An interesting mixture of the existing election systems with sortition might be the following:
Elections for seats in the parliament are done in the usual fashion. However the number of seats selected by vote in the parliament is only equal to the percentage of voters. The other seats, basically representing the non-voters, are selected by lot.<p>On can justify this by arguing that non-voters are on the one hand not satisfied with the given choices and on the other hand indifferent to who is ruling them. So selecting the seats by lot might actually represent the will of the non-voters best.