Andrew Lilco of the influentual website Conservative Home is currently proposing sortition for the reformed House of Lords:
I propose that half the members (300) should be selected randomly. It would be better if randomly-selected members knew their random selection from an early enough date to prepare for the role. Thus I would prefer hereditary – probably with new hereditary families. But I suspect that would be so controversial as to derail the whole scheme, and it is more important that there be random membership than whether people are prepared. So I propose that half the members be selected by lot, as with jury service. If you are selected for Second Chamber service, you must serve there for six months. I suggest that there is overlapping turnover – so, each month one sixth of the membership leaves to be replace by a new set. Hopefully, after a while people would see the benefits of expertise, responsibility and obligation being bred from an early stage, and so hereditary would once again be feasible. But a jury-style (or Athenian-style) component to the chamber would be a good base.