Interaction Bias on Spreading Dynamics
On May 7th, 2019, second-year PhD student Matteo Neri presented his project, "Effect of interaction bias on spreading dynamics over networks".
His motivation comes from the interaction bias observed in online social networks. Nowadays, the majority of the news and information we consume comes from online platforms, where they are selectively displayed by algorithms designed to maximize our use of the platform. That means that the posts that are shown to us are chosen based on the attributes the algorithms assign to us. The posts from our friends and contacts who are more similar to us have a higher probability of being shown on the news feed. Similarly, contents similar to what we have already rated positively have a higher probability of being shown. Therefore, we most of the time come in contact only with posts that correspond to our own opinion and taste. This is called intrinsic bias, and reinforces the effects of homophily (i.e. the tendency to connect to people that are similar to ourselves), which is naturally present in social networks.
Matteo is interested in generalizing the concept of bias on dynamic processes on networks, and studying the effects of bias independently of the process itself. For that, he started from an existing framework for binary-state dynamics on networks, the AME. This approach is applied to cases where each node on the network can have two states. Then, it describes the way in which node states change over time, using two quantities: the infection rate, and the recovery rate. These are related to the number of neighbors of each node, and the number of infected nodes. He looked at two models:
1) the voter model, where each node changes its state (or opinion) whenever it comes in contact with a node of different opinion; and
2) the majority vote model, in which a node changes its state depending on which state is represented by the majority of its neighbors, according to a certain probability. In general, we expect that, after a certain time, whatever state or opinion was held by the majority at the beginning will spread to the whole network.
To this existing framework, Matteo added a formulation of bias, in order to study its effect. The bias was defined as a probability b that a node would disregard each one of its neighbors who have an opinion different from itself. The probability of each neighbor being selected is as shown in figure (a). If bias is zero, all neighbors are treated equally (b). If bias is one, any neighbor with a different state is excluded with probability 100% (c). In the voter mode, adding bias did not have any major effects; it only accelerated the dynamics. But in the majority vote model, he observed something quite interesting: when the bias was strong enough, the majority opinion did not take over the whole network. Instead, two parties with different opinions were formed, and persisted indefinitely. In a social network, this illustrates the fact that, when there is strong bias, the different actors in the network are so limited to contact with alters that share the same opinion with them, that they may not even be aware of the majority opinion, and as result they do not conform to it.
In the next phase of his project, Matteo is testing some additional types of models, looking at the influence of network structure in the bias effect, and considering AMEs on top of the dynamics.
Blog post by Juliana Pereira