Human-Algorithm Interaction in Child Protection

The paper calculates net government cost by comparing the implementation and development costs of the algorithm with the savings from reduced child maltreatment. The initial fixed cost of developing the tool was $250,000, with an additional $15,000 in annual maintenance costs, totaling approximately $280,000 over the two years of the trial.

The paper assumes the change in lifetime costs to the government as a result of reduced child maltreatment is $62,500 per child. This is based on the lower bound estimate from the literature ($250,000 in 2020 dollars) and the assumption that about a fourth of this amount is due to reduced government spending on special education, criminal justice, and public health insurance. This $250,000 estimate is based on Fang et al. 2012, which estimates the cost as $210,000 in 2010 dollars.

Access to the algorithmic tool reduced the number of children at the top of the harm distribution by approximately 20 children relative to the control group, implying about 20 fewer victims of serious maltreatment and 20 * $62,500 = $1.25 million in reduced government expenditure.

The net cost is therefore $280,000 – $1.25 million = -$970,000

Given a negative net cost and positive willingness to pay, the MVPF is infinite.

The paper notes that these estimates likely understate the net government savings (e.g., from higher tax revenue or reduced transfer payments not captured in Fang et al. 2012), and may also understate private benefits for CPS-involved children.