A number of highly cited papers by Flyvbjerg and associates have shown that ex ante infrastructure appraisals tend to be overly optimistic. Ex post evaluations indicate a bias where investment costs are higher and benefits lower on average than predicted ex ante. These authors argue that the bias must be attributed to intentional misrepresentation by project developers. This paper shows that the bias may arise simply as a selection bias, without there being any bias at all in predictions ex ante, and that such a bias is bound to arise whenever ex ante predictions are related to the decisions whether to implement projects. Using a database of projects we present examples indicating that the selection bias may be substantial. The examples also indicate that benefit-cost ratios remain a useful selection criterion even when cost and benefits are highly uncertain, gainsaying the argument that such uncertainties render cost-benefit analyses useless.