 Eberhardt and collaborators have also explored causal discovery using soft interventions. A soft intervention influences the value of a variable without breaking the arrows into that variable. For instance, suppose we want to know whether increasing the income of parolees will lead to decreased recidivism. We randomly divide subjects into treatment and control conditions, and give regular cash payments to those in the treatment condition. This is not an intervention on income per se, since income will still be influenced by usual factors: savings and investments, job training, help from family members, and so on. Soft interventions facilitate causal inference because they create colliders, and as we have seen, colliders have a distinct probabilistic signature. Counterintuitively, this means that if we want to determine whether X causes Y it is desirable to perform a soft intervention on Y (rather than X), to see if we can create a collider \(I\rightarrow Y\leftarrow X\) (where I is the intervention). Soft interventions are closely related to instrumental variables. If there are no latent common causes, we can infer the true causal structure using soft interventions. Indeed, if we can intervene on every variable at once, we can determine the correct causal structure from this one intervention. However, if there are latent common causes, it is not in general possible to discover the complete causal structure using soft interventions. (Although this can be done if we assume linearity.)