Conjunctive vs. disjunctive risk models

TagLast edit: 28 Oct 2022 15:03 UTC by Lizka

Models of catastrophic risks can be conjunctive or disjunctive. A conjunctive risk model is one in which the disaster is caused by the co-occurrence of multiple conditions ( $D = C_{1} \cap \dots \cap C_{k}$ ). In a conjunctive model, the probability of the disaster is less than or equal to the probabilities of the individual conditions. By contrast, a disjunctive risk model is one in which the disaster occurs as a result of any of several conditions holding ( $D = C_{1} \cup \dots \cup C_{k}$ ). In a disjunctive model, the probability of the disaster is greater than or equal to the probabilities of the individual conditions.

Examples of conjunctive and disjunctive risk models of AI risk:

Joseph Carlsmith’s models existential risk from power-seeking AI conjunctively, i.e. as the intersection of six conditions, all of which must be true for the existential catastrophe to occur.^[1]
By contrast, Nate Soares’s models AGI risk disjunctively, i.e. as the union of multiple conditions, any of which can cause existential catastrophe.^[2]

Both types of models are simplifying assumptions. In reality, a disaster can be caused by multiple conditions that interact conjunctively and disjunctively. For example, a disaster $D$ could occur if conditions $C_{1}$ and $C_{2}$ are true, or if condition $C_{3}$ is true: $D = (C_{1} \cap C_{2}) \cup C_{3}$ .