Granovetter's threshold model explores how the likelihood of individual participation in collective behaviors, such as riots or protests, is dependent upon the proportion of others' willingness to act. While this widely acknowledged framework is relatively generic in nature, the threshold model has up to now largely been employed for illustrative purposes, rather than as a numerical modeling tool. This talk highlights two major sets of issues that hinder such modeling applications and proposes extensions of the model to resolve them. First, often assumed distributions of activation thresholds unrealistically predict either no-one or the entire population to act. Classifying individuals according to their general attitudes towards a given action extends Granovetter's graphic approach to compute equilibria, such that the model produces nontrivial intermediate numbers of actors making each decision. Second, a conceptual cascade model is used to show that a broad, yet previously unexplained, distribution of activation thresholds emerges from microscopic networked interactions. This distribution can be approximated analytically and the thus refined model of collective behaviour explains the emergence of social tipping as a saddle-node bifurcation in which minority groups can trigger large shares of the population to engage in collective action.