The apportionment problem deals with the fair distribution of a discrete set of k indivisible resources (such as legislative seats) to n entities (such as parties or geographic subdivisions). Highest averages methods are a frequently used class of methods for solving this problem. We present an O(n)-time algorithm for performing apportionment under a large class of highest averages methods. Our...

Partisan bias occurs when the translation of the popular vote into legislative seats differs between competing parties. This paper contains a theoretical and empirical analysis of the consequences of an efficient gerrymander for the partisan bias of an electoral system. Under partisan apportionment, bias is shown to depend on some structural features of the electoral environment; namely, the si...

James Buchanan and Gordon Tullock took a keen interest in the United States Supreme Court’s reapportionment decisions of 1960s, which established “one person, one vote” standard for state legislative apportionment. This paper traces long arc Tullock’s opposition to standard. The Calculus Consent offers highly qualified efficiency argument against vote,” but over time grew even more vocally crit...