What is the test for a prison official to be found guilty of failing to protect an inmate from violence by other inmates?

The Eighth Amendment imposes a duty on prison officials to protect inmates from violence at the hands of other inmates. Farmer v. Brennan, 511 U.S. 825, 844 (1994). A prison official violates this duty when two requirements are met. Id. at 834. First, objectively viewed, the prison official's act or omission must cause "a substantial risk of serious harm." Id. Second, the official must be subjectively aware of that risk and act with "deliberate indifference to inmate health or safety." Id. at 834, 839-40 (internal quotation marks omitted). In other words, "the official must both be aware of facts from which the inference could be drawn that a substantial risk of serious harm exists, and he must also draw the inference." Id. at 837. Deliberate indifference is "something more than mere negligence," but "something less than acts or omissions for the very purpose of causing harm or with knowledge that harm will result." Id. at 835. A prison official's deliberate indifference may be established through an "inference from circumstantial evidence" or "from the very fact that the risk was obvious." Id. at 842.