A widely-used method of research funding is through competitive grants, where the selection of which of the applications to fund is made using anonymous peer review.  The aim of the present paper is to argue that the system would work more efficiently if the selection were made by random choice rather than peer review.  The peer review system has defects which have been revealed by recent criticisms, and the paper gives one such criticism due to the Nobel prize winner Sir James Black.  It is then shown, in support of Sir James' position, that the use of anonymous peer review leads to a systemic bias in favour of mainstream research programmes and against minority research programmes.  This in turn leads to the stifling of new ideas and of innovation.  This thesis is illustrated by the example of the recent discovery of the cause of cervical cancer – a discovery which has generated substantial profits for pharmaceutical companies.  It is then shown that selection by random choice eliminates this systemic bias, and consequently would encourage new ideas and innovation