Essay: Tipping Points^*

This paper formally defines tipping points as discontinuities between current and future states of a system and introduces candidate measures of when a system tips based on changes in the probability distribution over future states. We make two categorical distinctions between types of tips relevant in social contexts: The first differentiates between direct tips and contextual tips. A direct tip occurs when a gradual change in the value of a variable leads to a large, i.e. discontinuous, jump in that same variable in the future. A contextual tip occurs when a gradual change in the value of one variable leads to a discontinuous jump in some other variable of interest. We argue that while scholars and writers often focus on direct tips, contextual tips often make direct tips possible, such as when human rights conditions in a state deteriorate creating the potential for an uprising. The second differentiates tips between outcomes that belong to the same class —such as tips from one equilibrium to another — from tips that result in a change in the outcome class, such as tips that occur when an equilibrium system becomes chaotic or complex.