A Complete Information Index for Measuring the Proportionality of Electoral Systems

A crucial property of an electoral system is the manner in which it translates a vote distribution into a pattern of representation. Measures of this property are important in assessing the relative merits of differing electoral systems. I argue that indices that do not use the vote and seat shares of all competing parties are informationally incomplete. In this paper, a complete information index is developed and shown to have several desirable properties: (a) it is bounded between zero and unity; (b) it takes the value of unity in the limiting case of perfect proportionality; and (c) it takes the value of zero in the limiting case where the seat distribution is unaffected of the vote distribution. The index is shown to perform better than limited information indices in an illustration using data from Sicilian provincial elections