Weighted representative democracy

We propose a new system of democratic representation. Any voter can choose any legislator as her representative; thus, different legislators can represent different numbers of voters. Decisions in the legislature are made by weighted majority voting, where the weight of each legislator is determined by the number of voters she represents. We show that, if the size of the electorate is very large, then with very high probability, the decisions obtained in the legislature agree with those which would have been reached by a popular referendum decided by simple majority vote.