Hope Function

by gwern 7y1st Jul 20128 comments

22


Yesterday I finished transcribing "The Ups and Downs of the Hope Function In a Fruitless Search". This is a statistics & psychology paper describing a simple probabilistic search problem and the sheer difficulty subjects have in producing the correct Bayesian answer. Besides providing a great but simple illustration of the mind projection fallacy in action, the simple search problem maps onto a number of forecasting problems: the problem may be looking in a desk for a letter that may not be there, but we could also look at a problem in which we check every year for the creation of AI and ask how our beliefs change over time - which turns out to defuse a common scoffing criticism of past technological forecasting. (This last problem was why I went back and used it, after I first read of it.)

The math is all simple - arithmetic and one application of Bayes's law - so I think all LWers can enjoy it, and it has amusing examples to analyze. I have also taken the trouble to annotate it with Wikipedia links, relevant materials, and many PDF links (some jailbroken just for this transcript). I hope everyone finds it as interesting as I did.

I thank John Salvatier for doing the ILL request which got me a scan of this book chapter.