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Conjunctive vs. disjunctive risk models

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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 (). 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 (). 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:

  • Carlsmith (2021) 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.
  • By contrast, Soares (2022) models AGI risk disjunctively, i.e. as the union of multiple conditions, any of which can cause existential catastrophe.

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  could occur if conditions  and  are true, or if condition  is true: .

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