There are some fascinating experiments occurring with random selection. It's used in practices such as Citizen Jury, Deliberative Opinion Poll, televotes, but there are also examples of public appointments for boards that have relied upon random selection. The aim was to avoid the "tap on the shoulder" nature of many public appointments, in order to draw in a diverse group that is more reflective of the whole constituency. Two examples in the United Kingdom: the National Lottery Community Fund and the Shared Interest Society Ltd. Are there other examples?
For a rationale for random selection see Carson, L & Martin, B, 1999, Random Selection In Politics, Praeger, Westport, CT or visit http://www.hydra.org.au/activedemocracy/