms the initial seeding approach, and prevents the occurrence of the counter-intuitive (and unwanted) results where a greater effort results in a less successful spread. Keywords – Information Cascade; Social Networks; Linear Threshold; Viral Marketing; Scheduling Seeding. I. INTRODUCTION Social networks are an important communication tool which influence social and political processes [1], [2], [3]. Nevertheless, their main importance is in the private and public sectors, where they are used as a commercial tool to spread information on products and services. The study of social networks is closely connected to the studies of social influence in groups [4], [5], [6], [7] [8]. These groups, not only form new norms, but also influence individuals to perform according to these newly created norms. As such, most models which describe the spread of influence and information cascades through social networks include a dynamics which captures a tendency of adopting to a majority view. One such well-known model of information spread is the Linear Threshold model [9]. According to this model, the social dynamics is captured in the adoption probability, which is defined to be proportional to the number of adopters. If the weighted sum of adopting neighbors exceeds the node`s acceptance threshold; ∑  , ≥       , where b , is the influence of ; an active neighbor of  on node , such that the weights ∑  , ≤1     , and θ  is its acceptance threshold, the node adopts the spreading idea. This model is cited in over 3600 works, and important examples of such works are found in [10], [11], [12], [13]. It is based on an assumption that a message is first seeded to nodes (seeding is the act of intentionally infecting a node with an idea), at time t=0. This initial seeding is then followed by a viral process by which the message spreads through the network by “viral forces”, and the final spread is measured. While the Linear Threshold model is one of the pillars in the studies of information cascades, a large body of works show that the results of this model might contradict real experimental data [14], [15], [16], [17], [18], [19], [20], [21]. Unlike the common final system`s state in the Linear Threshold model, by which a message spreads to a relatively large fraction of the network, in reality, a viral spread of messages through large portions of a social network is a rather rare event. In fact, while many billions of messages flow through social networks daily, only a small fraction of these messages actually spread to more than one single person and the fraction of messages which spread to more than 1% of the network is negligible [17], [19]. There seems to be a contradiction between the well- established and well-accepted importance of social forces, by which it is known that society has substantial influence in changing the behavior and beliefs of an individual and the actual low frequency of large information cascades. This work does not directly bridge between these two contradicting studies. Rather, it presents some theoretical and simulative results which undermine the commonly used separation between the infection seeding stage and the spread or viral stage. The work presents the difficulties with such a separation, and proposes the Scheduling Seeding approach, a better alternative by which the viral spread is performed along the seeding and not before the seeding. The work starts by analyzing the actual influence function p  = f(x  ), a function that describes the probability of the adoption of a new idea by node v , as an outcome of the size of neighbors` coalition x  that supports the idea. The influence function in our model is constructed on the basis of well-established experiments results [4], where it was shown that p  ; the probability for conforming is proportional to the size of the coalition only in a limited range. Larger coalitions do not further increase the probability of adoption. We thus need to include the correct influence function f(x  ) in any modified model of information cascades and viral spread. The work continues by proposing a method for seed allocation through a Scheduling Seeding approach [22] [23]. We present a new and simple algorithm for budget allocation, where the budget for seeds is gradually planned for a near future and not seeded in advance. In the results section, we Why Spending More Might Get You Less, Dynamic Selection of Influencers in Social Networks