Q324. You are the board chairperson of a small non-profit and you are hiring new executive director. It has come down to two candidates, one rather plain vanilla and, frankly, a bit boring, but rock solid, and the other quite exciting and edgy. After all the interviews and due diligence, you and your board estimate that that with the boring candidate there is a 94% likelihood that she'll be OK, a 5% chance that she'll be amazing, and a 1% chance that she'll be a disaster. You estimate the "value" of OK to be 25, the value of amazing to be 100 and the value of disaster to be -100.
(A) What is the expected value of hiring the boring candidate?
The board estimates that there is a 60% chance that the edgy candidate is amazing and a 40% chance she will be a disaster.
(B) What is the expected value of hiring the edgy candidate? Other things being equal, what is the best decision here?
A consultant friend of your tells you about a personality test that you can administer to job candidates that helps distinguish between those likely to be amazing and those likely to be a disaster.
(C) With the above assumptions, how much would it be worth to have this test to use on your edgy candidate (the test would tell you for sure whether this particular edgy person is the amazing or the disaster type)?
But suppose it's not a perfect test, but it's pretty good. It turns out that with candidates who really are amazing it gets it right about 75% of the time. With those who are actually disasters waiting to happen, it gets that right 90% of the time.
(D) If the test were administered to our edgy candidate and she passed, how likely is it that she'd be amazing? And if she failed, how likely she was actually a disaster?
(E) How much would we be willing to pay for the imperfect test?