Before revision:  his core idea is that the votes of unelected candidates are carried over to the next election . All candidates thus accumulate votes over time and eventually each candidate is elected at some point. We provide a mathematical formulation of Frege's election system and investigate how well it achieves its aim of a fair representation of all political opinions in a community over time.
After revision:  his core idea is that the votes of unelected candidates are carried over to the next election , while the elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions over time.