Generalizing the framework to gradually emerging popularity

Determine how to generalize the slowing-factor framework for measuring the impact of hits to systems in which popularity builds up gradually through preferential attachment or through a gradual buildup of expectations before an event.

Background

The paper introduces a slowing-factor measurement that compares the decay of attention to existing items before and after the rapid appearance of a highly successful item. This approach is designed for platforms where hits reach high activity quickly, allowing the effect of the hit on other items to be measured over short before-and-after windows.

The authors explicitly identify a limitation: the framework’s suitability for rapidly emerging hits does not establish how it should be applied when popularity develops progressively. They specifically mention gradual popularity growth caused by preferential attachment and gradual expectation buildup before an event as settings requiring a generalization.